C

Calendar

The medieval calendar was made up of a number of overlapping components: the solar day and year, lunar month, the natural seasons, and artificial divisions (such as the reign of a king). In 725 C.E. the Venerable *Bede wrote that “all the courses of mortal life are measured in moments, hours, days, months, years, ages.” He went on to say that there are three kinds of time reckoning, operating according to nature, custom, or authority. Thus, the natural passage of the seasons is a different kind of time-reckoning than the thirty-day month or the divine requirement that the seventh day be a day of rest. The rest of Bede’s work, titled The Reckoning of Time, discusses the calendars, starting with the day, ending with the Ages of the World, and clarifying how to reckon dates according to each.

The Passing of Years

For Christian writers, the whole of history stretched out in a continuous line which started with Adam at year one, and the line divided into ages and generations. According to Bede, the first age—from Adam to Noah—is ten generations; the second—from Noah to Abraham—is also ten generations. Each age could be compared to a stage of life, with the first likened to infancy, the second to childhood, the third to adolescence, and so on. By parallel with the resurrection of Christ, the world will be destroyed at the end of the Sixth Age, and reborn in the Eighth Age. *Isidore of Seville organized his chronology of the Six Ages (Etymologiae book 5) according to the reigns of patriarchs, judges, and kings, dating each reign by its final year; he also fixed the beginning of the Sixth Age at Christ’s birth, as distinct from his earthly ministry or passion. Eusebius (263–339), who synchronized biblical and secular dates in a time-line chronicle beginning with Abraham. The fusions of world-chronicle and the Six Ages proposed by medieval authors was not unproblematic, however, since there are difficulties with the versions of the Bible—the Septuagint translation gives different numbers of years and generations from the Hebrew version, and many texts equated one age with one thousand years. Nonetheless, medieval authors continued to work on chronologies of the world, and in the later Middle Ages chronologies such as the Nuremberg Chronicle were among the earliest printed books. Another two hundred years later, in the seventeenth century, Bishop James Ussher famously combined biblical, secular and astronomical dates to calculate that the Creation had taken place on Sunday October 23, 4004 B.C.E.

Conflicts between various sets of criteria (astronomical, theological, and calendrical), notably between Rome and Alexandria, culminated in Dionysius Exiguus’ reworking in 526 C.E. of Alexandrian tables for a Roman calendar. An incidental but ultimately influential side-effect of his new Easter table was that it was projected according to an innovative dating system: the annus domini, calculated from the beginning of the reign of Diocletian, which had hitherto prevailed. The Dionysian Paschal table and its chronological scheme spread rapidly, although it was not until the Synod of Whitby in 664 C.E. that the English Church united and accepted the new way of determining the date of Easter.

To locate an event in time, it had to be given a year-number. One system, used in Europe from the eighth century onwards, particularly for official and administrative documents, was to number the years according to the reign of a particular monarch or pope. The regnal years began on the date of the king’s coronation. This system ran alongside year-numbers fixed according to the Christian Era, and difficulties for historians are compounded by the fact that there is no standardization about when the year began. Bede, Dionysius, and other writers considered that the year began with the Nativity (December 25). During the twelfth and thirteenth centuries this was replaced in many (but not all) places by dating from the Annunciation (March 25). The French Chancery used a year which started on the moveable feast of Easter, meaning that each year had a different number of days from the previous one. In the Roman calendar January was considered the first month, and January 1 was considered the first day of the solar year for the purposes of calculating feast days. The different systems were adopted by different cities and countries, as seen in the famous example given by R.L. Poole. If we suppose a traveler to set out from Venice on March 1, 1245, the first day of the Venetian year, he would find himself in 1244 when he reached Florence: and if after a short stay he went to Pisa, the year 1246 would already have begun there. Continuing his journey westward, he would find himself again in 1245 when he entered Provence, and on arriving in France before Easter (April 16) he would once more be in 1244.

Dividing the Year

The seasons of the year governed life for many people in medieval Europe—the planting, nurturing, and harvesting of crops was the cycle according to which life was lived. Celebrations of the end of winter and the start of spring were followed by periods of plowing the fields and planting crops. In the summer there was hay to be cut, wheat to be harvested and stored, and grapes to be harvested and made into wine. The fall was taken up with storing and preserving food, and preparing the fields for winter crops, and the winter was a cold and dormant time, occupied with keeping warm and well fed until the beginning of spring started the cycle again. The sequence of agricultural tasks is depicted in many medieval calendar manuscripts, as well as in books of hours made for the nobility. Each month would be illustrated with the task to be carried out at that time, an iconographic tradition seen in sculture, tapestry, and illuminated manuscripts including the sumptuous Très Riches Heures made for the Duc de Berry.

The year could also be divided into months according to the Julian calendar, with twelve months of around thirty days each, and an extra day every four years to keep the calendar in step with the solar year. According to the Roman system the days within each month were numbered according to the kalends, ides, and nones, and in the Middle Ages this system was used in parallel with the now more familiar one of the sequential numbering of days within a month. The first day of May could also be referred to as the kalends of May, and since the Julian calendar counted back from the kalends, the twentieth day of April was twelve days before the kalends of May.

Although the Christian calendar dominated medieval Europe, the Jewish and Islamic calendars were also used in some areas and by some groups of people. The Islamic calendar is a strictly lunar calendar of twelve months of twenty-nine or thirty days, instituted in 642 C.E. (ten years after the death of Muhammed). Years are numbered from the Hijira (the flight of Muhammed from Mecca to Medina): July 16, 622 in the Julian calendar. The Jewish calendar is also lunar, with twelve months of twenty-nine or thirty days, and the new year beginning on Rosh Hashanah, the first day of the seventh month (Tishri). Years are counted from the creation, which was in 3760 B.C.E. of the Julian calendar.

Days for Feasting and Fasting

As a quarter of the lunar month, the seven-day week has been used for thousands of years. It probably has Assyrian origins, and many cultures have taken one of the days of the week as a day of rest. Because there were also seven planets known, the days were linked to planets, according them cosmological significance and forming the basis for astrological calculations. Indeed, many of the weekday names used in Europe relate to the names of the planets.

As well as the numbering of days according to the Julian calendar’s ides, nones, and kalends, or the sequential numbering of days in a month, medieval scholars used a wealth of different systems for identifying days in the year, and giving information about them. Each day was allocated a letter A–G, starting with A on January 1, and the letter of the first Sunday of the year is called the dominical letter of the year. Linked to the dominical letters are the concurrents, which also indicate what day of the week a particular date is: the number indicates the number of days between the last Sunday of the year and January 1. The year also had a golden number: to calculate this add one to the number of the year in the Christian Era, divide this by nineteen, and the remainder will be the golden number, which gives the year’s position in the nineteen-year lunar cycle, useful for calculating the date of Easter. The indiction number for a year, a system originating with the Roman tax system, ranged from one to fifteen, and the epact indicted how old the moon was on March 22. Astronomical dates could be given in terms of the position of the Sun in the zodiac, in relation to the zodiac rather than the calendar months. Ecclesiastical dates might be given in relation to festivals and saints’ days, for example, the octave was the eighth day after a feast day (counted inclusively). In 1232 Pope Gregory IX established a standard list of eighty-five feasts and fixed their dates, but there was still much freedom to introduce local variations both with respect to which saints were commemorated, and on which dates.

Calendars and Calculations

All this information was gathered together in calendar manuscripts, of which there survive hundreds of examples from medieval Europe. Ranging from beautiful illuminated codices to small notebooks, one particular medieval calendar manuscript might look very different from another. Despite their differing physical appearance, most calendars are organized with a month to a page and the data for that month arranged in columns. With one row per day, the information given usually includes the golden number and dominical letters, to allow calculation of the date of Easter, new moons, times of sunrise and sunset, eclipses of the Sun and Moon, and, depending on the function of the manuscript, saints’ days and feast names might be listed, or astronomical data such as the rising and setting of stars. If saints’ days are listed, this can help date and locate the calendar by the particular selection of saints included, by matching the celebration of a particular saint on a particular day to a known local practice. If times of the rising and setting of the Sun and stars are given, this can again help to locate the calendar since these values change with latitude.

The medieval calendar thus contained all the information that might be needed to calculate the dates of moveable Church feasts, or the positions of the Sun and Moon, and the methods for these calculations were described in *computus texts. These could be in verse or prose, and were circulated attached to or separate from the tables of calendrical data. By following the methods described, a medieval scholar could calculate divisions of time, days, weeks, months, and seasons, solstices and equinoxes, solar and lunar cycles, and (most importantly) the date of Easter.

Easter was defined as the first Sunday after the first (calculated) full moon following the vernal equinox, which was fixed on March 21. The calendar dates for the Paschal full moons run in a nineteen-year cycle—called the Metonic Cycle—at the end of which the cycle repeats, and Easter is on the Sunday following the paschal full moon, or Easter limit. The golden number of a year refers to its position in this cycle, and for any year the golden number can be used to determine the date of the paschal full moon by consulting a set of tables or a calendar. Then, the dominical letter indicates which days that year are Sundays, allowing the date of Easter to be fixed. In addition to the longhand methods, computus manuscripts often included mnemonics and lists for easy reference. One example of this is the medieval mnemonic “post epi pri pri pri di di di pascha fi,” which reminds the reader that in a given year Easter is the third Sunday after the third new moon after Epiphany, a system that works in all but two very specific cases.

A common variation on the standard computus manuscript was the so-called computus manualis which explained how to use the hand as a way to calculate by counting along the fingers and around the palm, and allocating each joint of each finger to the months, dominical letters, and other important pieces of information. Material from the computus manuscripts was also extracted and included in texts including encyclopedias, astronomical and medical texts, and religious texts. For quick reference on the move, there survive a number of folded almanac manuscripts, which were worn hanging from the belt. Linked in particular to astrological medicine, and probably originating in late fourteenth-century England, these small books contain summaries of calendrical, astrological, and medical information. In addition, tables of calendrical information were made into instruments (such as the annulus of John of Northampton), or engraved onto quadrants, sundials, and astronomical compendia.

Moving away from the written books, which after all would have required a certain level of numeracy or literacy, there is evidence that mnemonic verses were circulating, which would have made basic calendrical information available to the non-literate. There were many versions of a poem often called Cisio Janus which provided a way of remembering the most important saints’ days of the year. The origins of this poem date back to the twelfth century, and it often appears in Latin computus manuscripts and, later, in vernacular versions. Other rhymes reminded people how to calculate Easter, how to divide the day into hours, minutes, and seconds, or how many days were in each month, as in this short poem, found in a number of English and French manuscripts:

“Thirti dayes hath nouembir
April, iune and septembir;
Of xxviijti is but oon,
and all the remenaunt xxxti and j.”

See also Almanacs; Astrology; Astronomy; Clocks and timekeeping

Bibliography

Carey, Hilary. Astrological medicine and the medieval English folded almanac. Social History of Medicine (2003) 16.3: 481–509.

Cheney, C. R., and Michael Jones. A Handbook of Dates for Students of British History. New York: Cambridge University Press, 2000.

Fussell, Stephen. Chronicle of the World: the Complete and Annotated Nuremberg Chronicle of 1493. Cologne: Tashen, 2001.

Heinsch, Bridget A. The Medieval Calendar Year. University Park, PA: Pennsylvania State University Press, 1999.

Higuera, Teresa P. Medieval Calendars. London: Weidenfield and Nicolson, 1998.

Means, Laurel. Ffor as moche as yche man may not haue the astrolabe: popular Middle English variations on the computus. Speculum (1992) 67: 595–623.

Mooney, Linne M. The Kalendarium of John Somer. Atlanta: University of Georgia Press, 1999.

Richards, E. G. Mapping Time: the Calendar and its History. Oxford: Oxford University Press, 2000.

Wallis, Faith. Bede: The Reckoning of Time. Liverpool: Liverpool University Press, 1999.

CATHERINE EAGLETON

Campanus de Novara

Campanus was born in the first quarter of the thirteenth century, possibly as early as the first decade. He was very probably from Novara in Italy, for he referred to himself as Campanus Novariensis, and used the meridian of Novara in his astronomical works. He accumulated a series of benefices and served as chaplain to three popes: Urban IV, Nicholas IV, and Boniface VIII. Campanus wrote several books on mathematics and astronomy, and many more works are ascribed to him. He was most famous for his redaction of the Elements of *Euclid. An edition of Tractatus de sphaera published in 1531 identifies the author as magistro campano euclidis interpraete (Master Campanus, interpreter of Euclid). The title Magister often given to him may indicate that he was part of a university faculty. Since Campanus’s will was drawn up on September 9, 1296, and a letter of Boniface VIII dated September 17, 1296, informs us that Campanus had just died at Viterbo, his death must fall between those two dates.

Astronomical Works

In addition to his fame as “interpreter of Euclid,” Campanus enjoyed a reputation as a skilled astronomer and astrologer. Benjamin and Toomer, in their authoritative study of Campanus, identify him as the certain or probable author of five works on astronomy and a set of *planetary tables. Manuscripts and early printed books inconsistently ascribe other texts on astronomy and *astrology to him, although in most cases the attribution is dubious.

The most important astronomical work by Campanus is his *Theorica planetarum. Its dedication to his patron Urban IV places its composition between 1261 and 1264, the period of Urban’s papacy. Campanus’s Theorica explains the manufacture and use of the equatorium, a calculating instrument ostensibly for use by those who cannot calculate planetary motions from tables. An equatorium imitates the orbs of a planetary model in cross-section. An outer circle indicates the ecliptic. Disks within the ecliptic represent the deferent and epicycle; a third disk is used to create equant motion (although astronomers did not consider the equant to be a physical orb). By turning the disks, the user recreates the motion of the planet, then reads its position from the outer circle.

The Theorica is the first known Latin description of an equatorium. The version Campanus describes is completely impractical, requiring several large wooden plates. No example survives, and it is possible that no one, not even Campanus himself, constructed the instrument according to these directions. Later Latin equatoria were compact and usable. Yet despite the near uselessness of the Theorica as a book on the equatorium, it was widely copied and cited. In order to explain the instrument, Campanus first had to explain *Ptolemy’s planetary models and the motion of each circle or orb. Readers therefore turned to the Theorica as a textbook of advanced astronomy that explained the motions of the planets.

In addition, Campanus gave the least and greatest distances for the planets. Ptolemy explained the calculation of celestial distances in the Planetary Hypotheses; Latin astronomers knew the work indirectly through translations of Arabic works. Ptolemy assumed that the planets were arranged in nested orbs with no intervening space. Given the relative least and greatest distances of the planets (fixed by the Almagest models), it becomes possible to find the sizes of their orbs, and hence their distances from Earth. Campanus used al-Farghani’s models to find celestial distances in terms of the Earth’s size, then, unusually, converted them into miles. Campanus’s values were adopted by Robertus Anglicus in his commentary on *John of Sacrobosco.

Campanus also wrote a *computus on the medieval art of time-reckoning. Astronomers sometimes wrote on this subject since it was based on the solar and lunar cycles. Campanus’s Computus maior followed the approach to time-reckoning standardized by *Bede in the eighth century, but with the introduction of more elaborate astronomy, including the theory of trepidation (oscillation of the equinoxes) associated with *Thabit ibn Qurra.

Campanus’s third major astronomical work was the Tractatus de sphaera, one of a group of medieval textbooks on elementary astronomy. Like others of its kind, the Sphaera concentrated on introductory *cosmology and on the celestial phenomena associated with the twenty-four hour rotation of the heavens. Unlike Sacrobosco, author of a popular alternative sphaera, Campanus discusses some details of planetary motion. Since it cites the Theorica and the Computus, the Sphaera must have been written later than either.

A minor work of Campanus, De quadrante, describes the manufacture and use of the quadrant, a standard instrument for measuring the altitude of celestial objects. A second, rarely copied work gives problems to be solved with yet another instrument, the astrolabe.

Campanus prepared a set of astronomical tables, based on the popular Toledan Tables but recalculated for the meridian of Novara. Tables for the Moon were extracted and circulated separately.

As an astronomer, Campanus was not innovative in the modern sense. His importance lies rather in his ability to understand and utilize the recently rediscovered astronomy of the ancients. His direct impact on the Renaissance was small: some of his astronomical works went through a few printed editions, while his Theorica was sometimes read but not printed. However, his works helped to establish the foundation on which later generations of astronomers would build their critical re-examinations of Ptolemy. In the early fifteenth century, *John of Gmunden prepared an extract of Campanus’s Theorica. John, a frequent lecturer in astronomy, helped to establish Vienna as a center of astronomical studies that soon produced *Georg Peuerbach and *Johannes Regiomontanus.

KATHERINE A. TREDWELL

Mathematical Works of Campanus

In the twelfth century, the Elements of *Euclid—including the non-Euclidean Books XIV and XV—were translated from Arabic into Latin by *Adelard of Bath, *Hermann of Carinthia, and *Gerard of Cremona. Besides these Arabic-Latin translations, a translation directly from the Greek was produced in Sicily in the twelfth century. The so-called Adelard II, very likely written by Robert of Chester, was by far the most popular and most influential Euclid text in the Latin West in the twelfth and thirteenth centuries. It is not a translation, but a compilation, and in almost all cases the Latin commentaries on the Elements composed in the thirteenth and fourteenth centuries used the definitions, postulates, axioms, and enunciations of Version II.

The best-known representative of the Robert tradition is the redaction of the Elements prepared by Campanus de Novara. A terminus ante quem of 1259 for Campanus’s version can be derived from what seems to be the earliest dated extant codex of the work, Firenze, BNC Magliab. XI, 112. The Campanus version dominated Latin mathematics until printed editions were made from Greek manuscripts in the sixteenth century. This medieval version was printed in Venice by Erhard Ratdolt in 1482, thus becoming the first printed edition of Euclid’s Elements in any language. Campanus borrowed most of his definitions, axioms, postulates, and enunciations from the Robert redaction, but he added to Book VII a number of definitions, as well as postulates and axioms derived from the Arithmetica of *Jordanus de Nemore (ed. Busard 1991), and there are indications that he also used Johannes de Tinemue’s version as a source. In Book V., Def. 16, he cites Ahmad ibn Yusuf’s Epistola de proportione et proportionalitate, translated by Gerard of Cremona from Arabic into Latin, while in his commentary on the same definition he refers to Jordanus’s Arithmetica, and later, in XIII. 9, he mentions *Ptolemy’s Almagest. It is very probable that Campanus was acquainted with the Greek-Latin translation of the Elements as well as Anaritius’s commentary on the Elements translated by Gerard of Cremona.

Campanus’s Euclid version was very influential. In 1267 *Roger Bacon, in a work addressed to Pope Clement IV, ranked Campanus among the excellent mathematicians (Benjamin/Toomer 1971, 7). *Witelo was acquainted with Campanus’s edition, for he gives Prop. V. 26–29 of Campanus in his Perspectiva Prop. I.6, I.10-12 (Unguru 1977, 218, 219–221). In the fourteenth century, *Bradwardine (d. 1349) says in his Geometria speculativa: “I have not seen a discussion of them, except only by Campanus, who only casually touches on the pentagon a little” (Molland 1989, 37), and “On account of this Campanus says in the first comment of the tenth book of Geometry that any rectilinear angle is infinitely greater than an angle of contingency” (Molland 1989, 71). The Campanus manuscript Nuremberg, Stadtbibliothek Cent. VI 13 belonged to *Regiomontanus (1436–1476); the first fourteen folios (up to Elements III. 8) are in the hand of Regiomontanus himself, while the remainder of the text in another hand contains long additions and marginal comments by Regiomontanus (Folkerts 1990, 367). Some indication of the popularity of Campanus’s version and commentary is provided by Folkerts’ (1989, 38–43) census of one hundred and thirty-one manuscripts containing the whole Campanus redaction or parts thereof.

Beyond this highly influential work, other mathematical texts have been attributed to Campanus with varying degrees of certainty. De proportione et proportionabilitate (On Composed Ratios, ed. Busard, 1971), written probably in the thirteenth century, depends ultimately on the transversal theorem of Menelaus through intermediate works by Ametus filius Josephi and *Thabit ibn Qurra that were translated in the twelfth century by Gerard of Cremona. It begins with four definitions, the first of which reads as follows: Proportio est duarum quantitatum eiusdem generis ad invicem habitudo (A ratio is the mutual relationship of two quantities of the same kind). Positive evidence that Campanus wrote the work is slight, consisting of attestations in two manuscripts. The fact that seven of the fourteen manuscripts are Italian might be thought to favor claims for Campanus’s authorship.

A related text, De figura sectore (On the Sector-Figure, ed. Lorch, 2001, 436–442), is aimed at proving the theorem of Menelaus for a spherical surface. It directly follows the Campanus text De proportione et proportionabilitate in five manuscripts and one manuscript contains both texts, but not consecutively. Therefore, it is very likely that Campanus wrote both De figura sectore and De proportione, for the two treatises together form a unit, reproducing the content of Thabit’s De figura sectore, with the exception of §7 and §8.

We have evidence that Campanus not only borrowed from Jordanus, but also added to the latter’s Arithmetica. In the manuscript P4 (Paris, BnF lat. 16198, fol. 150r), at the conclusion of Book X of the Arithmetica we find the following as a prefatory note to three appended propositions: Istas propositiones apposuit magister Campanus post 78am 9i libri vel secundum alium ordinem post 71am ita quod inter 78 et 79 vel 71 et 72 9i libri interseruit. Thus, Campanus added these three propositions to the Arithmetica of Jordanus (Busard 1991, 240f). The available manuscripts of the Arithmetica are divided into three distinct families. The manuscripts P4 and V1 (Venice, Bibl. Naz. Marc., fondo antico 332 [= 1647]), representing the second family, contain 25 (P4) and 31 (V1) added propositions. An indication that Campanus adjoined some added propositions is found in the margin of V1.

In addition to the foregoing works, other mathematical works have been attributed more tenuously to Campanus. Lorch (1996, 169) ascribed one of two Latin versions of the Sphaerica of Theodosius (c. 200 B.C.E.) to Campanus. Bjornbo (1902, 152) speculated that notes to Menelaus of Alexandria’s Sphaerica might have been written by Campanus, but this question needs further research. The De quadratura circuli (ed. Clagett 1964, 588–607 with an English translation) attributed to Campanus by *Albert of Saxony is sufficiently elementary and trivial to deny that Campanus had written it.

H.L.L. BUSARD

See also Arithmetic; Astrolabes and quadrants; Astronomy; Euclid; Gerard of Cremona; Jordanus de Nemore; Ptolemy; Quadrivium; Theorica planetarum; Toledo; Translation movements

Bibliography

Benjamin, Francis S. John of Gmunden and Campanus of Novara. Osiris (1954), 1st ser., 11: 221–246.

Benjamin, Jr., Francis S. and G. J. Toomer. Campanus of Novara and Medieval Planetary Theory: “Theorica Planetarum.” Madison: University of Wisconsin Press, 1971.

Bjornbo, Axel A. Studien über Menelaos’ Sphärik: Beiträge zur Geschichte des Sphärik und Trigonometrie der Griechen. Abhandlungen zur Geschichte der rnathematischen Wissenschaften (1902) 14: 1–154.

Busard, Hubert L.L. Die Traktate De proportionibus von Jordanus und Campanus. Centaurus (1971) 15: 193–227.

———. Jordanus de Nemore, De elementis arithmetice artis. A medieval treatise on number theory. Stuttgart: Franz Steiner Verlag, 1991.

Clagett, Marshall. Archimedes in the Middle Ages, Volume I. Arabo-Latin Tradition. Madison: University of Wisconsin Press, 1964.

Duhem, Pierre. Le système du monde. Paris: Hermann, 1958.

Grant, Edward. A Source Book in Medieval Science. Cambridge: Harvard University Press, 1974, pp. 136–150.

Folkerts, Menso. “Euclid in Medieval Europe.” In: The Benjamin Catalogue for History of Science, Questio II de rerum natura. Winnipeg, 1989.

———. “New Results on the Mathematical Activity of Regiomontanus.” In Ernst Zinner, Regiomontanus: His life and Work, translated by Ezra Brown. New York: North-Holland, 1990, pp. 363–372.

Lorch, Richard. “The Transmission of Theodosius’ Sphaerica.” In Mathematische Probleme im Mittelalter Der lateinische und arabische Sprachbereich, ed. M. Folkerts. Wiesbaden: Harrassowitz Verlag, 1996, pp. 159–183.

———. Thabit ibn Qurra On the Sector-Figure and Related Texts. Islamic Mathematics and Astronomy 108. Frankfurt am Main, Germany: Institute for the History of Arabic Science at the Johann Wolfgang Goethe University, 2001.

Molland, George. Thomas Bradwardine, Geometria speculativa. Stuttgart: Franz Steiner Verlag, 1989.

Price, Derek J. The Equatorie of the Planetis. New York: Cambridge University Press, 1955.

Unguru, Sabetai. Witelonis perspectivae, liber primus. Book I of Witelo’s Perspectiva. Warsaw, Poland: The Polish Academy of Sciences Press, 1977.

Van Helden, Albert. Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley. Chicago: University of Chicago Press, 1985.

Canals

Digging canals implied a process of repeated surveying or leveling operations in order to ensure that the water ran downhill. An eleventh-century Iraqi document, probably dictated by a surveyor or contractor with practical experience, describes three different kinds of instruments used to survey irrigation canals. The one most used was a canal-level, a pipe filled with water that had been described by Hero of Alexandria in his Dioptra. This level is called anbub, “pipe,” in Arabic. “If the water issues from the two ends at the same time, it is because the surface is horizontal. But if it flows only from one end, it is because the side on which it flows is lower than the other.” The operation, which is to be repeated along the entire length of the proposed course, was the one used at the time in “most of the districts of Iraq and Khurasan” (Cahen). There was also a learned science associated with leveling called ‘ilm al-mizan (“science of the balance”).

The same document gives specific details regarding the digging of canals. The author states that before any work is done, one must first estimate the depth desired and the debit of the canal. He then gives sample problems for computing work and salaries. “Take a canal 400 cubits long by one-half plus one-third [cubit] wide and two-thirds deep, with a spade and two porters. How much work will there be?” The earth removed was measured in units of 100 cubic cubits. A service road was constructed alongside the canal (or the proposed route), and the number of men required to do the job calculated mathematically. For each man digging with a spade, one or two porters were required to remove the earth or silt in baskets. This standard modus operandi appears to have been continuously practiced in Mesopotamia since the times of the ancient empires. In the irrigation systems ancient of the ancient Near East, where silting was such a massive problem, digging out canals was quite literally reduced to a science. The state had to pay workers to dig out silt and had therefore to calculate how much was being removed. Old-Babylonian problem-texts survive on cuneiform tablets from around 1700 B.C.E., and give examples of how to calculate expenses for digging a canal of specific width, depth and length, the number of workers required to complete the task in a single day, or the costs of digging our or expanding the volume of an old canal that has been silted up (Neugebauer and Sachs).

In late medieval Valencia, the most common method of leveling canals was with an A-level, a large instrument carried about on a pack animal. A plumb-line was hung from the apex of the A. The legs of the instrument could be placed at any point on the proposed route and the gradient read from a scale on the bar of the A. Levelers (llivelladors) were generally master masons, used to working with levels, who specialized in canal surveys. They not only laid out the courses of new canals, or surveyed proposed courses, but also executed more precise measurements, especially of divisors, structures located at the point where a main canal splits into two branch canals carrying a specific proportion of the debit, generally 1:1. Any interference with the flow of the water in the environs of the divisor, or the deposition of silt in the structure itself, could alter the proportions, and thus divisors were frequently “leveled” by experts.

Ditching and Land Reclamation

The introduction of the iron-shod spade in the tenth and eleventh centuries greatly eased the labor involved in digging ditches and canals. Only then was it cost-effective to systematically dig drainage ditches around dry-farmed fields (in irrigated areas fields were commonly bounded by canals, on more than one side). In the Rijnland of medieval Holland, where excess water was a permanent, structural feature of agriculture, parcels were enclosed by ditches in the early Middle Ages, whether for bounding fields or for drainage. Reclamation of peat bogs in the late Middle Ages was accomplished purely by building drainage ditches, water from the top layers of the bog seeping into the ditches which carried it away. Parallel ditches or drainage canals were dug in these bogs around 120 yards (110 meters) apart, the channels constituting standard parcel boundaries, with houses located at the front of each parcel. The common length of ditches and parcels in the western Netherlands eventually stabilized at around 1,367 yards (1,250) meters, creating standardized parcels of around 35 acres (14 hectares).

In northern France, Guillerme describes “mini-Venices,” with seven cities ranking ahead of Venice in the ratio of intramural waterways to total surface area. The canals of Beauvais were supplied by the Therain River. The floors of the canals were partially paved because they had been Roman streets. Canals dug down to the Roman street level were typically just over one yard (one meter) deep and six feet six inches (two meters) wide. In Nimes, too, a Roman road was converted into a canal; inasmuch as a clay substrate underlay the road, there was minimal seepage. The enlargement of moats surrounding these cities caused upstream fields to become waterlogged. Such marshlands were drained in the twelfth and thirteenth centuries where flax and hemp were cultivated from networks of shallow canals. Retting pits where flax was steeped in vats or stagnant ponds and fermented before being reduced to pulp constituted the hydraulic infrastructure of the linen cloth industry (and, later on, of *paper, which used the same preparation technology).

Further south, the coastline of much of the Mediterranean was naturally marshy. It was extremely difficult to build stable canals (whether for irrigation or drainage) when the water table was very high. In the swamplands (marjals) near the city of Valencia digging canals so close to the water table had the paradoxical effect of expanding the marsh. In the 1390s the city sought to stabilize the area by building new main canals and giving settlers tax breaks to encourage them to move there. Stability depended on sufficient population density to provide constant upkeep for the canal system.

See also Agriculture; Instruments, agricultural; Irrigation and drainage; Water supply and sewerage

Bibliography

Cahen, Claude. Le service de l’irrigation en Iraq au début du XIe siècle. Bulletin d’Etudes Orientales (1949–1950) 13: 117–143.

Glick, Thomas F. Levels and Levelers: Surveying Irrigation Canals in Medieval Valencia. Technology and Culture (1968) 9: 165–180.

———. Irrigation and Society in Medieval Valencia. Cambridge: Harvard University Press, 1970.

Guillerme, André E. The Age of Water: The Urban Environment in the North of France, A.D. 300–1800. College Station: Texas A&M University Press, 1988.

Neugebauer, O. and A. Sachs, eds. Mathematical Cuneiform Texts. New Haven: American Oriental Society, 1945.

THOMAS F. GLICK

Cartography

Medieval maps in Europe were shaped by several major, not always compatible traditions, and the various genres of cartography show little or no apparent relation to each other until the High Middle Ages. The superimposition of Christian cosmology on the pre-Christian Greek, mostly astronomical and theoretical, and Roman, mostly applied, cartographic traditions introduced a tension between the classical ideas of sphericity of the Earth and universe and the biblical ideas of a flat and rectangular Earth. The teaching of the spherical Earth prevailed, but the problems of projecting location of objects on the Earth’s surface received little attention from medieval geographers until the thirteenth century. Apart from a few celestial maps, all known medieval maps focus on the inhabited part of the Earth, the equivalent of the Greek oikumene, limited to the northern part of the eastern hemisphere. Extant maps are found in copies dating from the eighth century C.E. Among them, world maps are the most numerous (over one thousand one hundred are known), although most are small and diagrammatic. Usually circular, they could also be oval or mandorla, in the almond shape of the Christian aura. Most other maps (regional, topographical, cadastral) date from the fourteenth and fifteenth centuries and are rectangular in shape.

Historians of cartography generally hold a low opinion of the role of geographical theory in medieval mapping, and indeed it was not until the rediscovery of *Ptolemy’s Geography with its instructions for map production in the fourteenth and fifteenth centuries that major progress may be observed in the development of European cartographical method. Maps created during the Middle Ages had primarily narrative, historical, didactic, and symbolic, rather than scientific functions. The main type of circular world map in medieval western Europe is that of mappamundi (Latin: “picture of the world,” plural mappaemundi). Based on a Roman prototype and usually inscribed in Latin, mappaemundi primarily followed the O-T template, in which the circular outline of the inhabited Earth (the orbis terrarum) was divided into three continents‚ Europe, Libya (Africa), and Asia—by prominent hydrographic features coming together to form the T: the Don (Tanais) river separating Europe from Asia, the Nile (or the Red Sea) separating Asia from Africa, and the Mediterranean Sea separating Africa from Europe. The O-shaped rim represented the Ocean, which early on was thought of as a river, but gradually became firmly associated with the sea (Mare Oceanum). Africa was thought to lie wholly in the northern hemisphere, but sometimes a fourth continent is shown in the southern hemisphere, as in the maps of Beatus (late eighth century). The early medieval author credited with popularizing this type of map as well as with bringing it into compliance with Christian theology was the encyclopedist *Isidore of Seville (c. 560–636). He oriented the map to the east, the site of earthly paradise, and designated Jerusalem as the center of the world. This type of map is also called T-O or O-Y, when the bodies of water are represented in a different schema. It includes a variation in which the dividing lines form the tau cross, symbolizing the passion of Christ. Isidore’s T-O map was influential and popular, and became the first map printed in Europe (1477).

A more complex Christian symbolism is best seen in the Ebstorf map (c. 1240) where the head, hands, and feet of Christ are represented at the four cardinal directions, with the map itself standing for the body of Christ. From Eden flow the Four Rivers of Paradise, identified with the Tigris, Euphrates, Indus, and Ganges. In Africa, in addition to the Nile, the Niger is shown (as a land-locked river). The map, destroyed in 1943, was the largest mappamundi (140 x 141 inches/3.56 x 3.58m) known to have been drawn (on kidskin) during the Middle Ages (in Lüneburg, Germany). The late-thirteenth-century Hereford mappamundi is another instance of combining Roman and early Christian sources. Its legends cite among the sources Pliny, Solinus, Orosius, and Isidore, and its axis links the circular Paradise at the top with Jerusalem and Rome, then leading to the Pillars of Hercules at the western limits. The Hereford map outline and content correlate closely with the twelfth-century mappamundi by Henry of Mainz which, however, follows an ancient Greek tradition in placing at its center sacred Delos, rather than Jerusalem. The clearest example of the Roman (Agrippa) prototype is seen in the Cotton “Anglo-Saxon” map of the tenth or eleventh century.

Until the fourteenth century, travel information only slowly made its way into maps. For example, the influence of *Marco Polo’s narratives shows clearly only as late as 1459, in the map by Fra Mauro and the 1492 globe by Martin Behaim. Earlier, however, St. Brendan’s legendary voyage in the North Atlantic resulted in the appearance in the extreme northwest of the world maps of a Brendan Island. The circular, hemispherical world map in Liber Floridus (early twelfth-century France) names Norway and Venice. The Vinland map of the world, an alleged forgery outside the tradition of Scandinavian mappaemundi, claims to show both Greenland and Vinland (North America). The map seems to follow in outline Andrea Bianco’s 1436 world map drawn in Venice. The Near Eastern Crusades had little immediate impact on general cartography, but dozens of diagrammatic and stylized maps of Jerusalem survive from 1140 on. The twelfth-century “Jerome” map of Palestine shows the rivers of Paradise as real water-courses. Burchard of Mount Sion, in his 1283 Descriptio terrae sanctae (Description of the Holy Land), proposed a division of Palestine into four quarters fanning out from a central point in Acre. Marino Sanudo’s 1321 Opus terrae sanctae was accompanied by maps of the world, the Near East, and Jerusalem probably drawn by Pietro Vesconte. The map of the Holy Land contains a grid with each square representing two leagues, an important aid for travel or military purposes. As noted by Brincken, this pairing was the first European example of a map made essential to the interpretation of a corresponding text.

The Hereford mappamundi is of unknown date, but the scholarly consensus puts its completion at c. 1290. (Topham)

Medieval cartographers rarely articulated theoretical views or their methods. A book composed in the early 1120s by *Hugh of St. Victor, Descriptio mappae mundi, appears to be meant as a guide for mapmaking. Jerome’s map of Asia uses an azimuthal logarithmic projection where the central part of the map—of most interest—is enlarged in scale, so that Asia Minor is almost as large as the rest of Asia. In 1178 Roger of Hereford calculated the longitudes of Hereford, Marseilles, and Toledo in relation to the meridian of Arin. *Roger Bacon discussed in his Opus maius (1268) a map, now lost, with a projection where he fixed the position of a point by its distance from the equator and a central meridian. Both these instances suggest an awareness of Arabic geographical concepts described below; in Ptolemaic geography, the prime meridian was drawn through the “Fortunate Islands” (now identified as the Canaries). An early Arabic connection also comes through in the use of “Mozarab” coloring by Beatus. Color coding in European maps is rare, but the Walsperger map of 1448 marks Christian cities in red and Muslim cities in black. The Red Sea was often colored in red, an exception.

Maps and Travel

The post-Crusade increase in travel and especially navigation was a major factor in cartographical progress prior to the Renaissance. Medieval books of sailing instructions were known as portolani, and the charts, sketched in Italy from at least the twelfth century, received the same name. Portolans were based on practical knowledge of the Mediterranean and were soon required to be carried on board. Drawn on parchment or vellum without a cartographic projection, the charts were based on coast outlines and were accurate only in small-scale versions. They were developed through careful measurement of directions and distances, and gradually corrected. For orientation, Mediterranean sailors originally used the directions of the eight winds named by the ancients. This skill was dramatically advanced by the appearance on the Mediterranean of the mariner’s compass, first mentioned by *Nequam in 1187. The wind rose, with twenty-four and later thirty-two points, was added to the charts, and the bodies of water became crisscrossed with a network of color-coded rhumb lines, which helped the mariner hold the course. The first description of a nautical chart is by Ramon Llull (c. 1233–1315), a Majorcan Franciscan with direct experience at sea. The oldest extant is the Pisan Chart dating from between 1275 and 1291. From Italy chartmaking spread to the port cities of Spain and subsequently to Portugal, eventually reaching northwestern Europe. Some one hundred eighty portolan charts, all oriented to the north, survive from the fourteenth and fifteenth centuries.

The famed Catalan Atlas (1375) is a multi-sheet hybrid of a mappamundi and portolan chart. It was created in Barcelona for King Charles VI of France by the Catalan cartographers Abraham Cresques (1325–1387), his wife, and their son Jafuda Cresques, Jewish converts from Palma de Mallorca. The Atlas shows Asia and Africa considerably enriched by the recent information from the travels of Marco Polo, Mongol embassies, and the 1324 pilgrimage to Mecca of Mansa Musa, the Muslim ruler of Mali; it also has the first known example of an ornamental compass rose on a portolan chart. Portolans became conduits of information obtained in the Atlantic exploration by the Portuguese, although we have none from Portugal. The Canary Islands, discovered in 1336, appear on a chart dated 1339. The influence of portolan charts is seen in the Gough map of Britain (c. 1360). Pietro Vesconte, who worked in Venice c. 1310–1330, made portolan charts, and his world maps have distinctive depictions of the Black Sea and the eastern Mediterranean. On a map for navigation, scale was essential, and Vesconte’s map of Palestine provides an early example of applying scale to a land-based map. Portolan charts also contributed to the new genre of Isolarii, or “books of islands,” which proliferated between 1500 and 1700. Maps without coastal outlines were not commonly drawn to consistent scale until the sixteenth century.

Another link between maps and travel was maintained in itinerary maps. The Peutinger map is a twelfth- or early thirteenth-century copy of a fourth-century Roman itinerary map. Significant medieval itinerary maps come from England. In the mid-thirteenth century Matthew Paris produced pilgrim itinerary maps that are seen primarily as mnemonic devices and examples of sacred topography, but his maps of Britain and Palestine show attention to proportion and scale, are oriented to the north, and have four points of the compass marked on the edges. The more detailed and “modern” Gough map of England (mid- to late fourteenth century) is seen as a collection of itineraries with distances written in locally measured miles. Medieval regional and local maps made prior to 1350 are very few, but the numbers grow quickly from 1500. The Italian school again predominates: maps of Italian cities are included in some manuscripts of Ptolemy, and Genoa and Venice appear on some portolan maps; northern Italian district maps appear from the thirteenth century. As noted by Harvey, Venice appears to be the only state in fifteenth-century Europe to make regular use of maps in the work of government.

Byzantine Cartography

Byzantine cartography inherited both the Greek and Roman antecedents, but cartographical innovation lapsed, and few new maps were produced. Military maps are known to have existed. Emperor Theodosius II (r. 408–450) commissioned a map of the empire, which was described in the ninth century by the Irish monk Dicuil and probably owed much to the first-century map of Agrippa. From Byzantine Alexandria comes the Christian Topography of *Kosmas Indikopleustês (fl. 540), whose maps are the earliest to illustrate a biblical interpretation of the world. His visible world is shaped as the Ark. He makes the ocean into a rectangle surrounding a flat earth, with Jerusalem at the center. The sky consists of four walls meeting in the dome of heaven that is the ceiling of the tabernacle and also resembles the elongated vaults of the early churches. He shows the four seas (Mediterranean, Arabian, Persian Gulf, and the Caspian in the north) as gulfs of the ocean, but otherwise his map completely lacks practical information. Probably the best known Byzantine map is the Madaba mosaic in Jordan, datable to between 560 and 565 and originally measuring 72 feet 2 inches by 22 feet 11 inches (22 x 7m). Intended to instruct Christians and showing biblical lands, it gives a prominent place and exaggerated size to Jerusalem. The map is oriented to the east and configured on the basis of a Roman road map, with inscriptions in Greek. Byzantine world maps of the T-O type, though few, have been found as far east as Mosul (ninth century), and a Byzantine plan of Jerusalem was used in a tenth-century Latin treatise. An eighth-century instrument-maker Leontios of Constantinople recreated Aratus’s globe and wrote instructions for constructing it (De preparatione sphaerae Aratae). Michael Psellus revived Byzantine cosmographical theory by writing c. 1050 On the Geographical Maps, based on the work of Strabo. Narrative land itineraries and periploi, books of sailing instructions, exist but lack accompanying maps. Greek charts of the fourteenth and fifteenth centuries show influence of the Italian portolan charts.

The few scientific achievements of the Byzantine millennium included archival preservation of Ptolemy’s Geography and maintenance of map-making skills. In the late thirteenth century, the scholar Maximus Planudes (c. 1260–1310) undertook a search for Ptolemy’s Geography, whose significance to geographical science he was one of the few to perceive. He found the text, but without maps, which he subsequently had drawn to Ptolemy’s instructions. In 1350 one Nikephoros Gregoras, in producing a copy of the Geography in Constantinople, made four additional maps (of Asia, Europe, and Libya) with an original projection reminiscent of the much later Mercator’s. Copies of the Geography, in two versions with twenty-seven or sixty-five maps, soon reached Italy, where the work was translated into Latin in 1406. These maps signaled the dawn of the “Ptolemaic revolution” in Western cartography. Together with the compass and the discoveries they made it no longer relevant to center maps on Jerusalem, facilitated reorientation of maps to the north, and made widespread the use of frame, scale and coordinates of latitude and longitude. About 1425 scholars associated with the University of Vienna and the Monastery of Klosterneuburg produced several world maps for which series of coordinates are preserved in table form from 1449. From 1477 on, Ptolemy’s maps were frequently reproduced in print, sometimes with addition of more contemporary information.

Islamic Cartography

The first Islamic reference to map-making dates to 702 C.E., although most extant maps are copies dating from the thirteenth century onward. Pre-Islamic Arab concepts of cartography included an image of the Earth in the shape of a bird with spread wings whose head is in the east (China) and tail in the west. Islamic cartography proper, originating in ninth-century Baghdad, experienced strong Iranian influences, including map orientation to the east and the division of the Earth into seven regions (kishvar) with Iran at the center, for which Muslim scholars quickly substituted Iraq. In the corpus of round world maps forming the so-called Atlas of Islam the world became centered on Mecca, while the eleventh-century Turkish world map by Mahmud al-Kashghari is centered on Balasaghun, capital of the then Uighur state. From India was borrowed the idea of prime meridian passing through Mount Meru from the North Pole to Sri Lanka via the Cupola of the Earth, or Cupola of Arin (Arabic Arun, from Ujjain, site of an ancient Indian observatory). From the Greeks came the limitation of world maps to the inhabited quarter of the Earth, surrounded by the ocean, and the system of seven latitudinal climates (iqlim) marked on extant copies of authors from the ninth to the fourteenth century, including Ibn Khaldun. Ptolemy’s Geography was translated several times in the ninth and tenth centuries, but apparently without his instructions for map-making and without maps. In the twelfth century *al-Idrisi, working at the Norman court of Sicily, produced a detailed world map that represents the highest achievement of Islamic cartography. Adopting Ptolemy’s map of the world as a base (though oriented to the south), he subdivided each of the seven climates into ten longitudinal sections, starting from the west. The resulting seventy rectangular regional maps, filled with information compiled from contemporary and earlier sources, surpass all other Islamic maps in quantity and detail of cartographic data. Al-Idrisi reportedly created a silver planisphere, now lost, based on the so-called map of al-Ma’mun, in the projection of Marinus. Apart from al-Idrisi, few authors gave instructions for map production, and the projections used are not yet fully understood. City plans must have existed, but those extant date from the sixteenth century and later. There are no topographical maps, although some color-coding of features occurs. An important Islamic map genre is the special qibla (direction of the prayer) maps for orienting the Muslim viewer to the Ka’ba sanctuary in Mecca from any location. Nautical charts are mentioned in texts referring to the Indian ocean, but none survives; the few extant North African charts, as also the more numerous post-1500 Turkish ones, strongly suggest European influence.

See also Geography, chorography; Kosmas Indikopleustês; Ptolemy

Bibliography

Arentzen, Jörg-Geerd. Imago Mundi Cartographica: Studien zur Bildlichkeit mittelalterlicher Welt- und Ökumenekarten unter besonderer Berücksichtigung des Zusammenwirkens von Text und Bild. Münstersche Mittelalter-Schriften 53. Munich: Wilhelm Fink, 1984.

Beazley, Charles Raymond. The Dawn of Modern Geography: A History of Exploration and Geographical Science from the Conversion of the Roman Empire to A.D. 900. 3 vols. London: J. Murray, 1897–1906. New York: Peter Smith, 1949.

Berthon, Simon and Andrew Robinson. The Shape of the World: the Mapping and Discovery of the Earth. Chicago: Rand McNally, 1991.

Brincken, Anna-Dorothee von den. Fines terrae: Die Enden der Erde und der vierte Kontinent auf mittelalterlichen Weltkarten. Monumenta Germaniae Historica, Schriften 36. Hanover: Hahn, 1992.

Brown, Lloyd A. The Story of Maps. Boston: Little Brown, 1949; London: Cresset Press, 1951; multiple reprints.

Edson, Evelyn. Mapping Time and Space: How Medieval Mapmakers Viewed Their World. London: British Library; Toronto: University of Toronto Press, 1997.

Harley, J.B. and David Woodward, eds. The History of Cartography. Vol. 1: Cartography in Prehistoric, Ancient, and Medieval Europe and the Mediterranean, esp. chapters 15–20. Vol. 2, Book 1, Cartography in the Traditional Islamic and South Asian Societies, esp. chapters 1–14. Chicago: Chicago University Press, 1987–1992.

The Image of the World: An Interactive Exploration of Ten Historic World Maps. CD-ROM. Produced by Karen Brookfield. London: British Library, 1995.

King, David A. World-maps for Finding the Direction and Distance to Mecca: Innovation and Tradition in Islamic Science. London: Al-Furqan Islamic Heritage Foundation, 1999.

Harvey, P.D.A. Medieval Maps. London: British Library, 1991.

Sezgin, Fuat. The Contribution of Arabic-Islamic geographers to the Formation of the World Map. Frankfurt: Institute for the History of Arabic-Islamic Sciences, 1987.

Skelton, R.A. The Vinland Map and the Tartar Relation. New Haven: Yale University Press, 1965.

Tolmacheva, Marina. “Ptolemaic Influence on Medieval Arab Geography: The Case Study of East Africa.” In Discovering New Worlds: Essays on Medieval Exploration and Imagination, edited by Scott D. Westrem. New York: Garland, 1991, pp. 125–141.

———. Bertius and al-Idrisi: an Experiment in Orientalist Cartography. Terrae Incognitae (1996), 28: 36–45.

MARINA TOLMACHEVA

Catapults and Trebuchets

Scholars now generally agree that the successor states of the Roman empire in the early medieval West inherited two basic types of artillery from their imperial predecessors. The first of these consisted of torsion-powered engines (Roman: ballista, chieroballista, onager; Medieval: manga, mangonellus) that propelled their projectiles through the transformation of potential energy stored in twisted fibrous material, ranging from gut to horsehair and hempen rope, into kinetic energy that drove a wooden beam. The wooden beam, which could be equipped with a basket attached directly to the beam, or with a sling attached to its end, then transferred this kinetic energy to a projectile, usually a stone, located in the basket or sling. These engines generally were light artillery with rounds weighing 22–33 pounds (10–15kg). The second type of artillery available in late antiquity and throughout the Middle Ages was tension-powered. Tension engines (known as gastraphetes in the ancient world but balistae in the medieval world) used the same principle as hand-held bows and crossbows, transferring the potential energy of the bow to the projectile, usually a long thin shaft equipped with an iron head, which looked like a large arrow or a crossbow bolt.

The range of engines (petraria, trubecheta, blida) that were probably the particular inventions of the Middle Ages employed the lever principle. Engines of this type were essentially long beams fixed to a fulcrum. The front, shorter end of the beam—i.e., the end closest to the target—is described by scholars as the target end, and the back, longer end is identified as the projectile end, because the projectile was attached there. Energy was generated by the rapid descent of the target end and the concomitant rapid rise of the projectile end.

Medieval engineers had two means of causing the rapid descent of the target end. The first method was to have a large number of well-trained men pull down, in unison, on ropes attached to the target end. Engines employing this method have been identified by scholars as a “traction type.” The traction lever engine was the only type of lever engine available in the Latin West and in the Levant until the end of the twelfth century.

The second method used to cause the rapid descent of the target end was to attach a very heavy weight to it. These weights, called trubae in some medieval sources, could weigh up to 220 pounds (1,000kg) and varied considerably in material composition and construction. In many cases, artillery engineers used large lead castings. However, wooden containers filled with stone, or even clay, were also fixed to the target end. The projectile end, in this type of engine, although substantially longer, was therefore much lighter than the target end. In order to use this engine, the artillerymen had to drag down the projectile end and secure it. After it was loaded, the projectile end was set free and the much heavier weight on the target end fell rapidly, causing the projectile end to rise rapidly with the result that the projectile was sent on its way. Engines equipped with weights on their target ends have been designated by scholars as “counterweight” lever engines. Counterweight engines did not appear in the Latin West until the first quarter of the thirteenth century.

The technology available to artillery engineers remained relatively static from the late Roman period through the end of the twelfth century. Although some scholars have questioned whether torsion or, conversely, traction-lever artillery was produced in the Middle Ages, it is now generally agreed that both types of propulsion were used consistently. Nevertheless, there is even at present controversy on this point because of the nature of the sources of information that deal with artillery in the period before c. 1200. One of the major problems faced by scholars, who have tried to identify the types of artillery actually deployed in late antiquity and the Middle Ages, is the lack of precision in the use of terminology in contemporary narrative sources. Many of the authors of historical narratives, in which artillery is discussed, were personally unfamiliar with military technology and used generic terms, such as instrumentum (instrument), machina (machine), ingenium (engine), and catapulta (catapult) to describe the weapons that were deployed. Many authors of narrative sources also used terms such as tormentum, scorpio, petraria, and onager, which may have had a technical meaning as a particular type of artillery. The lack of description for these weapons, however, makes it virtually impossible to determine whether they were torsion- or lever-powered, much less their specific characteristics, e. g., one-armed or two, wheeled or stationary. Finally, the narrative sources frequently used closely related terms, e.g., manga and mangonellus, without making clear if these terms refer to the same type or to different types of artillery.

Perhaps the most famous example of terminological confusion concerns the type of artillery known to modern readers as the trebuchet. The Latin version of this word begins to appear in medieval narrative sources in the thirteenth century. The first mention of a trubechetum in England, for example, occurs in the context of Prince Louis of France’s invasion of the island in 1216. Louis is reported to have brought a trubechetum with him to help conduct sieges. The thirteenth-century narrative sources, however, do not provide detailed information about the construction of the trubechetum. In light of this ambiguity, the English term trebuchet frequently has been used by scholars in a generic manner to refer to all lever-powered artillery from the ninth century onward. In fact, however, trebuchet was not used by contemporaries as simply another generic term for lever-powered artillery, but rather referred to a sophisticated technological improvement introduced by government officials to replace the older type of traction lever engine with a counterweight design. (The term for the counterweight engine as a whole may have been derived from the word truba, noted above, which some medieval authors used to designated counterweights.) Instead of deploying an engine that required dozens if not scores of well-trained men to operate, the trebuchet required only a small crew to lock the projectile end of the piece of artillery into position. It has been suggested by scholars that the counterweight engines could propel much heavier stones than their traction-lever cousins, with rounds weighing as much as 100–200 pounds (45–90kg), over distances of 328 yards (300m).

It is a happy coincidence that the first major development in the technology of artillery in many hundreds of years coincides with the survival of major new sources of information that shed significant light on how the trebuchet differed from earlier engines. The number of surviving administrative documents in England, where we have the best information about developments in the construction of artillery, increases dramatically for the period 1200 and after. These documents include large numbers of reports from engineers and military officials concerning the construction of artillery. This is significant because, unlike the contemporary authors of narrative sources, these engineers and officials were very familiar with military technology, and had a range of very precise terms to discuss the types of engines that they built. It is from these reports that it is possible to determine that the trebuchet was a relatively small type of counterweight lever artillery that began to be produced in England c. 1225. By the early 1240s, engineers in England began to build much larger counterweight lever artillery, which they at first designated as blidae, but then later simply referred to as engines (ingenia).

Cultural Significance

It is widely accepted by medieval military historians that sieges were the dominant form of warfare from the late Roman Empire until the massive introduction of gunpowder weapons at the end of the fifteenth century. The pursuit of politico-military objectives throughout this period required the capture, or the holding, of fortifications and major fortified cities. In the late antique West, the Roman government long maintained a monopoly on the ability to produce and deploy the sophisticated siege engines, particularly stone-throwers, that facilitated the reduction of these fortified places short of starving the population and garrison into submission or storming the walls with overwhelming numbers and concomitantly high rates of casualties. The late fourth-century Roman military officer and historian Ammianus Marcelinus emphasized in his works that barbarians were quite simply unable to capture Roman fortress towns, or even substantial forts, because they lacked “modern” technology. Attila the Hun likewise famously lacked sophisticated siege engines during his assault on the city of Orléans in the north of Gaul in 451 C.E., as his men were reduced to trying to pull down the walls stone by stone with hand tools. By contrast with the barbarians, the Christianized rulers of the Roman successor states devoted tremendous human, material, and financial resources both to producing artillery and to maintaining as well as improving the Roman military infrastructure of fortifications and fortified cities, that could withstand these engines. Indeed, medieval engineers engaged in an ongoing and increasingly expensive cycle of competitive development in the technology of siege engines and of fortifications. This pattern of military spending, what one might term part of the pre-modern “military industrial complex,” continued throughout the Middle Ages.

Stone-throwing engines were constructed of specially designed wooden pieces, iron clamps and bolts, ropes, slings, baskets, and, in the case of trebuchets, counter-weights. All of these elements of the engines’ material construction had to be built or produced by highly trained specialists. Not every carpenter knew either the designs or the techniques necessary to build the wooden framework for a piece of artillery, much less all of the types of artillery deployed by his government. Similarly, not every blacksmith knew how to produce the fittings necessary to withstand the stresses of holding together an engine that could hurl hundreds of rounds of stone ammunition weighing 100–200 pounds (45–90 kg). In order to ensure that a sufficient number of the correct types of artillery were available at the right place at the right time in good working order, governments in late antiquity and throughout the Middle Ages required a thoroughly articulated logistical system supported by a well-financed and highly structured military administration.

The Norman and Angevin kings of England, like many other rulers in medieval Europe, employed a corps of specialists in the construction of artillery, including torsion, tension, and lever engines of both the traction and counterweight types. These specialists, identified in contemporary English administrative sources as engineers (ingeniatores), were among the most highly paid officers of the crown. Some of them even became substantial landowners as a result. Each of these engineers employed numerous carpenters, blacksmiths, ropemakers, leatherworkers, woodcutters, carters, sailors, and bargemen. To gain a mere glimpse of the effort required to sustain this work, one can note that the royal forests of England rang with the axes of woodsmen preparing thousands of logs to be shipped to London, Dover, Carlisle, and other towns that served as major production centers for hundreds of enormous wall-breaking engines, as well as the even more numerous smaller pieces of artillery used as antipersonnel weapons. The lead mines of Cornwall produced hundreds and hundreds of tons of lead that were carted or shipped out for use as counterweights. The hides of whole herds of cows were required to produce slings. Masons chipped and shaped tens of thousands of stones to be used as ammunition, some of which can still be found at the sites of medieval sieges. To these basic elements of construction, one might add the thousands of carts, wagons, barges, and ships that were required to transport these supplies, as well as the completed artillery and ammunition. It is also necessary to keep in mind the mountains of grain and other foodstuffs necessary to feed the animal and human personnel who undertook these transportation duties. In economic terms, the production of weapons, in general, and of artillery, in particular, was a big industry that employed many thousands of workers. In sum, if we are permitted, as modern politicians are, to see the commitment of resources as a gauge of the importance attached by the government to a particular program, it is clear that the kings of England, and they were certainly not alone, valued artillery, including the trebuchet, very highly indeed.

See also Arms and armor

Bibliography

Amt, Emilie. Besieging Bedford: Military Logistics in 1224. Journal of Medieval Military History (2002) 1: 101–124.

Bradbury, Jim. The Medieval Siege. Rochester: Boydell Press, 1992, pp. 250–270

Chevedden, Paul E., Zvi Shiller, Samuel R. Gilbert and Donald J. Kagay. The Traction Trebuchet: A Triumph of Four Civilizations. Viator (2000) 31: 433–486.

DeVries, Kelly. Medieval Military Technology. Peterborough, Ontario: Broadview Press, 1992, pp. 125–138

Dinzelbacher, Peter. Quellenprobleme bei der Erforschung hochmittelalterlicher Bewaffnung. Mediaevistik (1989) 2: 43–79.

Finó, J.-F. Forteresses de la France médiévale: Construction–Attaque–Défense. 3rd edition. Paris: A. et J. Picard, 1977, pp. 150–158.

———. Machines de jet médièvales. Gladius (1972) 10: 25–43.

Hill, Donald R. Trebuchets. Viator (1973) 4: 99–115.

Huuri, Kalervo. Zur Geschichte des mittelalterlichen Geschützwesens aus orientalischen Quellen. Helsinki: Societas Orientalis Fennica, 1941.

Köhler, Gustav. Die Entwicklung des Kriegswesens und der Kriegführung in der Ritterzeit von Mitte des 11 Jahrhunderts bis zu den Hussitenkriegen. 3 volumes in 4. Breslau: W. Koebner, 1886–1890. volume 3.

Nicolle, David C. Arms and Armour of the Crusading Era 1050–1350. White Plains: Kraus International Publications, 1988.

Rogers, Randall. Latin Siege Warfare in the Twelfth Century. Oxford: Clarendon Press, 1992, pp. 251–273.

Schneider, Rudolf. Die Artillerie des Mittelalters. Nach den Angaben der Zeitgenossen dargestellt. Berlin: Weidmannsche Buchhandlung, 1910.

DAVID S. BACHRACH

Cathedral Schools

In late antiquity, Christians were generally satisfied with the existing urban schools and the classical training they offered, so that the Church did not consider it necessary to build up its own educative system. Nevertheless, it is likely that in the community of clerks organized by some bishops, such as Augustine in Hippo at the end of the fourth century or Caesarius in Arles a hundred years later, within the domus ecclesiae, some kind of education was already provided for the youngest people. But it is during the sixth century, when the ancient schools had disappeared, that formal cathedral schools were created. The first evidence is given by the Council of Toledo (527) which ordered the bishops to provide a teacher to educate the boys under eighteen of whom they were in charge. In the following centuries, other cathedral schools are mentioned in different episcopal sees in Gaul and Italy. These first cathedral schools were very modest, their main purpose being to give the young clerics a practical training in reading, song, and other liturgical duties; but the really educated members of the higher clergy were taught elsewhere, either within their families or in monastic schools which were, at this time, much more sophisticated.

School reform was an important part of the cultural policy of Charles the Great and his successors. The various directives issued for this purpose—Admonitio generalis in 789, Epistola de litteris colendis in 794, Council of Attigny in 822, Capitulary of Olonna for the kingdom of Italy in 825, etc.—are reminders that bishops were responsible for the education of their clergy and that they had to maintain one school in their cathedral—or even several, if the diocese was too large. In these schools, the pupils had to receive a good training in liberal arts, in particular in grammar, in order to be able to read and understand the Holy Scripture. This policy was not entirely effective: many cathedrals remained without a school and, with the exception of the brilliant cathedral school of Laon in the time of *John Scottus Eriugena, the monastic schools were always the great intellectual centers of the Carolingian Empire.

The eleventh and twelfth centuries were the golden age of cathedral schools in the West. This was due to the new context of that period. Many monastic schools were closed, and the new orders, such as Cîteaux, refused the admission of schoolboys; the towns were in rapid expansion, the reform of the Church required a competent and well-trained secular clergy. At this time, most episcopal sees had a more or less permanent school: this was the case in Italy, France, and Spain (at least in Catalonia) as well as in Germany and England. These schools were under the responsibility of the bishop and his chapter. Sometimes bishops, including Fulbert in Chartres, taught personally, but in most cases they entrusted the supervision of the schools to a canon who could be the archdeacon, the chancellor or a more specialized scholasticus. This man was the head of the school; he could appoint assistant teachers and, more generally, was entitled to grant after examination the licentia docendi, i.e., the right to teach, to anyone who wanted to open a new school in the diocese.

Cathedral schools were primarily intended for the training of young clerics, but they could also admit the male offspring of the local nobility, even if they were not destined for a career in the church. Learning in eleventh-and twelfth-century cathedral schools extended beyond the elementary level of reading and song, to the arts of trivium, biblical exegesis (sacra pagina), and even, in some cases, canon law. Normally, the role of a cathedral school did not exceed the boundaries of the diocese but after the end of the eleventh century some cathedral schools won a much larger reputation. Thanks to the professors whose fame and works were greatly widespread—Anselm at Laon, Bernard and Thierry at Chartres, Peter Comestor and Peter the Chanter at Paris—these schools attracted foreign students and became centers of intellectual innovation. The most famous cathedral schools were in northern France (Laon, Paris, Chartres, Reims) and in Germany (Liège, Cologne, Mainz, Bamberg, Magdeburg); naturally, these great cathedral schools had a tendency to become more and more autonomous, and increasingly acted independently of local authorities, bishops, and canons. There were cathedral schools in Mediterranean Europe too—Italy, Provence, Languedoc—but they had to compete with private and lay schools of law and medicine.

The development of cathedral schools was strongly supported by the Papacy; Canon Eighteen of the Third Lateran Council (1179) ordered that in every cathedral a prebend should be reserved for the schoolmaster so that he could teach freely to poor students; this canon was repeated at the Fourth Lateran Council (1215) which added that this master would teach grammar and the various liberal arts, and that in metropolitan churches at least there should also be a master of divinity.

Yet these canons were, in some way, already outmoded because in the thirteenth century the emergence of universities led to the irreparable decline of cathedral schools. On the whole, the first *universities (Bologna, Oxford, Montpellier) did not arise out of cathedral schools; even in Paris, the origins of the university lie more with the private schools of the rive gauche than with the cathedral school of Notre-Dame, which was only partially integrated within the university. But other universities (Salamanca, Toulouse, Orléans) resulted from the transformation of cathedral schools into autonomous and privileged studia generalia, and, on the whole, the old institutions were depreciated by the new ones, both because the former were unable to deliver recognized degrees and because their teaching appeared more and more outdated and conservative, reluctant to admit the new Aristotelian philosophy.

Nonetheless cathedral schools did not disappear in the late Middle Ages and probably deserve greater attention than they have so far received. They obviously remained of particular importance in Germany, where universities emerged only at the end of the fourteenth century. But they usually confined themselves to a purely local role, delivering elementary training to the youngest members of the cathedral clergy; for some of them, it was a preparatory stage before going to the university.

See also Aristotelianism; Quadrivium

Bibliography

Benson, Robert L. and Giles Constable, eds. Renaissance and Renewal in the Twelfth Century. Cambridge: Harvard University Press, 1982.

Classen, Peter. Die hohen Schulen und die Gesellschaft im 12. Jahrhundert. Archiv für Kulturgeschichte (1966) 48: 155–180.

Delhaye, Philippe. L’organisation scolaire au XIIe siècle. Traditio (1947) 5: 211–268.

Ferruolo, Stephen C. The Origins of the University. The Schools of Paris and their Critics, 1100-1215. Stanford: Stanford University Press, 1985.

Paré, Gérard, A. Brunet, and Pierre Tremblay. La Renaissance du XIIe siècle. Les écoles et l’enseignement. Paris-Ottawa: Vrin-Institut d’Études médiévales, 1933.

Pixton, Paul B. The Misfiring of German Cultural Leadership in the Twelfth Century: The Evidence from the Cathedral Schools. Paedagogica Historica (1998) 34: 348–363.

Renardy, Christine. Les écoles liégeoises du IXe au XIIe siècle: grandes lignes de leur évolution. Revue belge de philologie et d’histoire (1979) 57: 309–328.

Riché, Pierre. Écoles et enseignement dans le Haut Moyen Age, 2nd ed. Paris: Picard, 1989.

Riché, Pierre. Éducation et culture dans l’Occident barbare, VIe-VIIIe siècles, 3rd ed. Paris: Éditions du Seuil, 1972.

La Scuola nell’Occidente latino dell’alto Medioevo, 2 vols., Spoleto: Centro italiano di Studi sull’Alto Medioevo, 1972.

Verger, Jacques. “Une étape dans le renouveau scolaire du XIIe siécle?” In Le XIIe siècle. Mutations et renouveau en France dans la première moitié du XIIe siècle, éd. par Françoise Gasparri. Paris: Le Léopard d’or, 1994, pp. 123–145.

JACQUES VERGER

Cecco d’Ascoli

Physician, astrologer, and poet, Cecco d’Ascoli (Francesco Stabili) was born in or near Ascoli Piceno around 1269. Nothing is known about his studies and life before 1320. Between 1322 and 1324 he was professor of *astrology at the University of Bologna. In 1324 he was dismissed and condemned for heresy by the inquisitor Lamberto da Cingoli. This first condemnation was probably caused by the discussion of magic and astrological theories during his lectures.

Following this sentence, he was prohibited from lecturing in every Italian university; his doctoral degree was withdrawn and his library confiscated. In 1326 he joined the court of Count Charles of Calabria (son of Robert of Anjou) as doctor and astrologer, and in 1327 followed him to Florence. There he came into disagreement with the physician Dino del Garbo; at the same time, he fell into disgrace with Charles, according to legend because he predicted that Giovanna, the count’s daughter, would become a lustful woman. Investigated again by the Florentine inquisition, he was condemned by the inquisitor Accursio as a relapsed heretic and burned at the stake on September 16, 1327. According to the Florentine historian Giovanni Villani (Cronica 10, 39), Cecco’s condemnation was determined by his own arrogance, which cost him the sympathies of protectors and colleagues, and by the unorthodox theories he developed in his works. The condemnation included a prohibition on reading his writings. Nevertheless, some of them survived in manuscript and were later printed.

Cecco’s most representative writings are L’Acerba—a didactic poem in Italian whose alternative title, Immature, points to the unfinished character of the work and to its readers’ difficulty in grasping it—and the Latin commentary on *John of Sacrobosco’s Sphaera. He also composed a commentary on al-Qabisi’s De principiis astrologiae, a treatise De eccentricis et epicyclis, and some sonnets of alchemical content.

L’Acerba was written between 1324 and 1327 and left unfinished. In it, he accused Dante of having written a poem based on fiction and reporting a vision, not describing reality. Cecco, on the other hand, intended to write a very didactic poem that provided scientific data useful to his readers, and for this reason, in his view, his own poem was to be preferred to The Divine Comedy. However, L’Acerba clearly shows the influence of Dante’s poem, particularly in the use of terza rima. L’Acerba is divided into five books of composite character: the first deals with astronomy and *cosmology, the second combines a treatise on vices and virtues with elements of *physiognomy and astrology, and the third consists of a bestiary and a lapidary based on *encyclopedias such as the De proprietatibus rerum of *Bartholomaeus Anglicus and collections such as the Physiologus. The fourth book is structured in question-and-answer form, and concerns *alchemy, occultism, biology, astronomy, and *meteorology. Among its sources we find Aristotle’s Meteora and the pseudo-Aristotelian Problemata. The fifth and final book, which was left incomplete, was planned to discuss moral philosophy and ethics. Cecco also started the composition of a commentary on L’Acerba, but finished only the first two books.

Despite the condemnation, L’Acerba was widely diffused—we know of approximately forty manuscripts—and first printed in 1476. Some selected passages of the second book were translated into Hebrew during the sixteenth century, probably by Abraham ben Hannaniah Yagel.

The commentary devoted to Sacrobosco’s Sphaera was composed by Cecco before 1324, while he was professor of astrology at the University of Bologna, and left unfinished. Its content reproduces the lessons given by Cecco and the curriculum of lectures on astronomy established by the University of Bologna for the first year of studies, the bulk of which was represented by Sacrobosco’s Sphaera. The commentary attracted the attention of the Inquisition and contributed to Cecco’s condemnations in 1324 and 1327. Compared to other commentaries on Sacrobosco’s work, which focuses exclusively on astronomy, Cecco’s explanation is characterized by the interest in astrology, magic, and diabolic necromancy. Also particularly important in Cecco’s view is the interpretation of history according to the principles of astrology.

In his commentary, Cecco showed a wide scientific culture. Some of his astrological, hermetic, and necromantic sources do not seem to have survived, and are also unknown to the author of one of the most complete lists of astrological and magical works, the Speculum astronomiae, formerly attributed to *Albertus Magnus.

Pico della Mirandola attributed to Cecco the redaction of a horoscope of Jesus Christ, which is not preserved. It has been assumed by some scholars that this horoscope was contained in a preliminary version of the commentary on Sacrobosco’s Sphaera, and eliminated after Cecco’s condemnation.

See also Aristotelianism; Bestiaries; Lapidaries; Pseudo-Aristotle

Illustration by an unknown artist from 1475 edition of Cecco d’Ascoli’s L’Acerba. The painting shows (top to bottom) the virtue Nobility and the vices Anger and Envy. (Mary Evans Picture Library)

Bibliography

Primary Sources

Albertazzi, Marco, ed. Cecco d’Ascoli, L’Acerba. Trento: La Finestra, 2003.

Thorndike, Lynn, ed. The Sphere of Sacrobosco and its Commentators. Chicago: University of Chicago Press, 1949.

Secondary Sources

Albertazzi, Marco, ed. Studi Stabiliani. Trento: La Finestra, 2002.

Boudet, Jean-Patrice. Les who’s who démonologiques de la Renaissance et leurs ancêtres médiévaux. In Le diable en procès. Démonologie et sorcellerie à la fin du Moyen Age. Edited by M. Ostotero and É. Anheim. Médiévales (2003) 44: 117–141.

Busetto, G. “Cecco d’Ascoli.” In Lexikon des Mittelalters, vol. 3. München-Zürich: Artemis Verlag, 1983.

Camuffo, Maria Luisa. Presenze dantesche nell’Acerba di Cecco d’Ascoli. Rivista di letteratura italiana (1987) 5: 91–100.

Camuffo, Maria Luisa and Aldo M. Costantini. Il Fiore di Virtù: una nuova fonte per l’Acerba. Rivista di Letteratura Italiana (1988), 6: 247–258.

———. Il Lapidario dell’«Acerba». Lettere Italiane (1988) 40: 526–535.

Debenedetti Stow, Sandra. “A Judeo-Italian Version of Selected Passages from Cecco d’Ascoli’s Acerba.” In Communication in the Jewish Diaspora. The Pre-Modern World, edited by S. Menache, Leiden: E.J. Brill, 1996, pp. 283–311.

Faracovi, Ornella Pompeo. Gli oroscopi di Cristo. Venezia: Marsilio, 1999.

Frasca, Gabriele. «I’ voglio qui che’l quare covi il quia». Cecco d’Ascoli “avversario” di Dante. In Dante e la Scienza, edited by P. Boyde and V. Russo. Ravenna: Longo, 1995, pp. 243–263.

Picchio Simonelli, Maria. L’Inquisizione e Dante: alcune osservazioni. Dante Studies (2000), 118: 303–321.

Tester, S. Jim. A History of Western Astrology. Woodbridge: Boydell Press, 1987, pp. 193–196.

Thorndike, Lynn. A History of Magic and Experimental Science. New York: Columbia University Press, 1923, vol. II, pp. 948–968.

———. More Light on Cecco d’Ascoli. Romanic Review (1946) 37: 293–306.

———. Relations of the Inquisitions to Peter of Abano and Cecco d’Ascoli. Speculum (1926) 1: 338–343.

Van der Lugt, Maike. Le ver, le demon, la vièrge. Les théories médiévales de la génération extraordinaire. Paris: Les Belles Lettres, 2003, pp. 309–315 and 453–454.

Weill-Parot, Nicolas. Dans le ciel ou sous le ciel? Les anges dans la magie astrale, XIIe-XIVe siècle. Mélanges de l’École française de Rome, Moyen Age (2002) 114: 753–771.

IOLANDA VENTURA

Chaucer, Geoffrey

Probably born in the early 1340s, the English poet Geoffrey Chaucer was the son of a wine merchant. By 1357 he was a page in the household of the Countess of Ulster and soon after this he was involved in the war in France, resulting in his capture and ransom for £16 in 1360. In 1366 he married Phillippa, and soon afterwards was employed in Edward III’s household. More important positions followed: in 1374 Chaucer was appointed Controller of Customs, and in 1389 he became Clerk of the Works. In 1394 he was granted an annuity of £20 by Richard II, but all was not well financially and in 1398 there were actions against Chaucer for debt, from which he was protected by the king. In the following year, however, Richard was deposed, and Chaucer is last known to have been alive in 1400. No one is certain when, where or how he died, but a monument was raised to him in London’s Westminster Abbey in the sixteenth century.

Despite being busy with all these responsibilities, Chaucer found time to write throughout his working life. His surviving writings include ten large works, among them The Canterbury Tales and Troilus and Criseyde, as well as more than twenty short poems, and he probably wrote other things that no longer survive. A quick glance at his works shows the variety of styles and subjects found in his writings: he was clearly an educated, witty, and intelligent man. We know that he traveled widely—to Spain, Italy and France—but we know surprisingly little about other aspects of his life, such as where or how he was educated, or what he was like as a man. Despite this, his learning shines through, and there are many references to scientific and medical subjects throughout Chaucer’s literary works. The examples here are drawn from his most famous work, The Canterbury Tales, and give a picture of the breadth of his influences and interests.

Chaucer’s works—especially The Canterbury Tales and Troilus and Criseyde—contain many references to astronomical events, and some scholars have used them to date his writings. Linne Mooney, however, argues that they give stronger evidence for Chaucer’s interest in astronomy in general than for the dates of particular works. She links Chaucer’s choice of such material to a fashion at court, influenced by Richard II’s queen, Anne of Bohemia.

One astronomical reference is Chaucer’s description in the General Prologue of The Canterbury Tales that the Sun has gone half way through Aries. This is one of the ways that he fixes the date of the pilgrimage in early April. Along with this astronomical date, there are descriptions of natural phenomena in springtime, and a direct statement that the date is early April. You can read this section without knowing any astronomy, but you will only get the full depth of meaning if you know a little about the motion of the Sun through the heavens.

There are also several references to the ways that the characters tell the time while on the pilgrimage. In “The Shipman’s Tale” the lecherous monk uses a cylinder dial which he keeps in his pocket. In “The Parson’s Tale” the manciple works out that it is four o’clock by looking at the length of shadows relative to the objects that cast them, presumably using a reference table rather than doing spherical trigonometry in his head.

Some of the astronomical references show that the depth of Chaucer’s learning went beyond being able to use a sundial or *calendar. In “The Squire’s Tale” the king has a wife named Elpheta, an Arabic star name, and his children also have names that can be linked to the heavens. In “The Miller’s Tale” the shelves in the student’s room include a copy of *Ptolemy’s Almagest, as well as an astrolabe and a set of counting stones: tools of the student’s astrological activities. The student lodges with a carpenter, who finds him locked in his room one day and blames too much astronomy for the student’s condition, telling a story of an astronomer who was so busy looking at the stars that he fell into a clay pit because he wasn’t looking where he was going. So even though we know that Chaucer was interested in astronomy, he has one of his characters tell us of the dangers of studying astronomy too much. This highlights a problem when we are assessing Chaucer’s interests in scientific and medical subjects: to what extent, if any, can we work out his opinion on the more controversial subjects, such as *astrology or *alchemy, from the opinions expressed by his characters?

Throughout The Canterbury Tales Chaucer uses astrology to describe the characters, and as with the astronomical time and calendar references, you could understand the stories without knowing any astrology, but it adds more depth to the descriptions if you do. One area in which astrology was accepted, even encouraged, was in medicine. The description of the physician in the General Prologue shows us that he is learned and successful—he wears blue and red silk robes, and knows the causes of diseases. Another of the doctor’s skills is astrology, which he uses to find the ascendant for his patient and so understand what is wrong with him. Chaucer himself seems to have known much about the casting of horoscopes and the ways that the stars shaped peoples lives. There are horoscopes datable to 1392 in “The Nun’s Priest’s Tale”; the Wife of Bath explains in the Prologue to her tale that her character is shaped by the planets. She says that she has followed the inclination set out for her by the stars at the moment of her birth, implying that she might have chosen otherwise and therefore has some free will.

Alongside references in his fictional works, there is more direct evidence of Chaucer’s astronomical skill and interests in his Treatise on the Astrolabe, compiled in the early 1390s. This remarkable work is among the first technical treatises in English, and was based on sources including the work on the astrolabe then attributed to *Masha’allah and the De Sphaera of *Sacrobosco. Chaucer reworked his sources, reordering the material he took from them, and adding and removing some sections. One of the additional sections discusses the ascendant, a measurement essential in casting a horoscope. But even here there is no definite statement for or against, say, predictions of the future based on the casting of horoscopes. Chaucer limits himself to saying that the measurements used by astrologers are often inaccurate.

Medieval alchemy took in a wide range of activities, including what might now be described as metallurgy and distillation alongside things that might more often be associated with the name, including the transmutation of base metals into gold. In “The Canon’s Yeoman’s Tale” Chaucer shows his knowledge of alchemical equipment and processes in a long description given by a servant about his master’s alchemical activities. The alchemist is always unsuccessful though, despite spending large amounts of money and time on his search. Interestingly, despite Chaucer’s apparent knowledge of alchemy and perhaps even experience of chemical processes, the tale ends with a warning that alchemy is an attempt to pry into matters that are God’s, and that philosophers should leave it alone.

In The Canterbury Tales there are also references to magic, or to magical events and objects. In “The Squire’s Tale” a knight visiting the court of Ghengis Khan brings with him four magical gifts—a flying brass horse, a mirror, a ring, and a sword. Onlookers marvel at the magical objects, trying to understand them using their book learning. It is not clear whether Chaucer was saying that knowledge of the natural world allows you to see through trickery and apparently magical things, or whether he is instead implying that you should not try to explain away every marvellous thing you see. To add to the confusion, the tale is unfinished.

In another example, in “The Franklin’s Tale,” the situation is a little clearer. At a critical point in the story, a group of rocks off the coast of Brittany are made to disappear by the Clerk of Orléans. Chaucer explains that this was done using the Toledan astronomical tables, and involved calculations of the position of the Moon. Rather than magically making the rocks disappear, the Clerk seems to have instead predicted when an extraordinarily high tide would cover the rocks naturally.

A fifteenth-century portrait of Geoffrey Chaucer. (Topham/The British Library)

Chaucer was happy to show off his astronomical learning throughout The Canterbury Tales, as well as in other of his works, and he clearly knew much about astrology, alchemy, and magic. However, he sometimes seems reluctant to commit himself to whether the more controversial aspects of this learning were acceptable. This was probably wise, given his positions in and around the court, and his reliance on the king for his income: he perhaps could not afford to find himself out of fashion and so avoided making strong statements about some of the more occult subjects when they were in vogue at court.

If Chaucer himself seems to have been reluctant to state clearly his opinion for or against astrology, alchemy or magic, later commentators seem not to have felt the same restraint: as early as 1477 Thomas Norton cited Chaucer as an authority on alchemy. Posthumously Chaucer’s reputation grew and grew, and the audience for his writings widened from the courtiers and civil servants around him during his lifetime, in parallel with the increasing use of written English during the fifteenth century.

Sixteenth-century commentators sometimes emphasized Chaucer’s learning, and some referred to him as an expert in alchemy, astrology, and the occult arts. There survive sixteenth-century prophecies for the end of the world and spurious astrological and alchemical works that are wrongly ascribed to Chaucer in the manuscripts. Other scholars concentrated on his learning, and specifically mentioned his astronomical and philosophical learning. In 1585 Gabriel Harvey wrote:

“Others commend Chaucer and Lydgate for their wit, pleasant vein, variety of poetical discourse, and all humanity: I specially note their astronomy, philosophy, and other parts of their profound or cunning art. Wherein few of their time were more exactly learned. It is not enough for poets to be superficial humanists: but they must be exquisite artists, and curious universal scholars.”

See also Astrolabes and quadrants; Magic and the occult; Medicine, practical; Medicine, theoretical

Bibliography

Benson, Larry D. (ed.). The Riverside Chaucer. New York: Oxford University Press, 1987.

Crow, Martin M. and Olson, Clair C. (eds.). Chaucer Life Records. New York: Oxford University Press, 1966.

Curry, Walter C. Chaucer and the Medieval Sciences. London: George Allen and Unwin, rev. ed., 1960.

Mooney, Linne M. “Chaucer and Interest in Astronomy at the Court of Richard II.” In Chaucer in perspective: Middle English essays in honour of Norman Blake. Edited by Geoffrey A. Lester. Sheffield: Sheffield Academic Press, 1999, pp. 139–160.

North, John D. Chaucer’s Universe. Oxford: Clarendon Press, 1988.

Spurgeon, Caroline F. E. Five Hundred Years of Chaucer Criticism and Allusion 1357–1900. 7 vols. Chaucer Society Publications, Second Series, nos. 48–50, 52–56, London: K. Paul, Trench, Trubner & Co., and Oxford University Press, 1960.

Ussery, Huling. Chaucer’s Physician: Medicine and Literature in Fourteenth-century England. New Orleans: Tulane University Press, 1971.

CATHERINE EAGLETON

Clepsydra

Clepsydra (“water-thief”) is the generic name for devices that use flowing water to measure time. They are of two types: one in which water fills a vessel (inflow clepsydra), the other where it flows out of one (outflow clepsydra). Very ancient outflow clepsydrae, where water drips out of a vessel whose dropping water level is calibrated to represent the passage of time, are documented in ancient China, India, Babylonia, and Egypt. Simple outflow clepsydrae were used in Athens to limit the time of speeches in law courts and assemblies. The use of clepsydrae to measure specific allotments of minutes is associated with irrigation: for example, in those areas of the Islamic world where water was sold or apportioned in time units, irrigation time was measured by sinking bowls (a simple inflow clepsydra that floats in a bucket of water till it sinks) or simple outflow clepsydrae, jars which empty through an orifice in their bottoms in a determinate time. In both instances, time is governed by the rate of flow through an orifice, which is the only regulating device.

A Vitruvian clepsydra, which measured time by the rate of flow of water into the calibrated vase. (Mary Evans Picture Library)

Vitruvius describes an inflow clock, regulated by an outflow spout in such a way that the water level of a vessel fills uniformly. In this way a device attached to a float can be rigged to point to a scale, ring a bell, or—if converted to circular motion—cause a disk representing the heavens to revolve. Herophilus of Alexandria, physician of the third century B.C.E., used an outflow clepsydra to measure the pulse of patients, a practice still used by Nicholas of Cusa in the fifteenth century C.E.

In medieval monasteries, where the canonical hours of prayer were important, time was kept by sundials during the day, water-clocks by night. In the late tenth century, Abbo of Fleury had an outflow clock that signaled the time of the night offices in such a way that those on duty could awaken the monks with a hand-bell. This was most likely a dial with a pointer driven by a float and drum.

A series of complex and ingenious water-clocks is described by al-Jazari in his Book of Knowledge of Ingenious Mechanical Devices (Kitab fi ma ‘rifat al-hiyal al-handasiyya). Al-Jazari entered the service of the Turcoman Artuqids in 1181 and completed his book in 1204 or 1206. Books on mechanical devices constituted a distinct genre of literature in medieval Arabic science, meant to illustrate points of mechanics (‘ilm al-hiyal) rather than to serve any practical end. Al-Jazari’s various water clocks all resemble astrolabes, having water-driven disks on which are presented the zodiac, the Sun, the Moon, and so forth. The problem in all such contrivances was how to regulate the flow of water in such a way as to keep it constant, or to shift from daytime to nighttime hours (which differed in length through the solar year). Circular motion was attained with different combinations of weights and pulleys. These were elaborate toys, for the most part. Muslims designed water clocks that could measure either equal or unequal (equinoctial) hours, while in Europe equal hours were not used before the invention of the mechanical clock. Hours of the night and day are equal in length only on the two equinoxes.

Such elaborate clocks no doubt had an ancient precedent that the Arabs continued. As early as 807, the Abbasid caliph, Harun al-Rashid, sent an embassy to Charlemagne bearing an elaborate water clock displaying twelve hours, marked by bronze bells dropping into a brass basin. The Arab tradition was continued by the astronomers in the court of *Alfonso X the Wise of Castile. One such clepsydra drove the dial of an astrolabe and was used for telling time when neither the Sun nor the stars were visible. Alfonso’s famous mercury clock, which had an astrolabe set for the latitude of *Toledo, was a compartmented-clepsydra, the mercury passing from one compartment to another on the rim of a cylinder. The cylinder engaged the gears of a wheel on which wenty-four rods were mounted to strike each hour of the day on a bell.

Irrigation clocks, by contrast, were always very simple. Sinking bowls were commonly used in traditional irrigation systems in eastern Spain. Bowls of different sizes were used depending on the structure of water rights. In the Vall de Segó, a large bowl, the olla, sank in about an hour, while a smaller one sank in seven and a half minutes—one-eighth of an hour. In North Africa, outflow clepsydrae were common. *Noria pots, which commonly had a hole in the bottom to allow air to escape as it scooped up water, were pressed into time-keeping duty. Such a pot, as described by al-Bakri for the oasis of Touzer, Tunisia, in the eleventh century, emptied in seven and a half minutes.

See also Clocks and timekeeping

Bibliography

Borst, Arno. The Ordering of Time. Chicago: University of Chicago Press, 1993.

Cipolla, Carlo. Clocks and Culture, 1300–1700. London: Collins, 1967.

Dohrn-van Rossum, Gerhard. History of the Hour: Clocks and the Modern Temporal Order. Chicago: University of Chicago Press, 1996.

Glick, Thomas F. Medieval Irrigation Clocks. Technology and Culture (1969) 10: 424–428.

al-Jazari, Ibn al-Razzaz. The Book of Knowledge of Ingenious Mechanical Devices. Donald R. Hill, trans. Dordrecht: D. Reidel, 1974.

Sánchez Pérez, José Augusto. La personalidad científica y los relojes de Alfonso X el Sabio. Murcia: Academia Alfonso X el Sabio, 1955.

THOMAS F. GLICK

Clocks and Timekeeping

In medieval Europe, the temporal location of an event could be measured in lives, years, seasons, months, days, hours, minutes; and instruments, tables, texts, and rules of thumb were used to find the time. One of the earliest Latin texts on measuring time was written by *Bede in 725 C.E., and one of the opening sections explains that “all the courses of mortal life are measured in moments, hours, days, months, years, ages.” He goes on to say that there are three kinds of time reckoning, operating according to nature, custom, or authority. Thus, the natural passage of the seasons is a different kind of time-reckoning from the thirty-day month or the divine requirement that the seventh day be a day of rest.

One of the major motivations for dividing the day into hours was the fixing of times for prayers during the day: prime (sunrise), terce, sext (midday), none, vespers and compline (sunset). There were many ways in which churches and monasteries could determine the prayer times, including water clocks, candles, sundials, and the positions of the Sun and stars. In 1198 Jocelin Brakelond explains how, when putting out a fire, the monks of Bury St. Edmunds Abbey made a bucket chain to the clock to get water. Other monasteries had sundials, some with the prayer times marked on them as well as (or instead of) the twelve daytime hours. Other methods included the burning of graduated candles and the calculation of time from the position of certain stars, a method described in the sixth century by Gregory of Tours. Within the sequence of prayers, however, there was considerable flexibility about exactly when a particular office would take place, and the clock did not necessarily rule the religious life of an institution.

Monastic and church hours were unequal—daylight is divided into twelve hours, and nighttime into twelve. This means that the resulting hours will vary in length with the seasons, with daylight unequal hours being shorter in winter and longer in summer, and the day and night hours being the same length only at the equinoxes. Alongside this system, especially for astronomical and astrological purposes, time could be reckoned according to a system of equal hours, resulting from the division of day and night into twenty-four sections of equal length. And, in addition, different parts of Europe numbered the hours differently: “Italian hours” were counted from sunset, from one to twenty-four. In Italian hours, dawn could already be the twelfth hour. In England or Germany, by contrast, the hours were usually numbered one to twelve and one to twelve, starting at midday or midnight.

The choice of whether to use equal or unequal hours to tell the time was not the only one facing a medieval scholar. There are legal records showing that there was no universally accepted definition of the start of the day, no standardization of how to interpret temporal references in literary and administrative texts, and considerable philosophical debate about the structure of time. Alongside the variability in the ways that time could be conceived of and divided up, there were many possible ways of telling the time using instruments or rules of thumb. And a single instrument might tell the time in several different ways, using different methods. In contrast to philosophical discussions that divided minutes into smaller and smaller parts, measurements using instruments were not expected to be “accurate” in the modern sense: most medieval sundials are only marked with quarter-hours, even though astronomical tables and texts might give times accurate to minutes and seconds. Bede describes the difference between practical and theoretical divisions of hours, explaining that the punctus (a quarter of an hour) is named after the passage of the point on a sundial, and that there are smaller theoretical divisions of minuta (one tenth of an hour) and partes (one fifteenth of an hour). Later in the Middle Ages astronomical texts regularly discuss the division of an hour into sixty minutes and three hundred sixty seconds, although it is not until at least the sixteenth century that these were used in practical measurements of the time.

Timekeeping was closely linked to astronomy, since the year and the day were divided up according to the motion of the heavenly bodies. There survive many astronomical texts explaining how to make and use devices for telling the time, and how the various lines on them link to the structure of the heavens. Derek Price suggested that astronomical time-telling instruments were tangible models of the universe, useful for teaching astronomy, going as far as to say “I do not believe that then [in antiquity] or in the Middle Ages, instruments were used to tell the time, survey fields or navigate ships.” For Price, instruments showed the truth of a system by physically modeling it. To tell the time using an astronomical instrument was to understand the structure of the universe: as *John of Saxony wrote in 1327 in his canons to the Alfonsine Tables: “Time is the measurement of the primum mobile.”

Time-telling Instruments

In medieval Europe there were many varieties of sundial, quadrant, and astrolabe, all of which told the time. Hundreds of examples survive. Many astrolabes are preserved in museums all over the world, and these could tell the time in a multitude of ways from the Sun and stars, as well as convert between equal and unequal hours. Quadrants could tell the time from the Sun and, with the help of a method outlined in several manuscript texts on the instrument, by the stars as well. The cylinder dial was another popular instrument, to judge from the number of surviving manuscripts including instructions for its construction. Evidence from probate inventories and wills shows that wealthy people might own these kinds of objects, and medieval library booklists show them being kept alongside the astronomical books for the use of scholars.

However, it would probably be impossible, and definitely misleading, to try and give a typology of all the timekeeping instruments that were used in medieval Europe. The surviving evidence for the ownership of instruments is extremely patchy, and when combined with the material evidence preserved in museums shows only how much has been lost. Many of the instruments in use in the Middle Ages no longer survive, having been made from wood and paper. Others, if they were made of brass or copper, might have been melted down for their metal when they were no longer of interest as time-measuring instruments. For example, a number of fragments of small wood and brass compass dials dating from the fifteenth century have been found. However, references to them in texts and images are rare, one exception being an early sixteenth-century drawing by Urs Graaf showing a man holding a compass dial. This instrument, in common with several of the surviving instruments, has a nocturnal on the lid so that the owner could tell the time by day or by night. Another example is that of the sandglass, of which very few survive from the medieval period. If one were to consider only the fragmentary material evidence, it would be easy to dismiss this instrument as a rare and unimportant thing. But there are many artistic representations of people with sandglasses, and references to them in the accounts of navies and merchants, making it clear that the sandglass was in fact a relatively common object.

Nevertheless, it is likely that only a tiny fraction of the population of Europe could afford to own instruments designed for measuring the time. Most people instead probably told the time by listening for the bells ringing at the local church or monastery to signal the prayer times, or by rule-of-thumb methods. There survive notes explaining that an hour is the time it takes to say two nocturnes of the psalter, or that an hour is the time it takes to walk two miles in winter or three miles in summer. Medieval manuscript texts explain how to turn your hand into a basic sundial and tell the time, as well as how to calculate the date of Easter by counting along your fingers. In addition, people probably got to know the positions of the Sun relative to local landmarks, or to estimate time from the length of shadows. There are a number of surviving medieval copies of tables relating the length of a six-feet-tall man’s shadow to the date and time, with equal-hour versions available from the late fourteenth century, and one of the pilgrims in *Chaucer’s The Canterbury Tales uses this method to find the hour.

Clocks and Clockwork

In addition to these technologies and techniques, the Middle Ages saw a major development in timekeeping: the mechanical clock. There had been complex water clocks in antiquity and earlier in the Middle Ages, measuring the passage of time according to the flow of water into or out of a vessel graduated with scales. Cassiodorus explained the relationship between the sundial and the water clock in a letter sent to King Gundoband of Burgundy by Emperor Theoderic in 507: “We have provided you with a sundial for use during the day and a water clock for use at night and on the not infrequent days when there is no sunshine.” Three hundred years later, in 807, Harun-al-Rashid, the Abbasid Caliph of Baghdad, gave an elaborate water clock to Charlemagne. It was described as: “A marvelous mechanical contraption, in which the course of the twelve hours moved according to a water clock, with as many brazen balls, which fell down on the hour and through their fall made a cymbal ring underneath. On this clock there were also twelve horsemen who at the end of each hour stepped out of twelve windows, closing the previously open windows by their movements.”

Later, water clocks were fitted with elaborate mechanisms modeling the motion of the heavens, automata, and striking bells. Then in the thirteenth century there appear the first descriptions of weight-driven clocks. Robertus Anglicus described in 1271 the attempts of astronomers to construct a mechanical device that would accurately model the motion of the heavenly bodies, and so allow the equal hours to be determined, powered by weights. The first unambiguous evidence for the construction of weight-driven clocks dates from the fourteenth century, when clock-construction expenses appear in the accounts of several monasteries and towns, and literary descriptions attest to interest in the new device. These clocks relied on a new device: the escapement, a toothed wheel that converts the motion of the weights into the rotation of a wheel powering the gear train. This device, combined with the gears, automata, and striking mechanisms of the old water clocks, made mechanical weight-driven clocks possible. Some medieval clocks are still working, for example the clock at Salisbury Cathedral, England, built in 1386.

Just like the water clocks, the mechanical clock told the time during the day and night, and did not need a clear day to allow a reading to be taken. However, they still had to be regulated using sundials in order to keep them in time with the heavens. Anthony Turner has clarified the distinction between sundials and clocks, separating timekeeping instruments from time-finding instruments. Sundials are time-finding instruments since they measure time directly from the motion of the heavenly bodies; they track the motion of the heavens. Clocks are time-keeping instruments which keep track of the passage of time, but do not measure it directly from the heavens.

Jacques Le Goff, in his influential article on the impact of clocks, linked them to the need of merchants to control labor time in the expanding cities. This “merchant’s time” and “clock time” is said to have replaced the “Church time” which had until that point dominated. Gerhard Dohrn-van Rossum, in his careful analysis of the transformations of time-consciousness linked to the mechanical clock, outlines the spread of the mechanical clock in the fourteenth century, starting in northern Italy. He shows that the introduction of a public clock in a particular town should be seen as part of a wider process of urban modernization, in conjunction with mills, foundries, and church organs, schools, and the improvement of financial and administrative governance: merchants and traders did not stand out from any other part of the political community.

The Passage of Time

In 1344 Jacopo Dondi installed a clock on the Palazzo del Capitano at Padua: it was no ordinary clock, but an astronomical clock that earned him the title “Dall’Orologio.” His son Giovanni (1315–1389) completed an even more impressive clock, the astrarium, in 1364. This instrument had seven dials, one for each planet, and it showed the motions of the Ptolemaic system. Despite the fact that many early astronomical clocks were inaccurate, the metaphor of the universe as heavenly clockwork with God as a master-clockmaker proved popular. In an influential article, Derek Price linked the interest in clockwork, gears, and machines to the growth of mechanistic philosophy, suggesting that growing interest in the latter encouraged the making of automata and clocks. In around 1410, the author of an English manual titled Dives et Pauper used the metaphor of the clockwork universe to compare the influence of the planets and the clock on men’s lives. He argues that just as the planets do not rule men, neither should the clock.

The mechanical clock also captured the imagination of medieval writers and artists. Some marvelled at the device, including Froissart, who wrote a poem titled L’Orloge Amoureus, in which he explained that the clock is beautiful and remarkable, pleasing and profitable, because it shows the hours night and day, even when there is no sunlight. Others were less positive; the Welsh poet Davydd ap Gwilym (1320–1370) described it as “churlish clock with foolish chatter.” Later in the fourteenth century Chaucer includes several references to clock time in his writings, although many of his characters still tell the time using sundials and rules of thumb.

During the fourteenth and fifteenth centuries, there are increasingly frequent references to clock time, and a 1396 manual of useful phrases for Englishmen traveling to France includes how to ask “What has the clock struck?” and “What time is it?” Chronicles increasingly give the times of events in terms of clock hours rather than prayer times, and city decrees regulated working hours and breaks according to the clock.

At the same time, there was an increasing quantification of time and regulation of the day by equal hours. Schools began to set limits on the length of classes, often using sandglasses, and humanist authors worried about wasting time: Francesco Petrarch, in his De vita solitaria of 1366, described how study could enable a scholar to cheat time by producing knowledge that would live on after his death. In around 1404 Petrus Paulus Vergerius suggested that time-measuring devices should be installed in libraries so that scholars could literally see time slipping away. In paintings, clocks and other time-measuring instruments are often seen in the studies of scholars, and the clock quickly became a powerful symbol of the passage of time and an admonition not to waste it.

See also Almanacs; Astrolabes and quadrants; Astrology; Astronomy; Calendar; Clepsydra; Cosmology; Navigation; Planetary tables

Bibliography

Boullin, D. G. An Iconographic Study of Sandglasses. Nuncius (1989) 4: 67–85.

Calouste Gulbenkian Museum. The Image of Time: European Manuscript Books. Lisbon: Calouste Gulbenkian Foundation, 2000.

Dembowski, P.F. (ed.) Le paradis d’amour. L’orloge amoureus. Geneva: Droz, 1986.

Dohrn-van Rossum, Gerhard. History of the Hour: Clocks and Modern Temporal Orders. Chicago: University of Chicago Press, 1996.

Hector, L.C. The Beginning of the ‘Natural Day’ in the Late Fourteenth Century. Journal of the Society of Archivists (1961) 2: 87–89.

Higgins, A. Medieval Notions of the Structure of Time. Journal of Medieval and Renaissance Studies (1989) 19: 227–258.

Landes, David S. Revolution in Time: Clocks and the Making of the Modern World. London: Viking, 2000.

Leclerq, J. The Experience of Time and its Interpretation in the Late Middle Ages. Studies in Medieval Culture (1976) 8–9: 137–150.

Le Goff, Jacques. Time, work, and culture in the Middle Ages. Chicago: University of Chicago Press, 1982.

Lippincott, Kirsten et al. The Story of Time. London: Merrell Holberton, 1999.

McCluskey, Stephen C. Gregory of Tours, Monastic Timekeeping, and Early Christian Attitudes to Astronomy. Isis (1990) 81: 8–22.

Mooney, Linne M. The Cock and the Clock: Telling the Time in Chaucer’s Day. Studies in the Age of Chaucer (1993) 15: 91–109.

Price, Derek J. de Solla. Automata and the Origins of Mechanism and Mechanistic Philosophy. Technology and Culture (1964) 5: 9–23.

Rothwell, W. The Hours of the Day in Medieval French. French Studies (1959) 13: 240–251.

Travis, P. W. Chaucer’s ‘Chronographiae’, the Confounded Reader, and Fourteenth-Century Measurements of Time. Disputatio (1997) 2: 1–34.

Turner, Anthony J. “Essential Complementarity: The Sundial and the Clock.” In Hester K. Higton, ed. Sundials at Greenwich. Oxford: Oxford University Press, 2002, pp. 15–24.

Wallis, Faith. Bede: the Reckoning of Time. Liverpool: Liverpool University Press, 1999.

Ward, F. A.B. An Early Pocket Sundial Illustrated in Art. Antiquarian Horology (1979) 11: 484–487.

EPACT: Scientific Instruments of Medieval and Renaissance Europe www.mhs.ox.ac.uk/epact

CATHERINE EAGLETON

Coinage, Minting of

The minting of coinage was a process whereby states and some seigniorial authorities created certain quantities of money as a monopoly. These coins were generally made from alloys containing variable proportions of gold, silver or bronze. Once the coins were put into circulation, they were used as media for the payment of commercial or other transactions and for fiscal payments. The conversion of pieces of metal into monetary signs required a stamp of authority on the flans (blank pieces of metal). To do this two dies had to be prepared, one for the obverse side and the other for the reverse. These dies were made of hardened steel, bronze or iron. The design of the die was made by melting it in a mold (bronze dies were most amenable to melting, normally in a matrix of lead), engraving the complete design directly on the surface, or else combining various punches with different forms (strokes, curves, and circles) or with part of an inscription. The lower pile or anvil-die was fixed, while the upper pile, known as the trussel, was movable, and operated with the left hand. A heated flan was placed between the dies before the trussel received a hammer-blow delivered with the right hand. This blow pressed the lower face of the flan into the hollows of the lower pile, creating an image in relief.

Normally, the flans were prepared by melting the metal in molds. The ingots thus obtained might take the form of a strip. Once heated, the ingots were treated on an anvil with a forging hammer to anneal the metal and obtain a uniform thickness. An image on a twelfth-century capital at the abbey of Souvigny (France) depicts a person working on a metal strip with a hammer in just this way. Then, blanks of the weight desired were cut from the metal strip with a chisel and rounded off with hammer and tongs. The ingots might also have a cylindrical or square form, such as those used by the mint of London in the thirteenth century, or as it is also explained in medieval Arabic treatises on the coining of money. These bars were cut into small pieces. After weighing and rounding off with a hammer, the blanks were heated, coined, and finally polished. The same Arabic treatises explained another procedure consisting of casting the blanks in molds. The pieces obtained were hammered to anneal the metal and to shape the blanks before making them into coins.

General Conditions of Coin Production

The production of coins required the prior establishment of legal standard for weight and value whose acceptance was obligatory. Only a continuous relationship between the pieces and the legally instituted units of weight and account could avoid the dissipation of coins into mere metallic objects. Similarly, all coinage contained an additional element of authority (seigneuriage) which increased the legal value of the piece beyond its metallic weight.

Once the legal system of weight and accounting was established, the authority could then proceed to mint coins. With them, the state or lord possessed a means with which to pay his own bills and to purchase services, especially those of a bureaucratic and military nature. At the same time, such payments constituted the initial channels for the distribution of coins. Nevertheless, markets were the principal agency for the diffusion of coinage. This necessary intervention of money in market exchanges can be clearly appreciated in, for example, the donations of mercatum et moneta made to the abbey of Corvey by the Carolingian kings in the mid-eighth century, or in the establishment of markets in burghs by English lords after the Norman conquest. The central role of the market in the circulation of coins was remarked by the eleventh-century Andalusi polymath Ibn Hazm when he described how coins—which he characterized as “snakes” and “scorpions”—came into the hands of peasants with the sale in markets of what they alone produced. In the final analysis, what underlay the need to acquire coinage in market exchanges was the obligation on subjects to satisfy some or most of the fiscal demands of rulers with money. In this way, the power that minted the pieces was assured not only that the metal would return to the mint but also of the liquidity of peasant production. In any case, the states or lords that produced coins habitually needed to obtain fresh metal to coin at least the same mass of metal as had been put into circulation. Evasion, fraud, and the imperfections of the system of tax and tribute collection resulted in the inevitable loss of metal. For this reason, the authorities strove to control the process of metal extraction. One of the habitual procedures, documented for example in tenth-century Italy and eleventh-century al-Andalus, was to acquire metal directly from miners—gold from placers in both cases—paying the price fixed by the state.

The manufacture of coins thus required mastery of various techniques, including melting and engraving of the dies used to stamp the coins, the refining of metals, the preparation of alloys, and polishing of the flans before being coined as well as of the coins already stamped. Eligius, a Frankish moneyer of the seventh century, patron saint of the goldsmiths, personified this technical relationship between the manufacture of coins and the production of other metallic objects. So important was the work of mint personnel that the authorities frequently confined moneyers to places in which they could have no contact with the outside world. In this way they tried to avoid the counterfeiting of coinage, a practice well documented throughout the Middle Ages. Severe punishments were also prescribed. For example, in an edict of 643 the Lombard king Rothar ordered the amputation of the hand of anyone fabricating coins without royal authorization.

See also Mineralogy

Bibliography

Cooper, Denis R. The Art and Craft of Coin Making. A History of Minting Technology. London: Spink, 1988.

Grierson, Philip. “Note on Stamping of Coins and Other Objects.” In A History of Technology, edited by Charles Joseph et al. Singer, ed. Oxford: Clarendon Press, 1954–1984. II, 485–492.

Sellwood, D. “Medieval Minting Techniques.” British Numismatic Journal (1962) 31: 57–65.

Toll, Ch. “Minting Technique according to Arabic Literary Sources.” Orientalia Suecana 19–20 (1970–1971), 125–139.

FÈLIX RETAMERO

Columbus, Christopher

The navigator Christopher Columbus (called Cristóbal Colón in Spain) was born Cristoforo Colombo in Genoa in 1451. Experience gained in sailing Atlantic waters as a merchant in the 1470s and 1480s (Iceland, Madeira, the Azores, and the Gulf of Guinea) convinced Columbus of the possibility of a westward voyage to India. Columbus established himself in Lisbon and between 1478 and 1484, when he left for Spain, he attempted to convince Portuguese officials to back his voyage westward. He presented his ideas to Ferdinand and Isabel in 1486 and 1487. Finally the king and queen convened a panel of experts (including “wise men, learned officials and mariners”) at the University of Salamanca to evaluate his plan. The experts rejected Columbus’s proposals, not because the Earth was flat (a false story that Spain’s enemies concocted years later) but because, according to Columbus’s biographer Bartolomé de Las Casas, it was not thought possible to sail to the Antipodes. It was widely believed that the “torrid zone” near the equator was both impassable and uninhabitable. To Columbus this was absurd: “The Torrid Zone is not uninhabitable, because the Portuguese sail through it nowadays, and it is densely populated…. Below the equator, where the days are always twelve hours long, is the king of Portugal’s fortress. I was there and it was a temperate place.” *Mandeville’s Book, one of Columbus’s sources, had debunked the Torrid Zone and Columbus had verified his conclusion by his own experience. The sovereigns finally relented in 1491, even though another royal commission had decided against Columbus, and he was granted the title of Admiral of the Ocean Sea and viceroy in whatever territories he might claim for Castile.

Columbus made four voyages across the ocean. He recruited his crew for the first expedition among experienced Atlantic seamen from the port of Palos de la Frontera, near Cádiz. Columbus’s ship, the Santa Maria, belonged to a local ship owner named Juan de la Cosa, who sailed as Columbus’s second in command and was to become the greatest cartographer of the early discovery period. The crossing actually began at Gomera in the Canary Islands on September 6, 1492, and made landfall in an island of the Bahamas on October 12. Columbus sailed the coasts of Cuba (which he first thought to be Japan, then mainland China) and Hispaniola, and began the voyage home on January 4, 1493. During the second voyage (1493–1496) he was involved with colonizing Hispaniola and sailing to the west of Cuba. On the third voyage (1496–1498), he explored the Paria Peninsula of Venezuela and the mouth of the Orinoco River, which he believed to be the entrance to the Terrestrial Paradise. On the fourth voyage (1500–1504) he sailed the coast of Central America and Panama (which he called Veragua). He was marooned on Jamaica (where he predicted a lunar eclipse) and returned to Spain on November 5, 1504. Juan de la Cosa was also on the second voyage, and after a third with Alonso de Ojeda in 1499–1500 he drew his famous world map depicting all Spanish and Portuguese exploration until that time.

Unsigned fifteenth-century portrait of Christopher Columbus. (Getty Images/Hulton Archive)

In the process of conceptualizing his voyage, Columbus consulted all manner of sources in order to substantiate his conviction that the ocean was narrower than many thought. In order to convince both prospective patrons and crew members he had to make a case for the trip’s feasibility. Columbus had seen a letter written to the king of Portugal by Paolo Toscanelli, an Italian physician and amateur geographer, estimating the distance from the Canary Islands to China as five thousand nautical miles. He found corroboration of the assertion of the apocryphal book of Esdras that land covered six-sevenths of the Earth’s surface in the Imago Mundi, a geographical encyclopedia compiled by *Pierre d’Ailly, who gave 225° for land and 135° for the sea (where *Ptolemy had had 180° for each). After further juggling of the figures, he finally arrived at a projected voyage from the Canary Islands to India of only 60°, a mere twenty percent of the real distance.

Columbus also used an overly small value for the mile. In a Latin marginal note to Pierre d’Ailly’s Imago Mundi he wrote: “Note that from Lisbon south to Guinea I frequently observed the course carefully and afterwards I many times took the Sun’s altitude with the quadrant and other instruments, and I found agreement with al-Farghani, that is, that 56 2/3 miles equaled one degree.” He thus concluded that the circumference of the Earth at the equator was 20,400 miles (32,800 km).

Columbus reflected on this experience in a 1501 letter to Ferdinand and Isabel: “I have conversed and exchanged ideas with learned men, churchmen and laymen, Latins and Greeks, Jews and Moors and many others of other religions…. [God] endowed me abundantly in seamanship; of astrology He gave me sufficient, and of geometry and arithmetic too, with the wit and craftsmanship to make presentations of the globe and draw on them the cities, rivers and mountains, islands and harbors, all in their proper places.”

Columbus’s method of navigation and how good he was at it are matters of controversy. Judging from his methodical recording of distance in his logs (only those of the first voyage survive), he sailed by dead reckoning, using a compass, marking his course on a chart, and determining speed by watching flotsam floating by his ship. He habitually overestimated the speed of his ships. He made a series of latitude readings in the Caribbean and on the return voyage by determining the altitude of the Pole Star with a quadrant. His errors were so great that Morison thought he had mistaken other stars for Polaris. A more recent view holds that Columbus had read the tangent scale of his quadrant rather than the direct declination scale, in which case his readings were only a few degrees off instead of fifteen or more. His finding of 19° latitude for Jamaica on his fourth voyage, within one degree of accuracy, suggests that his skills at celestial navigation had improved. It is possible that many such observations were rough approximations made without the use of observational instruments.

Columbus was the first European to record the shifting of positive (northeast) to negative (northwest) magnetic declination as, on the night of September 12, 1492 (on his first voyage westward), he passed a point of zero declination: “The compass needles which until then had varied towards the northeast, suddenly changed one-quarter to the northwest.” On subsequent voyages he used this geomagnetic reference to establish his longitude roughly one hundred leagues west of the Azores.

It has been supposed, based on a fleeting reference to an “Almanach” in a passage of his Book of Prophecies describing his lunar eclipse prediction in Jamaica in 1505, that Columbus carried, at least on the fourth voyage, a copy of *Zacuto’s Almanach Perpetuum. But the Almanach contains neither eclipse tables nor those for declination. Therefore he might have carried the tables of *Regiomontanus, either in book format or individual tables copied onto sheets. On a blank page of his copy of d’Ailly, he had copied a table of the longest day of the year for each degree of latitude and another of the number of degrees traversed by the Sun in each house of the zodiac. On occasion, he did attempt to ascertain latitude by the length of daylight, with mixed results.

Once his geographical views were formed, he held doggedly to them, an inflexibility made possible by the tremendous latitude allowed him by the great variety of medieval texts he consulted. Columbus insisted until he died (in 1506) that he been sailing off the Asian coast.

See also Navigation

Bibliography

Primary Sources

Columbus, Christopher. The Diario of Christopher Columbus’s First Voyage to America, 1492–1493. Eited by Oliver Dunn and James E. Kelley, Jr. Norman: University of Oklahoma Press, 1988.

———. The Book of Prophecies. Edited by Roberto Rusconi. Berkeley: University of California Press, 1997.

D’Ailly, Pierre. Ymago Mundi. Edited by Edmond Buron. 3 vols. Paris: Maisonneuve, 1930.

Secondary Sources

Alvarez, Aldo. Geomagnetism and the Cartography of Juan de la Cosa: A New Perspective on the Great Antilles in the Age of Discovery. Terra Incognitae (2003): 35: 1–15.

Fernández-Armesto, Felipe. Columbus. New York: Oxford University Press, 1991.

Flint, Valerie. The Imaginative Landscape of Christopher Columbus. Princeton: Princeton University Press, 1992.

Morison, Samuel Eliot. Admiral of the Ocean Sea. 2 vols. Boston: Little, Brown, 1942.

Pickering, Keith A. Columbus and Celestial Navigation: www1.minn.net/~keithp/cn.htm

Russell, Jeffrey Burton. Inventing the Flat Earth: Columbus and Modern Historians. New York: Praeger, 1991.

THOMAS F. GLICK

Commercial Arithmetic

The increase in European trade from the tenth century onward led to the replacement of the individual, nomadic merchant by the established, sedentary, trading house. Initially, it was cities such as Pisa, Genoa, Venice, and Florence with their access to the Mediterranean and the markets of the Levant that became trade centers with fondacos, or large commercial houses. With their regional and international network of warehouses and agents, these houses became conduits for diverse goods, commodities, and information. During their travels, merchants were avid observers and recorders of customs and practices pertaining to mercantile success and efficiency. Their ricordanze (diaries) became a record of tariffs and custom duties, foreign weights and measures, methods of storing and transporting goods, and the mathematical methods used to protect investments, establish costs and ensure profits. One particular new form of knowledge, commercial arithmetic, as practiced by the Arabs, was brought by merchants into Europe where it was refined and expanded to meet the rising complexities of trade within the developing monied economies.

Since classical times, merchants have always been involved with arithmetic, establishing a value, reckoning prices and the terms of a sale necessary to realize a profit for their efforts. In Greek times and even into the late Roman period, this type of working with numbers was considered crass and vulgar because it was felt that numbers, their properties and associations should be the subject of philosophical speculation. It would be primarily in the merchant houses of medieval Europe that this concept of number and calculation would be radically changed. Traditionally in the medieval merchant house, calculation was performed on an abacus, a mesa Pythagorica or tabula abaci, a table with ruled columns or rows which designated assigned numerical magnitudes—tens, hundreds, etc—and along which “counters” would be moved to perform a reckoning process. These counters were round, flat metal disks used to mark numerical positions on the computing board or table. Known as jittons in French or, more tellingly, Rechenpfennig (reckoning-penny), in German, they eventually became standardized and resembled coins. The counters were manipulated according to specific rules in performing the four fundamental operations of arithmetic with division singled out as “dura cosa e la partita” (literally, “hard thing is division”). Merchants worked with whole numbers, fractions, and mixed numbers. Facility on the abacus or counting board was enhanced by the memorization of tables (librettine) of numerous multiplication facts which had to deal with a great variety of monetary systems and weights and measures. Such tables were far more extensive than those usually required today. A merchant calculator also had to be able “to hold numbers in his hand,” that is, to use his hand and finger positions as a register to store numbers during abacus calculations. Finger mathematics was a practice employed since Roman times. Its various techniques and positions were transmitted through the writings of *Boethius. The results of calculations were usually checked by the “method of casting out nines” and recorded in account books using Roman numerals. Throughout the Middle Ages, the accounting table or board became the center of commercial transactions, giving rise to the modern expression “doing business over the counter.”

But the real essence of commercial arithmetic was in its application to business situations: fair division of property and profit in partnership arrangements; computation of commissions and brokerage fees; monetary exchange; estimation of tare and tret (allowances and deductions); the determination of interest; alligation; the mechanics of barter and, even in some situations, calendrical reckoning and astrological readings. Within these applications, the calculator would usually apply specific arithmetical techniques such as “the rule of two” or “the rule of three” and “the chain rule.” Although these were all regarded as powerful solution techniques, they were no more than simple applications of proportion. Italian merchants were the pioneers of commercial arithmetic on the European scene. As a result, many of the problem situations and solution techniques bore Italian names, even when they were used in Northern Europe. Merchants from all over Europe sent their sons to learn l’arte della merchandanta from the Italians.

The Rule of Three

An eastern import that found its way to Europe through Arabic sources, “the rule of three” was called la regula de le tre cosa in Italian and regula trium rerum in Latin but, reflecting on its use and value, in English it was more popularly known as the “Merchant’s Rule” or the “Golden Rule.” It involves the solving of a proportion where three values are known and from which a fourth, unknown, must be found, that is: a is to b as c is to x; from which x is found to be the product of b and c divided by a. The “rule of two” involved finding an unknown from a product of two knowns divided by their sum whereas the rule of five was a simple proportion between five known values and one related unknown. The chain rule, regula del chataina, particularly useful in determining monetary exchange, was a continuous proportion with different terms for different currencies.

Often the hazards and costs of a business venture were distributed by means of a partnership. If the venture failed, individual losses would be restricted, but if it was successful, profits had to be distributed fairly. Computations involving partnership almost always required an application of the rule of three. The problems encountered concerned two situations: (1) A number of partners contribute varying amounts of investment to a venture and at its successful completion must share the profits accordingly; and (2) The same scenario with time factors introduced, that is, when each partner has invested for a different period, and the duration of each’s involvement has to be taken into account when distributing profit. Medieval writers of arithmetic such as Johannes Hispalensis (c. 1140) and Leonardo Pisano (1202) devoted sections to the mathematics of partnership, known in Latin as Regula de societate.

Before the standardization and ready availability of money, barter (barattare) was a common method of exchanging goods. For the medieval merchant, barter was a major form of commerce. Barter computations involved placing a value on the merchandise to be exchanged so that it offset the barter value and ensured the desired profit. Even when solvent monied economies existed, barter was still often employed. In such cases, two prices would be established for a good: a cash price and a barter price. The barter price was always higher.

Alligation (legare e consolare le monete) was a method of standardizing different currencies so that merchants could compare like with like. For tradespeople dealing with differing coinage that contained varied amounts of precious metals such as gold or silver, the actual value of money was often in question. The exchange of different coinage required appropriate calculations, and tables of information were available to assist merchants with this task. Often the value set for a product that, in itself, was comprised of a mixture of substances of different quality and price had to be determined. For example, different grades of grain, wool, oil or wine could be mixed to comprise saleable products.

Tare (tara) was the determination of the weight of a shipment of goods with appropriate deductions for the weight of the containers, such as crates or barrels. Tret (tratto) is the allowance made for possible damage to and/or deterioration of merchandise experienced during shipment. In the transport of any merchandise, calculations had to be made for tare and tret. Merchant handbooks (pratica della mercantura) contained advice and tables that assisted in this task.

Certain chronologically-based phenomena were important in the professional lives of merchants. Change of seasons, planting and harvesting times determined agricultural markets. The periodic flow of tides and the shifting of wind patterns controlled maritime trade. Rainy periods curtailed overland trade. In Christian Europe, church feast days and holidays disrupted money transactions and trade patterns. Merchants had to be able to coordinate their transactions according to these factors and thus, in this era before the appearance of reliable public calendars, had to be able to reckon dates in advance. The Christian *calendar is compiled around the occurrence of Easter, which was officially declared to be the first Sunday after the full moon following the vernal equinox on March 21. If the full moon happened to coincide with a Sunday, Easter would be the following Sunday. The astronomical computations involved in this issue were settled by the year 525 C.E., and the necessary tables of interpolation were compiled by Dionysius Exiguus and Bede to assist in determining the date of Easter. These tables were included in merchants’ manuals. To use these tables one had to determine the “Golden Number,” by adding 1 to the existing date and dividing by 19. The remainder was the “Golden Number,” which allowed the tables to be referenced. Merchants, in their travels and business ventures, were constantly tempting the “fates.” *Astrology was used to remedy this situation. Astrological advice was frequently directed towards the hazards of travel and the uncertainties of the marketplace. Many commercial reckoning books and manuals contained sections on astrological computations.

From the twelfth century onward, increased demand by merchants for a knowledge of and facility with commercial arithmetic stimulated the rise of two complementary industries: the writing and publishing of manuscripts and books devoted to the subject, and the development of a system of private schools and teachers to impart the new knowledge to students.

In their travels Arab merchants encountered new and effective mathematical techniques and applications which they refined and adopted for their own use. Italian traders in their contacts with the Arabs learned of these applications and began to use them themselves. Leonardo Pisano (c. 1175–1250), more commonly known as *Fibonacci (son of Bonacci), the child of a Pisan merchant, spent his youth in Bugia, a Pisan trading colony on the Barbary Coast. Leonardo was instructed in the methods of commercial arithmetic by local Arab teachers. During business travels through the Levant he further extended his knowledge of the subject. Impressed by the power of mathematics and its applications in the commercial world, he published his findings for a European audience. Liber abaci (Book of Calculations) appeared in 1202. Written in Latin, the book had a limited readership but a second edition appeared in 1228. While ostensibly written to convey information on the Hindu-Arabic numeral system to Europeans, over a third of the text is devoted to solving business-related problems: monetary conversion; barter computation; conversion methods for weights and measures; calculations involving partnership and the distribution of profits; simple and compound interest, and the alloying of money. As a practica or handbook of commercial arithmetic, the Liber abaci spawned numerous similar texts. Until this period of European history, arithmetic texts were rather scholarly, intended for those who wished to learn arithmetica, the philosophical and theoretical aspects of numbers, or to compute the Church calendar. The mathematics of the workplace had been left mainly to oral instruction between the master and his apprentices. Warren Van Egmond, in his research on this literature intended for merchants, termed such material “Abacus manuscripts.” It should be noted that at this time the word “abacus” and its many variants referred not only to the computing table but also designated working with numbers, computing, and arithmetic itself. Many of the practica published did not bear the word “abacus” in their title but rather were algorisms, such as Jacopo da Firenze’s Tractatus algorismi (1307). An algorism was any small treatise that explained the use of Hindu-Arabic numerals and their computing algorisms. Algorisms also served as handbooks of commercial arithmetic. In fact, partly through the influence of algorisms, Italian merchants became the first European professionals to adopt and extensively use the new numerals. As a result these numerical symbols were designated as figura mercantesco (the figures or numbers of the merchants), in contrast to the traditional figura imperiale (Roman numerals).

Further to accommodate the demand for knowledge of commercial arithmetic a new class of secular teachers arose in Europe: in Italy, they were known as maestri d’abbaco; in France, maistres d’algorisme, and in the Germanic regions, Rechenmeister. These men were practitioners of applied mathematics who sold their services and, in many cases, taught the subject. They opened schools of commercial arithmetic (scuole d’abbaco) for the instruction of merchants’ sons. It is known that by 1338 there were six such schools in Florence.

In practicing commercial arithmetic, medieval merchants refined and extended its scope. The use of Hindu-Arabic numerals led the way for their adoption in the rest of Europe. In the use of arithmetic, merchants developed the techniques of double-entry bookkeeping and the concept of percentage (per cento). Many present-day applications of arithmetic owe their origins to the commercial arithmetic of the medieval merchant community.

See also Arithmetic

Bibliography

Lopez, Robert. “Stars and Spices: The Earliest Italian Manual of Commercial Practice.” In Economy, Society and Government in Medieval Italy. Edited by David Herlihy, Robert Lopez and Vsevold Slessarev. Kent, Ohio: The Kent State Press, 1969, pp. 35–42.

Pullan, J. M. The History of the Abacus. New York: Frederick Praeger, 1969.

Sigler, Laurence. Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. New York: Springer-Verlag, 2003.

Smith, David. History of Mathematics. 2 volumes. New York: Dover Publications, 1958, pp. 552–582.

Swetz, Frank. “Figura Mercantesco: Merchants and the Evolution of a Number Concept in the Latter Middle Ages.” In Word, Image, Number: Communication in the Middle Ages. Edited by John Contreni and Santa Casciani. Micrologus’ Library 8. Florence: Edizioni del Galluzzo, 2002.

Van Egmond, Warren. “The Commercial Revolution and the Beginnings of Western Mathematics in Renaissance Florence, 1300–1500.” Ph. D. Dissertation, Indiana University, 1976.

FRANK J. SWETZ

Communication

The notion of scientific communication includes the ways in which scientific ideas are communicated to scientists and others, including personal interaction, the diffusion of texts, patterns of translation, literacy, and the rise of science in vernacular languages.

Scientific and medical communication can be understood in terms of textual communities. If the community changes, or is broadened, owing to translation or vernacularization, that may alter the way in which the text is perceived. Translation alone would not significantly alter the nature of the scholarly textual community, because in an Aristotelian world basic assumptions proved remarkably pliable in the face of the linguistic change. When an idea or set of ideas is the focus, rather than as discrete text, perhaps one might conceptualize multiple semantic communities clustered around the same text or set of texts. Such communities included both producers of texts (authors, translators, scribes) and consumers—all who had access to a text, listeners as well as readers.

The term “vernacular science” usually refers to the production of scientific texts in spoken languages, particularly in the cultural area where Latin was the language of learning. An analogue in the Muslim world was the relatively late, minoritarian production of scientific texts in Persian, rather than Arabic. However, the analogy is purely social, because Persian was every bit as much a classical language as were Arabic and Latin. So the discussion here will be limited to Europe. It must also be observed that Latin itself cannot be regarded as a single register of expression. When Arabic texts were said to have been translated vulgariter, what was often meant was that the target language was a Latin accessible to persons not trained in the Classics, not the vernacular.

Practical science was vernacularized earlier than that of a more theoretical nature: thus medicine, astrology, and alchemy all have rather strong vernacular traditions in late medieval Europe. In the thirteenth-century court of *Alfonso X the Wise of Castile, “The astronomical works translated from the Arabic were not of interest or important for what they revealed about the nature of the stars, but for how their movements influenced men’s lives. For this reason they were translated into Castilian rather than Latin, which was the language of a minority” (Castro, 1971: 538).

Emerging vernacular science was, of course, sharply configured by the established conventions of Latin writing. But both in translations from Latin or Arabic into the vernacular and literary creation directly in vernacular languages, new means of expressing scientific ideas had to be invented. Of course, oral teaching practices had themselves figured in the development of forms of written scholarly discourse: quaestiones, commentary, and compilations all to some extent were formalized versions of vernacular discourse that could be repatriated to their original domain. Taavitsainen (51–59) identifies uroscopies, *Guy de Chauliac’s surgeries, various Hippocratic and Galenic medical texts, and Beneventus Grassus’s ophthalmological treatise as vernacular commentaries (signaled by the repeated allusions to scholarly opinion (“Galien saith…”). Grassus contributed an English vernacular commentary on *Hunayn ibn Ishaq’s (Johannitius’) treatise on the eye. Encyclopedias were the most obvious form of vernacular compilations, overlapping, at least stylistically, with the commentary.

Vernacular quaestiones were also popular, particularly in verse form, which facilitated the memorization of complex issues such as humoral pathology:

“Telle me now, if that thou can
The perilousest thinges than ben in man.
Foure colours a man that him inne
That of foure complexiouns bigynne…

(Taavitsainen, 65)

Vernacular science was highly didactic, and much effort was devoted to the explanation of scientific and medical terms in plain language. That is why scientific vernacularization, as well as translation, were creators of new vernacular forms of expression.

Part of this process is revealed in the resolution of conceptual problems that translation presented. Castro argued that scientific translation in and of itself was a powerful force in the creation of literary Castilian generally, while Millás explained that the literalism of the Castilian translations from the Arabic of Alfonso X’s translators can be explained by, e.g., the need to coin new and somewhat clumsy abstract nouns to represent a kind of abstract discourse that had not previously existed in the language. Word-for-word translations from Latin to vernaculars and from Arabic into Latin appear as relexified versions of Latin and Arabic linguistic structures, respectively. In extreme cases, translators even tried for morpheme-by-morpheme renderings.

In technology, it is less appropriate to speak of textual communities, as opposed to communities of users of the same or related tool kits. Related tool kits can admit indefinite variation, however, in consonance with varying cultural, economic or social conditions, without thereby altering their function. No two *watermills are exactly alike, to cite a notorious example, even though their builders and operators may partake of identical tool kits.

“Community of discourse” is an even more comprehensive concept than readership or textual community, because one need not have read anything to participate in one. Some scientific and medical concepts, moreover, were so broadly diffused that perhaps an even more inclusive concept, such as field of knowledge, may be appropriate. For example, the percentage of the population conversant with humoral pathology as diffused through folk medicine in Europe must have been very high. The same can be said for the notion of the four qualities as understood in medieval *agronomy. Many illiterate cultivators knew that cold, dry seeds required hot, wet soil for their nurture. They must have identified these qualities by touch, according to traditional norms passed down orally, because agronomical treatises do not say how the system worked on a practical basis. The same is true, in Chinese medicine, of basic concepts such as yin-yang, qi, the five-phase system (wood, fire, earth, metal, water), and so forth. Everyone who has heard of the concept is in the field, and that is a very large percentage of the population. The same is true of astrology, where one did not have to be literate or know anything about cosmological theory to understand the meaning of horoscopes.

Anglo-Saxon England was precocious—uniquely so in Western Europe—in vernacular scientific texts, particularly medical. The first extant French vernacular medical texts did not appear until the thirteenth century. By the fifteenth century, vernacular scientific texts appeared all over Europe. In the Spain of Alfonso X the Wise (r. 1252–1284), Romance vernacular was first used as a medium for science. This was ten years before France, and one hundred years before England. The language in which the Alfonsine corpus was written shows the influence of Arabic in its semantic, syntactic and stylistic makeup. Of the technical terms used in Arabized Castilian science, five percent are Arabisms, thirty percent Latinisms with Arabized meanings, and the remaining sixty-five percent linguistic calques. A calque is a literal translation, the original meaning of which is lost in the target language of translation. An example is Castilian cuerda, “sine,” which retained the original Sanskrit meaning of “bowstring.” The spoken language had been much simpler than that in which the translations were rendered. Syntax had to be expanded to represent the internal complexity of subordinate clauses, which were required in order to convey, for example, the hierarchical relations among the different terms of mathematical equations (“multiple subordination”), in an age before the development of modern mathematical notation.

*Chaucer’s Treatise on the Astrolabe is a set-piece in the discussion of the creation of science in the vernacular. Chaucer begins the work by stating he is “but a lewd compilator of the labour of olde astrologiens.” In fact, some parts of the work, composed for his son around 1391, are translations, direct or expanded, from *Masha’allah’s De operatione uel utilitate astrolabii and from *John of Sacrobosco’s De sphaera, while much is composed by Chaucer himself. The text has a higher percentage of Romance words than is usual for Chaucer, indicating that Latin prototypes determined his choice of word.

The combination of the specific problems posed by translation from the Arabic and vernacularization (of which Chaucer’s Treatise is not only the first, but the best, exemplar from England) led to the creation of a new register of “nominalized” discourse which we recognize as scientific. Chaucer’s Treatise is replete with both concrete/technical and abstract/scientific nouns, extended nominal groups typical of mathematical writing, and clause complexes that carry the argument forward. “Spoken gestures,” another hallmark of vernacular scientific writing, are also found abundantly in Chaucer: “set the fix point of thy compass,” “mak a marke,” “loke in thyn almenak.”

A comparative study of vernacular science writing would be even more revealing than those of single languages. For example, in both Spanish and English, translation from the Arabic forced the creation of new abstract nouns. Thus in Chaucer’s Treatise, an abundance of nouns ending in -ioun, such as declinacioun, solsticioun, operacioun; in the Alfonsine translation of *Ibn al-Zarqalluh’s Treatise on the Saphea, abstract nouns ending in -iento (echamiento, ponimiento, minguamiento, catamiento), in -ura (longura, cortura), and in -ario (ascensionario, circulario, appositario).

In English, vernacular science was expressed in a “plain style,” shorn of rhetorical excess, that also characterized Chancery and legal English of the fourteenth century (law courts were obliged to use English in 1362), and unadorned vernacular translations of the Bible (Wycliffe, Tyndale). It is this tradition, after an interval of Elizabethan rhetoric, that reemerges among the members of the Royal Society, which enshrined plain writing as a norm of modern science.

Practical texts in particular were intended to memorized. For example, materia medica texts in the Dioscoridean tradition presupposed that the practitioner knew the systems of classification, whereby simples were indexed by their properties, according to humoral pathology, rather than by alphabetical order. (Medieval Latin authors shunned alphabetization as an organizing principle because it was not hierarchical.) Memorization of both diagnostic and remedial information turned the medical corpus into a hypertext: the physician could easily match diagnosis with cure because both were understood in terms of humoral pathology. In the vernacular realm, memorization was frequently aided by rhyming.

Code Switching

Code switching (or code mixing) refers to the use of more than one language in a single text. The process of scientific creation in medieval Europe reflects a kind of structural diglossia in that Latin texts were read by persons who presumably discussed and assimilated in the vernacular. But in many scientific and medical texts (nearly half of one hundred seventy-eight English manuscripts between 1375 and 1500 surveyed by Voigts, 1996) eighty-six contained more than one language. The mixing of languages can thus be viewed as a rhetorical or discursive strategy associated in particular with medical texts first and foremost, and then those on *astrology, astronomy, and *alchemy. In the case of a bilingual population, such as that of medieval England, the linguistic patterns are even more complex. In 1455, an English cleric named George Kirkeby compiled an alchemical miscellany drawn from the tradition of the Catalan Ramon Llull, with both Latin and Catalan versions. In a passage in Catalan on cosmology, Kirkeby intermingles Latin words and phrases with the Catalan, and in one place uses a Norman French adverbial expression. The Catalan version is given to enhance the authority and authenticity of the text, with Latin expressions perhaps used to sharpen technical points.

*Adelard of Bath in his translation of *Thabit ibn Qurras’ book on talismanic magic, Liber prestigiorum, retains the original Arabic wording for spells, ostensibly so that their power would not be diminished through translation. In his translation of *al-Khwarizmi’s astronomical tables, moreover, Adelard includes jingles with astrological content in transcribed Arabic, which reflects Andalusi pronunciation. In an explanation of the abacus, Adelard included a poem, as a mnemonic device, which explained the Arabic names of the counters, e.g., Octo beatificos themenias exprimiti unus: “One themenias [Arabic: thumun, ‘eight’) expresses the blessed eight” (Burnett, 22). All of this reflects (according to Burnett, 44) “an oral milieu of teaching, with a considerable amount of familiarity with the Arabic language.” In a treatise of Indian mathematics, one Ocreatus slots in Arabic transliteration for a technical operation of finding a square: cum vellem ducere finaph[s]ihi (Arabic, fi nafsihi, by itself): “When I want to multiply (the number) by itself.” Among a group of scholars who know only a little Arabic, conceptual clarity can still be maintained by switching into Arabic, particularly where there was no European tradition to fall back on. The resemblance of such astronomical/astrological jingles to incantations must have contributed to the perception of Arabic science as black magic.

Sometimes the languages used have different functions in the same text. For example a medical text in which the etiology of the illness appears in Latin, frequently followed by Middle English medicinal recipes. The provenance of some astrolabes has been identified by Romance vernacular influence detected in their Latin star names or zodiacal signs.

Some texts were interlinear with a vernacular translation given between the lines of Latin text; or technical terms in a Latin text could be glossed with vernacular equivalents in the margins. Vernacular writers might switch to Latin as an aide to organizing a text, by placing Latin rubrics in an otherwise vernacular text. One might switch from Latin to transliterated Arabic or from vernacular to Latin to introduce a voice of authority. Or Latin may hide something held secret or indecorous (women’s ailments, for example). Latin blessings and charms appear in vernacular treatises, as when a specific prayer is included in a recipe for a specific condition. Polyglot receptaria (recipes for remedies or other technical operations) are particularly common. A vernacular recipe might end with Latin sanabitur (“it will cure”), for emphasis. “The code-switched special terms contribute to the precision and specificity required of scientific discourse” (Pahta, 83–92).

Scholars have noted with fascination the polylingual nature of translation, whereby translators might work in teams, mixing languages freely in the process of translation. But this easy mixing of languages was common and not confined to scientific pursuits. Medieval European society was everywhere multilingual and predominantly oral, according to Clanchy (206); a Latin charter might be read aloud in French or English, while a statement made at court in the vernacular might be recorded by a notary or scribe in Latin.

Scholarly Interaction

Collins observes that scientific creation obeys the “law of small numbers”: original work occurs in very small groups displaying a high grade of connectivity. This is true of certain distinctive groups of medieval scientists. For example, the “trigonometrical revolution” occurred in the interacting circle of Central Asian Arab/Persian mathematicians active between 950 and 1000, including al-Khazin, al-Buzajani, al-Kuhi, al-Khujandi, al-Sijzi, and, somewhat younger, *al-Biruni. The Andalusi Aristotelians who developed a distinctive approach to cosmological theory (Ibn Bajja, al-Bitruji, etc.) certainly illustrate the point, although Collins (438) sees them as enmeshed in a geographically broader, interconnected group that includes *Ibn Rushd, *Maimonides, and *Abraham ibn Ezra.

In the Arab world, travel “in search of knowledge” (fi talab al-‘ilm) was a key modality of scientific communication. Merchant/scholars, both Jewish and Muslim, could support themselves by trade at the same time as they studied with eminent teachers. When they returned to their homelands, they disseminated both books and ideas among their more sedentary colleagues. The connectivity of a world already tightly linked by commercial networks explains the rapidity by which certain ideas and techniques spread. The “prime vertical” method of using fixed boundaries to divide the “houses” of the ecliptic, devised by *al-Biruni, was known to *Ibn al-Samh in Spain during Biruni’s lifetime. Scholars also came from outside the Islamic sphere: *al-Razi told the story of an insistent Chinese who called at his house and demanded that his host read his medical works aloud so that he could record them in Chinese.

One way in which the new Arabized Greek science reached Europe was by travel. First, there was a stream of Latin scholars going to Spain, in particular *Toledo (*Gerard of Cremona, Adelard of Bath, *Michael Scot, Daniel of Morley, Robert of Ketton). The opposite current is represented by *Pedro Alfonso, who campaigned for the new science in his writings and also went to England, where he composed astronomical tables and instructed Englishmen in their use, and *Abraham ibn Ezra, who likewise made his living by traveling from town to town in Italy and France composing astronomical tables.

Circles of Affinity

Established scholars held open discussions (called majlis) with students and colleagues usually in their own studies. Ibn Bajja presided over a famous Aristotelian majlis in Zaragoza. Maimonides held his own majlis for his medical students in Cairo, and also attended a more philosophical majlis, that of the Arab courtier and judge, Ibn Sana’ al-Mulk. In Toledo, Gerard of Cremona’s relationship with his socii (associates, but in the sense of Arabic sahibuna, our fellows [Weber]) is analogous. The circles of scholars that kings brought into their courts were centers of scholarly communication and production. Both Alfonso the Wise and *Frederick II of Sicily took active roles of scholarly discourse and presided over majlis-type meetings of their scientific courtiers, that included both Christians and Jews. Another affinity group, bridging Barcelona and Montpellier, was that whose central figure was Ibn Tibbon (*Profatius Judaeus).

On a more technical level, scriptoria were of course centers for the diffusion of science. Arabic numerals first appeared in Europe in the scriptorium of the Spanish monastery of Silos. Reading was a skill, but writing was a technique, not linked to reading. A specific technology had to be mastered because of the difficulty in writing on parchment with a quill pen. The arsenal of scribal tools included knife, pumice, and animal teeth to prepare the writing surface; stylus, pencil ruler, plumb line, and awl for ruling the lines; and finally quillpens, inkhorn, and various kinds of ink.

See also Aristotelianism; Dioscorides; Herbals; Translation movements; Translation norms and practice

Bibliography

Burnett, Charles. The Introduction of Arabic Learning into England. London: The British Library, 1997.

Castro, Américo. The Structure of Spanish History. Princeton: Princeton University Press, 1954.

———. The Spaniards. Berkeley: University of California Press, 1971.

Clanchy, Michael. From Memory to Written Record: England 1066–1307. 2nd ed. Oxford: Blackwell, 1993.

Collins, Randall. The Sociology of Philosophies: A Global Theory of Intellectual Change. Cambridge: Harvard University Press, 1998.

Comet, Georges. “Les céréales du Bas-Empire au Moyen Age.” In Miquel Barceló and Grançois Sigaut, eds. The Making Feudal Agricultures? Leiden: E.J. Brill, 2004, pp. 131–176.

Halliday, M. A. K. “On the Language of Physical Science.” In Mohsen Ghadessy, ed. Registers of Written English: Situational Factors and Linguistic Features. New York: Pinter, 1988, pp. 162–178.

Jones, Claire. “Discourse Communities and Medical Texts.” In Taavitsainen and Pahta (2004), pp. 23–36.

Millás Vallicrosa, José M. “El literalismo de los traductores de la Corte de Alfonso el Sabio.” In Estudios sobre historia de la ciencia española. Barcelona: CSIC, 1949, pp. 349–358.

Pahta, Päivi. “Code-Switching in Medieval Medical Writing.” In Taavitsainen and Pahta (2004), pp. 73–99.

Pahta, Päivi and Irma Taavitsainen. “Vernacularisation of Scientific and Medical Writing in its Sociohistorical Context.” In Taavitsainen and Pahta (2004), 1–18.

Pereira, Michela. Alchemy and the Use of Vernacular Languages in the Late Middle Ages. Speculum (1999) 74: 336–356.

Samsó, Julio. “Al-Biruni in al-Andalus.” In From Baghdad to Barcelona: Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet. 2 vols. Barcelona: Universitat de Barcelona, 1996, II: 583–612.

Taavitsainen, Irma. “Transferring Classical Discourse Conventions into the Vernacular.” In Taavitsainen and Pahta (2004), 37–72.

Taavitsainen, Irma and Päivi Pahta, eds. Medical and Scientific Writing in Late Medieval England. New York: Cambridge University Press, 2004.

Tebeaux, Elizabeth. The Emergence of a Tradition: Technical Writing in the English Renaissance, 1475–1640. Amityville, NY: Baywood, 1997.

Wilson, R. M. “Linguistic Analysis.” In Derek J. Price, ed. The Equatories of the Planets. New York: Cambridge University Press, 1955: 137–148.

Voigts, Linda E. What’s the Word: Bilingualism in Late-Medieval England. Speculum (1996) 71: 813–826.

THOMAS F. GLICK

Computus

The term computus denotes any kind of reckoning or accounting, but is also used in a special sense to mean the calculation of *calendar adjustments, particularly in connection with determining the date of Easter. For historians of science, computus is significant for two reasons: first, it was one of the few problems of a scientific character to arouse sustained debate in the early medieval period; and secondly, it was the arena in which the capabilities of the mathematical astronomy introduced from Greek and Arabic sources in the central Middle Ages were first systematically tested. The issue at stake was the recalibration of the calendar to ensure its conformity with celestial phenomena; but that recalibration was necessitated by the religious and symbolic meaning of the date of Easter.

Computus and the Calendar

Because the Christian Church adopted the Julian solar calendar of Rome as its basic framework for time-reckoning, a medieval calendar found in any computus manuscript looks very much like a pre-Christian Roman calendar. It is a generic calendar of twelve months—the familiar Roman months used today—in which the dates are listed vertically, and numbered, according to the Roman convention, in relation to the marker-days of kalends, nones and ides. To the right of each date is the feast or saint commemorated on that day, along with astronomical notices (e.g., solstices and equinoxes, the entry of the Sun into zodiac signs). To the left of the dates are key letters used to customize the generic calendar for a particular year. The seven letters A–G, in sequence representing the seven days of the planetary week, permitted the adjustment of date to week-day in any given year (on years designated with A, all A-days were Sundays, etc.). These were known as the “dominical” or Sunday letters. A second set of key-letters translated calendar dates into days of the lunar month or the position of the Moon in the zodiac: two such lunar letter schemes, together with the counter-tables for converting the letters into lunar dates, are described by *Bede in De temporum ratione chapter nineteen and chapter twenty-three. The “Golden Numbers” placed to the left of certain dates indicate the year of the nineteen-year Paschal lunar cycle in which a new moon falls on that date; they serve as a handy reference point from which to calculate the lunar phase on any calendar date. Customizing the generic Julian calendar into the calendar for a particular year could, of course, also be carried out by mathematical formulae known as argumenta.

The Problem of Determining Easter

Determining the calendar date for Easter Sunday, however, was a challenge of a very different order. Easter commemorates Christ’s death and resurrection at the Jewish feast of Passover, celebrated in the full moon of the first lunar month (Nisan 14 in the Jewish calendar). Since Passover is a spring festival, Christian writers assumed that it had to fall after the vernal equinox. In the original Julian calendar, the equinox was fixed at March 25, and so it remained in popular lore for many centuries. However, because the calculated solar year of 365.25 days is longer than its true tropical year (365.2422… days), the date of the astronomical equinox gradually moved backward with respect to the solar calendar. This problem was noticed in antiquity, and the Alexandrian Church, whose computus eventually formed the basis of both Eastern and Western Paschal reckoning, adopted the correct date of March 21 in the fourth century. But the root of the problem was neither recognized nor addressed, and the slippage of the equinox continued until Pope Gregory XIII mandated the reform of 1583.

The calculation of Easter involves solving several inter-locking puzzles. First, one must know the age the moon will be on the next vernal equinox, since the full moon which follows this will be the terminus a quo of Easter. This lunar age will vary from year to year, because twelve lunar months of approximately 29.5 days each is about 11 days short of a solar year of 365.25 days. Hence the moon will be 11 days older on the spring equinox next year than it is this year. After about three years, this increment will amount to more than 30 days, so an entire lunar month (an “embolismic month”) must be inserted to bring the lunar and solar years roughly into phase. To calculate the age of the moon on future equinoxes therefore requires a luni-solar cycle, that is, a whole number of solar years into which a whole number of lunar months can be inserted, so that the lunar phases fall on the same calendar dates after the end of the cyclic period. Several cycles already in use in antiquity were tried out, of which the most accurate was the nineteen-year cycle of Meton of Athens. The second problem arises from the custom of celebrating Easter only on a Sunday. The weekday of the Easter terminus must be known in order to locate Easter on the next following Sunday. The Julian calendar contains 52 weeks plus one day, which means that calendar dates advance one weekday each year, and two weekdays after February in leap years, over a cycle of 28 years (7 weekdays times 4 years in the leap-year cycle). The remaining issues are not so much scientific as theological. What is the permissible seven-day range of lunar dates (i.e., dates in Nisan) on which the Paschal terminus can fall? Termini of luna 14–20 implies that Easter is a Christian Passover, since Passover begins on Nisan 14. Opting for luna 16–22, on the other hand, puts the accent on the lunar anniversary of the Resurrection, which occurred on Nisan 16, while 15–21 aligns Easter with the Jewish Feast of Unleavened Bread. Finally, in the light of all the conditions enumerated above, within what range of dates in a Julian calendar could Easter fall?

Finding a formula for Easter therefore entailed grappling with some explosive theological problems (particularly the relationship of Easter to the Jewish Passover), reaching consensus on dating the vernal equinox, and proving that a luni-solar cycle could be translated into a pattern of lunar and calendar dates within agreed termini. The solution had to be a formula which would unfailingly produce correct Easter dates and which would present these in a table for ready consultation. The Alexandrian computus current in the Eastern Church held a position of preeminence, but it took Bede’s De temporum ratione to provide a detailed and accessible exposition of this system in terms of the Julian calendar. The Alexandrian computus used the 19-year Metonic lunar cycle, the March 21 equinox, lunar limits of 15–21, and calendar limits of March 22–April 25. A table based on this system and adapted to the Julian calendar had been published by Dionysius Exiguus (c. 532), a Greek monk living in Rome, in response to the defective Easter table of Victorius of Aquitaine. De temporum ratione explained and defended Dionysius’ table, exposing the failings not only of Victorius, but also of the version of the old Roman 84-year Paschal table current among the British and some sectors of the Irish church. It also demonstrated that Dionysius’ system would produce a cycle of Easters over 532 years.

As knowledge of the Church’s computus was considered an essential element of clerical training, Bede’s text rapidly became a standard schoolbook. Carolingian schoolmasters such as Hrabanus Maurus simplified it, eleventh-century scholastici such as Abbo of Fleury devised new tables to supplement it, and in the twelfth century Alexander of Villedieu versified it for use in the new urban schools. Schemes for memorizing the Paschal data by mentally inscribing them on the joints of the hand, and then using the hand as a “calculator,” were popularized through the sub-genre known as computus manualis. Vernacular computi first appear in Anglo-Saxon England (Byrhtferth, Aelfric), and are diffused in virtually every western European language by the later Middle Ages.

However, beginning in the late eleventh century, purely astronomical time-reckoning or computus naturalis emerged in the wake of newly available translations, planetary tables, and astronomical instruments such as the astrolabe. Late medieval calendar treatises such as those of John Somur and Nicholas of Lynn also contain tables of eclipses and even of planetary positions—evidence of the influence of *astrology. The advent of computus naturalis also highlighted the discrepancy between the crudely calculated positions of the Sun and Moon used for the computus ecclesiasticus, and the reality of the heavens. It thus fueled debates over calendar reform.

Computus and the Reform of the Calendar

Medieval projects to reform time-reckoning focused on two issues: chronology, and the relationship of the calculated calendar to astronomical reality. Debates over the inaccuracy of Dionysius’ annus domini dominated the eleventh century, but did not result in any change to this system. From the perspective of the history of science, the controversies surrounding the defects in the calculation of the lunar and solar periods on which the Paschal computus rested are of greater interest. The drift of the equinox backward with respect to the calendar continued, and by the late twelfth century computus naturalis furnished computists such as Roger of Hereford, *Robert Grosseteste and *Roger Bacon with the means to calculate its rate. At the same time, computists tackled the problem of the embarrassing discrepancy between the calculated moon and the visible Moon, a consequence of the gap between the notional lunation of 29.5 days and the true mean synodic lunar month of 29.53059 days. From the early thirteenth century up to the Gregorian Reform of 1583, the calendar reform debate focused on how to bring the calendar back into line with the astronomical realities of the Sun and the Moon, and how to keep it there. The first goal could be accomplished simply by dropping a certain number of days from the Julian reckoning, and was a matter of communication and political will. The second problem was scientific: the tropical solar year was plainly shorter than 365.25 days, but by how much? In practical terms, how often would a leap year have to be omitted in order for the calendar to stay in step with the Sun? Estimates varied from once every 300 (Grosseteste) or 288 years (Sacrobosco), to 125 years (Bacon). A task force set up by Pope Clement VI proposed dropping one leap year in 134, and setting back the Golden Numbers by one day every 310 years, but no action was taken. The general councils of the early fifteenth century, and succeeding popes, also failed to enact a solution, although they commissioned studies of the true length of the tropical year by astronomers such as *John of Gmunden and *Johannes Regiomontanus. Copernicus’ De revolutionibus was another contribution to the same debate. In sum, the purely religious-symbolic criteria for Easter—its relation to the astronomical spring and the cycle of lunations, and the necessity of plotting these against the grid of calendar-dates and weekdays—posed a very precise problem of exceptional scientific difficulty. What is intriguing about computus is that the Church’s commitment to keeping its celebrations in line with the true aspect of the heavens opened up a channel of inquiry that flowed into the Scientific Revolution.

See also Astronomy; Calendar; Clocks and timekeeping

Bibliography

Blackburn, Bonnie and Leofranc Holford-Strevens. The Oxford Companion to the Year. Oxford: Oxford University Press, 1999.

Borst, Arno. The Ordering of Time. Chicago: University of Chicago Press, 1993.

Contreni, John. “Counting, Calendars and Cosmology: Numeracy in the Early Middle Ages.” In Word, Image, Number: Communication in the Middle Ages. Edited by John J. Contreni and Santa Casciani. Micrologus’ Library 8. Florence: SISMEL–Edizioni del Galluzzo, 2002, pp. 43–84.

Cordoliani, A. Comput, calendriers, chronologie. L’Histoire et ses methodes. Edited Charles Samaran. Paris: Gallimard, 1961, pp. 37–51.

Coyne, C.V., M.A. Hoskin, and O. Pedersen, eds. Gregorian Reform of the Calendar. Vatican City: Pontific Academia Scientiarum, Specola Vaticana, 1983.

Declercq, Georges. Anno Domini: the Origins of the Christian Era. Turnhout: Brepols, 2000.

Englisch, Brigitte. Die Artes liberales im frühen Mittelalter (5.-9. Jh.): Das Quadrivium und der Komputus als Indikatoren für Kontinuität und Erneuerung der exacten Wissenschaften zwischen Antike und Mittelalter. Sudhoffs Archiv, Beiheft 33. Stuttgart: Franz Steiner, 1994.

García Avilés, Alejandro. El tiempo y los astros. Arte, Ciencia y religión en la alta edad media. Murcia: Universidad de Murcia, 2001.

Ginzel, F.K. Handbuch der mathematischen und technischen Chronologie. 3 v. Leipzig: J.C. Hinrich, 1906–1914.

Gómez Pallarez, Joan. Studia chronologica. Estudios sobre manuscritos latinos de cómputo. Madrid: Ediciones Clásicas, 1999.

Jones, C.W. [introduction to] Bedae opera de temporibus. Cambridge: Mediaeval Academy of America, 1943.

Jones, C.W. Bede, the Schools and the Computus. Aldershot: Variorum, 1995.

McCarthy, Daniel and Aidan Breen. The ante-Nicene Christian Pasch: the Paschal Tract of Anatolius, bishop of Laodicea. Dublin: Four Courts, 2003.

McCluskey, Stephen C. Astronomies and Cultures in Early Medieval Europe. New York: Cambridge University Press, 1998.

Moreton, Jennifer. “Robert Grosseteste and the Calendar.” In Robert Grosseteste: New Perspectives on his Thought and Scholarship. Edited by James McEvoy. Instrumenta patristica 27. Turnhout: Brepols, 1997, pp. 77–88.

———. Robert of Hereford and Calendar Reform in Eleventh and Twelfth-century England. Isis (1995) 86: 562–586.

———. John of Sacrobosco and the Calendar. Viator (1994) 25: 229–244.

Mundy, John. John of Gmünden. Isis (1943) 34:196–205.

The Kalendarium of Nicholas of Lynn. Edited Sigmund Eisner. Translated by Gary MacEoin and Sigmund Eisner. Athens: University of Georgia Press, 1980.

Ó Cróinín, D. Early Irish History and Chronology. Dublin: Four Courts Press, 2003.

Stevens, W. Cycles of Time and Scientific Learning in Medieval Europe. Aldershot: Variorum, 1995.

Strobel, August. Ursprung und Geschichte des frühchristlichen Osterkalendars. Texte und Untersuchungen 121. Berlin: Akademie-Verlag, 1977.

Van Wijk, Walter Emile. Le numéro d’or: Étude de chronologie technique suivie du texts de la ‘Massa compoti’ d’Alexandre de Ville-Dieu. The Hague: Nijhoff, 1936.

FAITH WALLIS

Condemnation of 1277

On March 7, 1277, Bishop Etienne Tempier issued a syllabus of two hundred nineteen erroneous propositions (articuli), and forbade their dissemination and defense at the arts faculty of the University of Paris. Tempier’s prohibition has been widely considered to be the most dramatic and significant censure in the history of the University of Paris. Its impact on (natural) philosophy is clear from the many allusions in texts from the thirteenth and fourteenth centuries and from the debates it generated about whether or not *Thomas Aquinas was one of its targets. In addition, Tempier’s action has played a crucial role in helping to shape the historiography of medieval science as a respectable discipline. This latter development is connected to the name of Pierre Duhem (1861–1916), and to the far-reaching interpretation he gave of the 1277 event in preparing the way for modern science. Before discussing the possible importance of Tempier’s prohibition for the development of medieval science, it is useful to turn to the actual events.

The Events of 1277

The generally accepted picture of the events leading to the condemnation looks something like this. On January 18, 1277, Pope John XXI (1276–1277) informed Etienne Tempier that he had heard rumors of heresy, and charged the Bishop of Paris with the task of examining where and by whom these errors had been disseminated. Tempier’s response did not take long to formulate. On March 7, 1277, the bishop issued a letter to which he attached a list of two hundred nineteen propositions and of some books that were thereby condemned. In the letter he rebukes “some scholars of arts at Paris” (nonnulli Parisius studentes in artibus) for discussing and holding disputations about “manifest and damned errors” (manifesti et exsecrabiles errores). The errors are the two hundred nineteen articles quoted in the attached rotulus. On pain of excommunication, members of the arts faculty are prohibited to disseminate in any way the errors collected by Tempier.

The prefatory letter also gives some indication as to the procedure which Tempier followed in establishing his list or errors. Tempier indicates that he had received information from “important people.” In other words, the bishop reacted to complaints of false teaching, either from the pope or from local sources. As the leading ecclesiastical authority of the University of Paris, he had to investigate these allegations that “some scholars of arts at Paris” had been “transgressing the limits of their own faculty” (proprie facultatis limites excedentes). Tempier established an advisory board, which consisted of theologians and “other wise men.” Although the letter remains silent on the procedure that was followed, we know from similar cases that the theologians were probably charged with examining works or a prepared list of theses, and assess whether they contained any errors or heresies. The outcome is clear.

The Targets of the 1277 Condemnation

What we still do not know is who Tempier’s targets were. As mentioned above, the prefatory letter merely refers to some people engaged in the arts at Paris. Yet, *Siger of Brabant and *Boethius of Dacia are usually identified as the main advocates of the prohibited errors. This identification derives from the rubrics of only two of the many medieval manuscripts of Tempier’s condemnation. These clues proved not to be totally unfounded. The admirable study by Roland Hissette has established that seventy-nine of the two hundred nineteen theses can be identified with varying degrees of probability in the works by Siger and Boethius, and by three anonymous writings that originated at the arts faculty and that have so far been edited. The somewhat disappointing results in identifying the errors in specific works that were produced at the arts faculty may have their origin in wrong assumptions about Tempier’s targets. As the prefatory letter states, the two hundred nineteen errors were propagated by members at the arts faculty. It does not say that they were the authors. In other words, only a limited number of theses represent the proprietary views of masters of arts, whereas for others one has to cast the net further, and investigate Greek and Arabic sources that were translated into Latin. It is still controversial whether Thomas Aquinas was implied.

The long list of two hundred nineteen prohibited theses lacks any thematic organization. Possibly the theses appear in the order in which they were culled from the works that were examined, or from other lists, for the 1277 condemnation was by no means the only prohibition of (allegedly) false teaching. Shortly after 1277, the list was reorganized, as it was again at the beginning of the twentieth century by Pierre Mandonnet. He distinguished one hundred seventy-nine philosophical theses from forty theological ones in an edition that came to be widely used by historians.

A very helpful thematic survey of the condemned propositions has been provided by John F. Wippel. The first seven of the philosophical propositions bear on the nature and excellence of philosophy. Propositions eight through twelve (in the numbering of Mandonnet) have a bearing on the knowability and nature of God. Propositions 13–15 concern divine knowledge, and 16 through 26 divine omnipotence. Many of the articles, notably numbers 34 to 61, regard the separate intelligences (angels). Another interesting group of articles is 67–69. By condemning these articles, Tempier endorsed God’s absolute power to do whatever He wills. Other interesting themes that are touched in the philosophical articles are the world’s eternity (80 through 89), the unicity of the human intellect and its implications (117–133), and human freedom and free will (151 through 166). Among the theological articles, themes that appear are theology as a science (180–186), the doctrine of the Eucharist (196–199), Christian morality (202–205), and human immortality and reward and punishment in the life to come (213–219). It should be emphasized that Tempier’s theses express positions that cannot be maintained in the light of revealed truth, and for this reason each is followed by the qualification “error.”

Condemnation of 1277 and Medieval Science

Tempier’s 1277 condemnation should be seen as a stage in the appropriation of Aristotelian (natural) philosophy in the West, and, more specifically, as a reaction against a certain variation of *Aristotelianism which in the older literature has been labelled “heterodox Aristotelianism” or “Latin Averroism.” At an institutional level, the events of 1277 can be seen as an interdisciplinary struggle between the faculties of arts and theology. At a doctrinal level, Tempier’s action reveals theological concerns over certain views in physics, metaphysics, and ethics that harked back to Aristotle’s treatises and that were embraced by masters of arts and by some theologians as well. Already in the 1270s masters of arts were prohibited to discuss philosophical questions in a way that was contrary to the faith. In his preface, Tempier ridicules the hermeneutical method of distinguishing between a philosophical treatment of a topic and a discussion of that same topic according to the truths of faith “as if there were two contrary truths, and as if against the truth of Sacred Scripture, there is truth in the sayings of the condemned pagans.” In reality, no thinker held a theory of double truth, but Tempier’s attack shows a high level of suspicion toward those thinkers who claimed to uphold the truths of faith, while at the same time saving the “scientific” conclusions reached through natural reasoning. On the basis of such passages and specific articles in the syllabus, historians have viewed the condemnation as evidence for the presence of rationalist tendencies at the University of Paris, i.e., as signs of the existence of an autonomous (natural) philosophy, pursued for its own sake, which Tempier attempted to curb.

A different assessment of Tempier’s role was given by Pierre Duhem. He believed that 1277 marked the birth of modern science, because it was then that Christian thought was liberated from the yoke of Aristotelian natural philosophy and thus came to produce modern science. Duhem focused in particular on articles 34 (Mandonnet, art. 27: “that the first cause [God] could not make several worlds”) and 49 (Mandonnet, art. 66: “That God could not move the heavens with a rectilinear motion and the reason is that a vacuum would remain”). These articles were in line with Aristotle’s views. He had demonstrated that it is impossible for there to be other worlds beyond our own, and that it is impossible for a vacuum to occur naturally. If this is the case, so these natural philosophers claimed, then even God cannot make a plurality of worlds or a vacuum. Tempier declared these articles as erroneous, because they subjected God’s omnipotence to the principles and conclusions of Aristotle’s physics. In his view, God was not constrained by what is possible or impossible in Aristotle’s natural philosophy. For Duhem, this attitude provided the key to rejecting Aristotelian physics, and thus opened up the way to the Scientific Revolution. The condemned articles encouraged speculation about the possibility that God could create a plurality of worlds, or could move the world with a rectilinear motion. They carried with them the destruction of Aristotelian notions of space and time and cosmology. Duhem’s thesis about the importance of Tempier’s condemnation was severely criticized. Yet its impact was tremendous, because of the documentation of medieval science that it brought with it, both by Duhem and his critics. In this way, Duhem set the topics for the subsequent historiography of medieval science and thus helped to establish it as an autonomous discipline.

See also “Latin Averroists”; Religion and science; Universities

Bibliography

Primary Sources

Denifle, Heinrich and Emile Châtelain, eds. Chartularium Universitatis Parisiensis. 4 volumes. Paris: ex typis fratrum Delalain, 1889–1897, vol. 1, pp. 543–558.

Grant, Edward. A Source Book in Medieval Science. Cambridge: Harvard University Press, 1974.

Mandonnet, P. Siger de Brabant et l’averroïsme latin au XIIIme siècle; étude critique et documents inédits. Fribourg: Librairie de l’Université, 1899.

Piché, David, ed. La condemnation parisienne de 1277. Texte latin, traduction, introduction et commentaire. Paris: Vrin, 1999.

Secondary Sources

Aertsen, Jan A., Kent Emery, Jr. and Andreas Speer, eds. Nach der Verurteilung von 1277. Philosophie und Theologie an der Universität von Paris im letzten Viertel des 13. Jahrhunderts. New York: De Gruyter, 2001.

Bianchi, Luca. “1277: A Turning Point in Medieval Philosophy?” In Was ist Philosophie im Mittelalter? Edited by Jan A. Aertsen and Andreas Speer. New York: De Gruyter, 1998, pp. 90–110.

Grant, Edward. The Foundations of Modern Science in the Middle Ages. Their Religious, Institutional, and Intellectual Contexts. New York: Cambridge University Press, 1996.

Hissette, Roland. Enquête sur les 219 articles condamnés à Paris le 7 mars 1277. Louvain: Publications Universitaires, 1977.

Murdoch, John E. “Pierre Duhem and the History of Late Medieval Science and Philosophy in the Latin West.” In Gli studi di filosofia medievale fra otto e novecento. Edited by Alfonso Maierù and Ruedi Imbach. Roma: Edizioni di Storia e Letteratura, 1991, pp. 253–302.

———. “1277 and Late Medieval Natural Philosophy.” In Was ist Philosophie im Mittelalter? Edited by Jan A. Aertsen and Andreas Speer. New York: De Gruyter, 1998, pp. 111–121.

Thijssen, J.M.M.H. Censure and Heresy at the University of Paris, 1200-1400. Philadelphia: University of Pennsylvania Press, 1998.

Van Steenberghen, F. Thomas Aquinas and Radical Aristotelianism. Washington, D.C: The Catholic University of America Press, 1980.

Wippel, John F. The Condemnations of 1270 and 1277 at Paris. Journal of Medieval and Renaissance Studies (1977) 7: 169–201.

JOHANNES M.M.H. THIJSSEN

Consilia

The medical consilium was a text in which a learned physician wrote a response to a specific medical question put to him either directly by a patient or indirectly by another physician with respect to a particular case. A physician need not have been present himself to consult on the case, and many consilia were composed in absentia. They were written predominantly in Latin and issued together in collections. Vernacular versions of consilia do exist. Plague consilia, which became popular after 1348 as a consequence of the Black Death, often circulated on their own in the vernacular.

The ideal text commonly comprised three main sections. The first described the patient (name, place of residence, occupation, social status, sex, age), signs and symptoms of disease, diagnosis (in the medieval context, often merely a brief description of the patient’s complaint), and sometimes an identification of causes. The second part, most of which was dedicated to dietary recommendations, provided directions for the daily routine and care of the patient according to the six Galenic nonnaturals (air and habitation, exercise and rest, food and drink, sleep and waking, evacuation and retention, and the emotions). The third part addressed therapeutic medicines, baths, and surgical procedures such as cauterization and phlebotomy. Although primarily produced in the course of practice, consilia also served as aids to teaching and study. When asked for advice on a particular case, Guglielmo da Brescia, for example, suggested that a fellow doctor read a consilium he had written on a like case.

The general form and structure of the medieval western consilium seem to have first appeared at the University of Bologna in the thirteenth century. Earlier examples exist, but the earliest collections of medical consilia appear to be those produced by *Taddeo Alderotti (1223–1295) and his associates. Although there are analogues in the works of *Arnau de Vilanova, the genre was developed and predominated above all in northern Italy.

Antecedents and Influences

Hippocratic antecedents include the Epidemics (I–III), which describe particular cases in detail, but offer little therapeutic advice, and Affections and Diseases of Women, which outlines therapies for specific diseases. *Galen’s De locis affectis, De methodo medendi ad Glauconem, and Methodus medendi illustrate clinical cases with the purpose of demonstrating and confirming the validity of theoretical doctrines outlined in the treatises. This technique of relating the theoretical to the practical seems to have most influenced the development of medieval practical medical literature from 1250 to 1500. Galen’s written response to a young man, which appeared as Pro puero epileptico consilium, may have been the ultimate model of the consilium, although it was not available to Latin readers until the Renaissance. Despite ancient antecedents, the development of legal consilia at Bologna in the twelfth century and their proliferation in the thirteenth may have provided the most direct model. Arabic authors also produced and translated accounts of clinical cases. These accounts, however, were not generally available to western physicians until the twentieth century, and consequently do not seem to have influenced the western medical consilium directly.

Relationship to Other Genres

Consilia should not necessarily be viewed as constituting an autonomous genre. It may be more constructive to consider them in the context of other forms of practical medical literature emerging between 1250 and 1500, which increasingly sought to apply medical theory to practice. Other practical genres developing concurrently were collections of remedies, experimenta (tried and tested medical regimens), regimens of health, and practicae (large medical manuals geared toward the treatment of specific diseases). Like the consilia, the regimen of health was often addressed to a particular individual. *Ugo Benzi, for example, wrote the Libro da conservare la persona in sanitate for Niccolo d’Este, who was said to suffer from obesity. Generally the purpose of a regimen of health was the maintenance of wellbeing rather than the treatment of a specific disease. Sometimes distinctions between these genres, however, were sufficiently unclear that a physician entitled his text consilium sive regimen or regimen sive consilium.

Some consilia by virtue of their length and formality resemble treatises even though they exist as parts of consilia collections as in Alderotti’s De ruptura sifac, Ugo Benzi’s On the Kidney Stone, or the enormous treatise-like consilia on defects of the bladder by Bartolomeo Montagnana (d. 1460). Other consilia written at the request of a particular patient were, in fact, circulated as individual treatises as in the Tractatus de hernia by *Gentile da Foligno (d. 1348), or the Ad appariciones fantasticas oculorum by Guglielmo Corvi (1250–1326).

Medieval Developments

The thirteenth century saw the birth and development of the medieval medical consilium in the work of Taddeo Alderotti, Baviero Baviera (d. 1480), Guglielmo Corvi, and Guillaume Boucher (fl. 1400). Consilia written in this period vary in form and structure, exhibit a variety of terminology and vocabulary, and are generally more pragmatic in tone than those composed later. Of Alderotti’s one hundred eighty-five consilia, more than one hundred are merely medical recipes and very few describe the patient’s symptoms.

Those of Gentile da Foligno bridge the first phase of the genre and its further evolution in the fifteenth century. His consilia are generally more abstract and theoretical, diagnosis is often treated in greater depth, and terminology is more precise. The inclusion of the opinions of medical authorities may indicate that these consilia were produced for didactic as well as professional purposes.

In the fifteenth-century consilia of Bartolomeo Montagnana, Antonio Cermisone (d. 1441), and Ugo Benzi, the theoretical element is developed to such an extent that the works sometimes resemble small scholastic treatises. In some cases, descriptions of the disease and its treatment appear in the form of doctrinal debates, and it is not uncommon to come across a scholastic exposition on possible interpretations according to the opinions of the ancient and Arabic authorities, namely, *Hippocrates, Galen, *al-Razi, and *Ibn Sina. There is also present a more pronounced interest in nomenclature. Some consilia contain etymological examinations of Greek, Latin, and Arabic terminology. In contrast to the scholastic consilia influenced by university medical learning, however, the consilia of Antonio Benivieni (c. 1443–1502) draw heavily on fifteenth-century philosophical movements such as neo-Platonism, which thrived outside the university.

This genre was well suited to serve as a form of self-advertisement or self-aggrandizement. Because of the highly personalized nature of the individual consilium, a learned physician could use consilia collections to showcase the fame and prestige of his clientele. Alderotti, for example, wrote consilia for a doge of Venice, two bishops, two counts, one of the Malatesta, and nine other people of high rank. Although men of high rank account for the greatest number of consilia produced in the Middle Ages, many also address the illnesses of men, women, and children from more modest backgrounds, and show the diversity of patients treated by learned physicians.

Medieval medical works in general reflect the intellectual and social world in which learned physicians lived and practiced. Consilia in particular are rich sources for studying the influence of classical and Arabic authors on medieval medicine and the developments and transformations of medical doctrines. Because they often include detailed medical recipes they are also useful in the history of medieval *pharmacology. They can further shed light on how learned physicians applied the theoretical training of the universities to therapeutic practice. Furthermore, they are important for establishing the social context in which a professional physician worked. It should be noted, however, that the social context they recreate is commonly an aristocratic one. They are, therefore, not useful in establishing general disease patterns, or for exploring the types of diseases brought about by famine or poverty.

See also Medicine, practical; Medicine, theoretical; Regimen sanitatis; Scholasticism; Scientia; Universities

Bibliography

Agrimi, Jole and Chiara Crisciani. Les consilia médicaux. Turnhout: Brepols, 1994.

Crisciani, Chiara. History, Novelty, and Progress in Scholastic Medicine. Osiris (1990) 6: 118–139.

Lockwood, D.P. Ugo Benzi: Medieval Philosopher and Physician, 1376–1439. Chicago: University of Chicago Press, 1951.

Park, Katharine. Doctors and Medicine in Early Renaissance Florence. Princeton: Princeton University Press, 1985.

Siraisi, Nancy. Anatomizing the Past: Physicians and History in Renaissance Culture. Renaissance Quarterly (Spring, 2000) 53, 1: 1–30.

———. Medieval and Early Renaissance Medicine: An Introduction to Knowledge and Practice. Chicago: University of Chicago Press, 1990.

———. Taddeo Alderotti and his Pupils: Two Generations of Italian Medical Learning. Princeton: Princeton University Press, 1981.

ELIZABETH W. MELLYN

Constantine the African

Constantine the African was the first major translator of Arabic medical writings into Latin and hence the most important figure in the revival of scientific medicine in the West from the late eleventh century on. The only biographical data that can be firmly documented are his arrival in Salerno in 1077 and his death at the Italian Benedictine monastery of *Monte Cassino by 1098–1099 at the latest. (The death date of 1087 that is often cited in secondary accounts has no documentary foundation.)

Peter the Deacon (d. after 1154), another monk at Monte Cassino, provides the earliest account of Constantine’s life: he came originally, Peter claims, from Carthage, and traveled to “Babilonia” (Cairo), India, Ethiopia, and Egypt. Another telling of Constantine’s activities by the mid-twelfth-century physician Matheus Ferrarius of Salerno claims that Constantine initially visited Italy and, finding the Latins impoverished in their medical literature, returned to Africa to gather books, though several were lost when he was shipwrecked on his return. A third, entirely different account (perhaps written by a partisan for the rival school of Montpellier) presents him as a fugitive from Spain who nearly killed his royal patient. Given his clear associations with the medical community of the Tunisian city of Qayrawan (see below), it may well be that his origins lie there.

Although clearly of African origin, Constantine’s original religion remains unclear. Ferrarius explicitly refers to him as a “Saracen,” but it has been noted that Arabic-speaking Christian communities are documented in Tunisia. Ferrarius comments on Constantine’s initial need to rely on a Muslim slave as his translator, while another twelfth-century Salernitan writer, *Johannes de Sancto Paulo, ascribes Constantine’s linguistic limitations in Latin to his African origin. Even Constantine’s medical qualifications are not securely documented. Peter the Deacon never specifically calls him a physician (medicus) while Ferrarius claims he was a spice merchant.

Works and Sources

Peter the Deacon included in his biography of Constantine the earliest comprehensive list of his works. It includes such items as the De genecia (On gynecology) and Cyrurgia (Surgery) that were probably independently circulating excerpts of the translation of *al-Majusi’s Kamil as-sina’a at-tibbiya (“The Whole Art of Medicine,” in Latin the Pantegni). Omitted from the list (perhaps due to oversight) were the Isagoge (“Introduction [to the Medical Art]”) by *Hunayn ibn Ishaq (Johannitius), the De stomacho (“On the Stomach”) and De melancholia (“On Melancholy”) by the Tunisian writer Ishaq ibn Imran (d. before 907), the De oblivione (“On Forgetfulness”) by Ibn al-Jazzar (d. 979/980), and a work on charms and amulets by Qusta ibn Luqa (d. early tenth century). In all, Constantine translated some two dozen different texts from Arabic into Latin.

Although Constantine (or his early copyists at Monte Cassino) omitted the names of all his sources save for the Jew, Isaac Israeli (*Isaac Judaeus, d. 932), thanks to increasing knowledge of the corpus of medieval Arabic medical writing it is possible to identify the sources for at least half of Constantine’s oeuvre. Besides Hunayn, al-Majusi, and Qusta ibn Luqa, Constantine’s sources were writers active in Tunisia, specifically Qayrawan, in the tenth century. Ibn al-Jazzar was Constantine’s most important source, including not only his general work on medical pathology, the Viaticum, but also works on leprosy, sexual intercourse, and degrees of medicines. The predominance of North African texts suggests that Constantine did not, in fact, travel very far to assemble his treasure trove of works; Ibn al-Jazzar’s work was available on Sicily itself where it was translated into Greek in the twelfth century.

Very few of Constantine’s works have yet been critically edited, so it is still difficult to pinpoint his unique stylistic characteristics as a translator. Indeed, it is still unclear how much of the Constantinian corpus is really by Constantine. Beside a peculiar text on impotence caused by magic (which is attested only in thirteenth-century manuscripts), there are several works associated with Constantine in medieval manuscripts or in Renaissance editions that are either spurious or of suspect authenticity. Particularly puzzling is the origin of the second major part of the Pantegni, the Practica (“Practical Medicine”), which has been shown to be a pastiche from a variety of different sources, not a direct translation of al-Majusi’s Arabic text.

In terms of the larger significance of Constantine’s translation project, two principal questions are pressing: how does it relate to work that went before him, and how was his work carried on after his death? There may have been other translators from Arabic in southern Italy either just before or contemporaneously with Constantine. There was also considerable translation activity going on from Greek into Latin, including the important work on urines and pulses by, respectively, Theophilus and Philaretus. The interactions between Muslims and Greek Christians on Sicily have not yet been sufficiently examined, nor the role of the latter in serving as linguistic and cultural intermediaries between the Muslim world and the Latin-speaking Christians of mainland southern Italy.

Constantine had two pupils, both of them also monks at Monte Cassino: Johannes Afflacius (sometimes called Johannes Saracenus) and a former chaplain to the empress Agnes named Azo (or Adzo). Johannes was the dedicatee of five of Constantine’s translations, including the Viaticum itself. He also wrote his own original medical work, the Liber aureus (“Golden Book”), and may have retranslated Ibn al-Jazzar’s treatise on lovesickness. This was apparently the same Johannes who, together with a certain “Pisan rustic,” completed Constantine’s Surgery in 1113–1114. Johannes is perhaps the most likely individual to have also completed the second half of Constantine’s Pantegni, which makes use of the Liber aureus. As for Adzo, he was the dedicatee of Constantine’s translation of *Galen’s commentary on the Hippocratic Aphorisms and reportedly polished Constantine’s rough Latin prose.

Influence

As the first major translator of Arabic medical texts into Latin, Constantine was by necessity an innovator in creating new medical and pharmaceutical terminology. He displays a fondness for the use of pseudo-classical terminology (like “Pantegni”) though he also introduced many Arabic terms into Latin (like nucha for the spinal cord). Likewise, Constantine introduced from his Arabic sources new philosophical and nosological concepts, such as lovesickness (amor hereos), as formal disease categories.

No doubt due to Monte Cassino’s central position within the Benedictine order, Constantine’s works enjoyed rapid dissemination throughout western Europe. His works are documented beyond the Alps as early as the 1130s (in England even earlier). *William of Conches eagerly exploited the theoretical volume of the Pantegni and we can see Constantine’s influence in other twelfth-century writers such as *Hildegard of Bingen.

Constantine’s influence on the physicians of the “school” of *Salerno was perhaps not as immediate as would be expected given Constantine’s direct ties with the city (he had arrived there when he first came to Italy). If Constantine is indeed to be credited with the translation of Hunayn ibn Ishaq’s Isagoge, then his most immediate impact was in providing this foundational text of the Salernitan medical curriculum. The early Salernitan writer Copho makes little direct use of the Constantinian corpus; his employment of Arabic terminology and materia medica (like sugar or the compound remedy, trifera saracenica) may well be due to influences coming directly from Muslim practitioners in Sicily or their Greek-speaking intermediaries. By the time of Johannes Platearius in the mid-century, however, the influence of the Viaticum is apparent, and Constantine’s works on diets and urines would become increasingly influential as the century progressed.

Constantine’s works probably had their most powerful impact in the thirteenth century, when they were heavily exploited by the great mendicant encyclopedists, especially *Bartholomaeus Anglicus and *Thomas of Cantimpré. Also during this period, the Viaticum was subjected to several commentaries; aside from the Isagoge, it was probably the most widely circulated of all of Constantine’s works. After the middle of the thirteenth century, however, the new Arabic medicine coming out of Spain (particularly Avicenna’s massive Canon) began to eclipse the Constantinian corpus.

Only a few vernacular translations of Constantine’s works are known: his treatise on intercourse was translated into English in the mid-fifteenth century, that on melancholy into French. Constantine is cited in such literary works as the Romance of the Rose and *Geoffrey Chaucer’s The Canterbury Tales; in the latter, he appears both as a respected medical authority known well by the Doctor of Physick and, in the Merchant’s Tale, as a “cursed monk” who wrote on coitus.

Constantine’s works appeared in print principally in two different Renaissance editions: a collection of works attributed to Isaac Judaeus (only some of the works are in fact Isaac’s), and an Opera omnia that appeared in two volumes at Basel in 1536–1539. There are few translations into modern languages besides Italian.

See also Medicine, practical; Medicine, theoretical

Bibliography

Ammar, Sleim. Ibn Al Jazzar et l’Ecole médicale de Kairouan. Ben Arous: Presses d’Imprimerie Principale, 1994.

Burnett, Charles, and Danielle Jacquart, eds. Constantine the African and ‘Ali ibn al-Abbas al-Magusi: The ‘Pantegni’ and Related Texts. Studies in Ancient Medicine 10. Leiden: E.J. Brill, 1994.

Constantinus Africanus. Omnia opera Ysaac. Lyons: Bartholomeus Trot, 1515.

———. Opera. 2 vols. Basel: Henricus Petrus, 1536–1539.

Matheson, Lister M. Constantinus Africanus: Liber de coitu (Liber creatoris). In Sex, Aging, and Death in a Medieval Medical Compendium: TCC R.14.52, Its Language, Scribe and Text, ed. M. Teresa Tavormina. Tempe: Arizona State University, 2005.

Martín Ferreira, Ana Isabel, ed. Tratado médico de Constantino el Africano: Constantini Liber de elephancia. Valladolid: Universidad de Valladolid, 1996.

Sezgin, Fuat, ed. Constantinus Africanus (11th cent.) and His Arabic sources: Texts and Studies. Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1996.

Veit, Raphaela. Quellenkundliches zu Leben und Werk von Constantinus Africanus. Deutsches Archiv für Erforschung des Mittelalters 59 (2003), 121–152.

MONICA H. GREEN

Cosmology

Although there was no Latin term for “cosmology” in the Middle Ages, scientific cosmology in that period was a fundamental part of natural philosophy, not of astronomy. The understanding of cosmic structure and operations was overwhelmingly derived from the natural philosophy of Aristotle, whose relevant treatises in natural philosophy were translated from Greek and Arabic during the twelfth and thirteenth centuries and became the basic subject of study in the arts curriculum of medieval universities, especially at Paris and Oxford.

Most of Aristotle’s ideas about the cosmos were acceptable to Christians, but his firm conviction that the world is eternal—without beginning or end—was not. In effect, Aristotle rejected the idea that the world was created, and his views implied not only a denial of the divine creation of our world in six days, as described in Genesis, but also a denial of the basic Christian belief in the eventual destruction of the world (John 1.2–3 and 17.5). Although Christians were obligated by faith to accept these basic tenets, many of them also accepted *St. Thomas Aquinas’s argument that it is logically possible that God could have created an eternally existent world—that is, a world without a temporal beginning. But few believed that He had done so.

The account of creation in Genesis posed serious problems for Aristotle’s followers. They had somehow to reconcile statements in Genesis with Aristotle’s secular cosmos. What, for example, was the firmament, which God called heaven, created on the second day? And what were the waters it divided above and below? How did the firmament, or heaven, created on the second day differ from the heaven created on the first day? How does the light created on the first day differ from the light created on the fourth day? Most of the answers to these questions did not do violence to Aristotle’s cosmology and physics.

The cosmic sphere of the universe extends from the center of our spherical Earth, which coincides with the geometric center of the universe, to the sphere of the fixed stars and beyond. *Campanus de Novara estimated the distance from the Earth’s center to the sphere of the fixed stars as approximately seventy-three million miles. Although minuscule by modern estimates, those who contemplated it during the Middle Ages regarded the universe as a gigantic sphere that is everywhere filled with matter, thereby leaving no void spaces. Beyond the convex surface of the outermost sphere of the universe nothing whatever exists: no body, no void, no place, no time. Aristotle convinced his medieval followers that the universe is divided into two radically different parts: one celestial, the other terrestrial. The world as a whole was linked by a hierarchical ladder of perfection ranging from the least perfect Earth at the center of the world to the most perfect and noble parts at the outermost reaches of the cosmos. Perfection was measured by the degree of change that substances undergo. The greatest amount of change occurs in the Earth at the center of the world, and gradually diminishes as the distance from Earth increases. The dividing line between the terrestrial and celestial regions was assumed to be the concave surface of the lunar sphere. At that surface, change and corruptibility end, and change-lessness and incorruptibility begin for the celestial region. That part of the cosmos—from the Moon to the sphere of the fixed stars and beyond—was regarded as the noblest and most perfect part of the world, as evidenced by its incorruptibility. Change of place is the only change that can occur in the celestial region as the planets and stars are carried around the heavens.

The Terrestrial and Celestial Regions

Below the concave surface of the lunar sphere, and descending all the way to the center of the Earth, is the terrestrial part of the world. In stark contrast to the celestial region, all material bodies in this part of the world continually undergo four kinds of change—change of substance, change of quality, change of quantity, and change of place. These changes are the result of the interaction of four basic elements out of which all terrestrial bodies—animate and inanimate—are compounded, namely earth, water, air, and fire. The terrestrial region is divided into four concentric spheres, each of which is the natural place of one of the elements. The innermost sphere is the natural place of earth; the next is the natural place of water; the third is the natural place of air; and the outermost concentric sphere is the natural place of fire. If unimpeded, each element would move innately toward its natural place, and the terrestrial region would become a series of four static elemental spheres. But this will never occur because the elements are always embedded in compound bodies that are continually changing. They are corrupted as their elements depart and re-associate with other elements to generate new compounds, a never-ending process. The radical distinction between the celestial and terrestrial regions, based on whether change did or did not occur, is nowhere better illustrated than in the location of comets, shooting stars, and other occasional “celestial” phenomena, which were all located in the natural place of fire, that is, in the uppermost reaches of the terrestrial region, just below the Moon. As changeable phenomena, they had to be excluded from the heavens and placed in the upper reaches of the terrestrial region.

The incorruptible ether that filled the celestial region was subdivided into a series of concentric spheres. For astronomical purposes, astronomers, and even Aristotle, assigned numerous orbs to account for the motion of each planet and the fixed stars. Aristotle assigned anywhere from forty-nine to fifty-five orbs, and *Ptolemy assigned as many as forty-one. But natural philosophers, who were the cosmologists of their day, viewed the cosmos in simpler terms. They assigned to each planet a single orb. Since there were seven planets (in ascending order: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn), there were seven orbs arranged concentrically—that is, one orb within another, all with the center of the Earth as their common center. The fixed stars were usually assigned three distinct orbs, one for the daily motion, another for the precession of the equinoxes, and one for trepidation, a motion that was imagined to exist, but did not. The creation account in Genesis played a role. The fixed stars were assigned to the eighth orb, which not only carried the stars around in their daily motion, but was also frequently identified with the biblical firmament. Apart from its astronomical function, the starless ninth sphere was usually regarded as the biblical waters above the firmament. The ninth sphere was often called the crystalline orb, because its waters were regarded as solid, like ice. The tenth orb, also starless, simply performed its astronomical function. Finally, surrounding them all is the Empyrean heaven, which, unlike all other orbs, was assumed to be immobile. The Empyrean had no astronomical function, but was a purely theological construct that was regarded as “the dwelling place of God and the elect.” All told, natural philosophers assumed the existence of eleven concentric celestial orbs.

Although planets, stars, and orbs were made of the same celestial ether, the planets lay immobile in their respective spheres, which carried them around the heavens. Prior to the fourteenth century, the celestial ether was regarded as fluid, as were the celestial orbs, which were somehow imagined to retain their spherical shapes. This interpretation changed in the fourteenth century, when numerous natural philosophers came to assume that the planetary orbs were hard, shell-like objects arranged concentrically from the lunar sphere to the outermost sphere of the world. This became the predominant opinion until Tycho Brahe’s astronomical researches, near the end of the sixteenth century, made the fluid theory the more plausible option.

The cause of the uniform circular motions of the celestial orbs was attributed primarily to external intelligences, and occasionally to internal forces. Following Aristotle, each celestial orb was assumed to have an immaterial, spiritual intelligence associated with it, but yet distinct from it. An intelligence functioned as an “unmoved mover” because it had the power to move its orb without itself being in motion. It did so, as Aristotle explained, by being loved by its celestial orb, a relationship that was not further explained. Immaterial intelligences were often equated with angels. Some natural philosophers, however, chose a different path from Aristotle, and held that at the creation God impressed an immaterial internal force into every celestial orb, providing the power for its incessant motion through a celestial ether that offered no resistance.

Celestial orbs were nested one within another as they moved around the sky, but whether they moved in the same direction or opposition directions, their touching surfaces produced no friction. Throughout the Middle Ages it was assumed that the nobler and incorruptible celestial bodies exerted a dominant and controlling influence over the corruptible and ever-changing material bodies in the terrestrial, or sub-lunar, region. These effects were exerted in three basic ways: (1) by the celestial motions; (2) by light from the Sun; and (3) by invisible influences that could penetrate where light could not (for example, into the bowels of the Earth where celestial influences were thought to cause the generation of metals). The overwhelming dominance of the celestial region over the terrestrial was the ultimate basis for belief in astrology.

It was generally believed that God had not created a perfect world, but one that was as perfect as it needed to be. Because God was assumed to have absolute power to do anything He pleased short of a logical contradiction, it was always assumed that, if He wished, God could create better and better worlds, or as many other worlds as He pleased.

Does Anything Exist Beyond Our World?

Although Aristotle had argued that it was impossible for anything to exist beyond our finite world, his medieval followers insisted that God, by His absolute power, could create anything beyond our world that He wished, including other worlds. In 1277, the bishop of Paris condemned 219 propositions among which were assertions that God could not create other worlds and that He could not move our whole spherical universe with a rectilinear motion, because the departure of the world from its place would leave a vacuum. Although Aristotle regarded both the existence of other worlds beyond ours, and the existence of extracosmic void spaces, as impossibilities, his medieval Christian followers were convinced that God, by His omnipotence, could create both. Thus where Aristotle regarded such extracosmic phenomena as impossible and absurd, medieval natural philosophers regarded them as possible by supernatural action, although virtually no one believed that God had actually done so, or would do so. University scholars began to imagine numerous scenarios in which they showed that if other worlds existed, they would be compatible with each other. The most popular hypothetical situation was one in which a multiplicity of identical, self-contained worlds existed each with its own center and circumference. The multiplicity of centers and circumferences violated Aristotle’s conviction that only one center and circumference could exist, because only one world is possible. Scholastics also imagined that God annihilated matter within our world, thus creating a vacuum. They then argued—contrary to Aristotle—that successive, finite motions of material bodies would be possible in such a vacuum.

The most dramatic departure from Aristotle, however, was the assumption by some theologian-natural philosophers that an infinite, dimensionless, void space lay beyond our world. This was partly based on a strong intuitive sense that something must exist beyond our world. But it was on theological grounds that *Thomas Bradwardine (c. 1290–1349) identified God’s infinite, omnipresent immensity with a dimensionless, infinite void space. Because God is an unextended being, it was deemed essential that the infinite void He “occupied” also be regarded as extensionless. Except for extension, scholastic theologians conferred much the same properties on infinite space as did the major scientists of the Scientific Revolution, most notably Sir Isaac Newton. Nevertheless, the contributions of Copernicus, Tycho Brahe, Galileo, and Newton in the sixteenth and seventeenth centuries produced a radically different cosmos that wholly replaced its medieval predecessor.

See also Astrology; Astronomy; Nature: diverse medieval interpretations; Nature: the structure of the physical world; Scholasticism

Bibliography

Grant, Edward, ed. A Source Book in Medieval Science. Cambridge: Harvard University Press, 1974, pp. 494–568.

———. Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Seventeenth Century. New York: Cambridge University Press, 1981.

———. Planets, Stars, and Orbs: The Medieval Cosmos 1200–1687. New York: Cambridge University Press, 1994.

McCluskey, Stephen C. Astronomies and Cultures in Early Medieval Europe. New York: Cambridge University Press, 1998.

North, John. “Medieval Concepts of Celestial Influence: A Survey.” In Patrick Curry, ed. Astrology, Science and Society, Historical Essays. Woodbridge: Boydell, 1987, pp. 5–17.

Sacrobosco, John of. The “Sphere” of Sacrobosco and Its Commentators. Ed. and tr. Lynn Thorndike. Chicago: University of Chicago Press, 1949.

Steneck, Nicholas H. Science and Creation in the Middle Ages: Henry of Langenstein (d. 1397) on Genesis. Notre Dame: University of Notre Dame Press, 1976.

EDWARD GRANT