Senator Flavius Magnus Aurelius Cassiodorus (c. 485–c. 585) was born into a leading family of southern Italy87 and rose through the civil service to succeed Boethius in 525 as Master of the King’s Offices under the Ostrogoth King Theodoric and his successor, Athalaric (d. 534). While honing his skill in writing official papers and correspondence in formal, diplomatic Latin for these offices, Cassiodorus gradually turned his attention to religion and scholarship. In 554, before falling victim to the religious and political intrigue that brought down Boethius, Cassiodorus retired to his estate in southern Italy and founded two monasteries: one, an austere hermitage; the other, located on his estate and called Vivarium, in which monks devoted their time to copying, and thus preserving, manuscripts. In this way Cassiodorus inaugurated the tradition of literary monasticism, a Christian application of the Aristotelian idea, invoked by Augustine, that liberal education presupposes “leisure which is the privilege of old age or some fortunate circumstances.”88
Cassiodorus’s most important writing during retirement was entitled Introduction to Divine and Human Letters, which comprises two books. The first is devoted to the study of Christian writings, including those by the Church Fathers, in which Cassiodorus, while quoting Augustine’s On Christian Learning, endorses the belief expressed by Ambrose and Augustine that pagan learning and, particularly, the liberal arts had Egyptian, Hebraic, and thus Christian origins.89 The second book is presented as an extended footnote, summarizing the content and most important sources of the seven liberal arts and discussing their importance for an informed interpretation of sacred literature. Apparently intended as an encyclopedic primer and bibliographical guide for monks who lacked the elements of a classical education, this second book served as one of the most widely used textbooks of the liberal arts in schools throughout Western Europe during the middle ages.
Selection #10 from the second volume of Divine and Human Letters provides material from the Christianized account of the liberal arts that Cassiodorus compiled largely from the works of Boethius, Martianus Capella, and a few other secondary sources that were still available to him, even as the turmoil in Western Europe made these sources increasingly inaccessible. In subsequent centuries this second volume of Cassiodorus’s work became a prominent Christian source from which students in monastic, parish, and cathedral schools drew their understanding of the liberal arts. Divine and Human Letters thus became a textbook, whose distribution of material among the seven liberal arts in the standard Latin edition is: grammar, 4 pages; rhetoric, 12 pages; dialectic, 22 pages; arithmetic, 11 pages; music, 9 pages; geometry, 3 pages; and astronomy, 5 pages.90
Cassiodorus himself long enjoyed “leisure which is the privilege of old age or some fortunate circumstances,” and died at the age of nearly 100 on his estate.
[1] The preceding book, completed with the aid of the Lord, contains, as you have seen, the principles of instruction for divine readings. It is comprised of thirty-three chapters, a number acknowledged to correspond with the age of the Lord when he offered eternal life to a world laid low by sin and granted rewards without end to those who believed. It is now the time for us to present in seven additional chapters the text of the second book, on secular readings; this number, continuously repeated throughout the weeks as they succeed one another, is ever being extended to the very end of the world.
[2] One surely ought to know that the Sacred Scripture frequently expresses by means of this number whatever it desires to be understood as continuous and perpetual, as David, for example, says, “Seven times a day I have given praise to thee,” [Psalms 119: 164] though he elsewhere vows, “I will bless the Lord at all times; his praise shall be always in my mouth,” [Psalms 34: 1] and Solomon says, “Wisdom hath built herself a house, she hath hewn her out of seven pillars.” [Proverbs 9: 1] In Exodus as well the Lord said to Moses, “Thou shalt make seven lamps, and shalt set them to give light over against it.” [Exodus 25: 37] Revelation constantly mentions this number in various applications. And this number leads us to that eternity which can have no end; with justice, then, is it always used whenever perpetuity is indicated.
[3] Thus, the science of arithmetic is endowed with great praise, since God the Creator has arranged his dispensations by the use of number, weight, and measure; as Solomon says, “Thou hast ordered all things in measure, and number, and weight.” [Wisdom of Solomon 11: 21] Thus God’s creation is known to have been ordered in number, since our Lord says in the Gospel, “But the very hairs of your head are numbered.” [Matthew 10: 30] And likewise God’s creation has been ordered in measure, as our Lord bears witness in the Gospel: “and which of you by taking thought can add to his stature by one cubit?” [Matthew 6: 27] And likewise the prophet Isaiah says, “Who doth measure heaven with the span and hold the earth confined in his hand?” [Isaiah 40: 12] Again, God’s creation is acknowledged to have been ordered in weight, as it is written in the Proverbs of Solomon, “And he poised the fountains of waters,” and a little farther on, “When he balanced the foundations of the earth, I was with him.” [Proverbs 8: 28, 29–30] For this reason God’s extraordinary and magnificent works are necessarily confined to definite limits, so that just as we know that he has created all things we may in some measure learn to know the manner of their creation. And hence it is to be understood that the evil works of the devil are not ordered by weight or measure or number, since, whatever iniquity does, it is always opposed to justice, as the thirteenth psalm declares, saying, “Contrition and unhappiness in their ways: and the way of peace they have not known.”92 Isaiah also says, “They have abandoned the Lord of hosts and have walked along crooked paths.” [Isaiah 59: 8] God is really wonderful and extremely wise in having distinguished every one of his creatures by a unique dispensation lest unseemly confusion take hold of some of them; Father Augustine has discussed this topic in most minute manner in the fourth book of his work On Genesis Considered Word for Word.
[4] Let us now enter upon the beginning of the second volume, and let us attend with some care, for it is crowded with etymologies and full of a discussion of definitions. In this book we must speak first of the art of grammar, which is manifestly the source and foundation of liberal letters. The word “book” (liber) comes from the word “free” (líber);93 a book, in other words, is the bark of a tree, removed and freed—the bark on which the ancients used to write oracular responses before the invention of papyrus. In view of this, therefore, we are permitted to make short books or extended ones, since we are allowed to limit the size of books in accordance with their nature, just as the bark encloses both tiny shoots and vast trees. We ought, moreover, as [Marcus Terentius] Varro says, to understand that the elements of all arts came into existence because of some usefulness.
“Art” is so called because it limits (artet) and binds us with its rules; according to others this word is taken over from the Greek expression apo tés aretés, which means “from excellence,” the term applied by well-spoken men to skill in every manner. Second, we must speak of the art of rhetoric, which is deemed very necessary and honorable because of the splendor and fullness of its eloquence, especially in civil questions. Third, we must speak of logic, which is called dialectic; according to the statements of secular teachers, this study separates the true from the false by means of very subtle and concise reasoning. Fourth, we must speak of mathematics, which embraces four sciences, [namely], arithmetic, geometry, music, and astronomy. In Latin we may call mathematics the theoretical study; though we might apply this term to all studies which teach one to speculate on abstract principles, nevertheless, by reason of its excellence this study has claimed the common word strictly for itself, just as when “the Poet” is mentioned, Homer is understood in Greek writers, and Vergil in Latin writers, and when one refers to “the Orator,” Demosthenes is indicated in Greek writers and Cicero in Latin writers, although many poets and orators are shown to have used both languages. Mathematics is the science which considers abstract quantity; abstract quantity is that which we separate from matter or from other accidents by our intellect and treat by reasoning alone.94
[5] By stating the contents of the entire book in advance I have, as it were, given bail to secure the performance of my promise. Let us now, with the Lord’s aid, give an account of the individual topics, as they have been promised, by means of their divisions and definitions, since learning is in a certain sense twofold in character, inasmuch as a clear description first carefully permeates the sense of sight and then, after having prepared the ears, penetrates the hearing. And, moreover, we shall not fail to reveal the authors, both Greek and Latin, whose explanations of the matters which we discuss have become famous, in order that those who desire to read zealously may more lucidly understand the words of the ancients after having first been introduced to them in abridged form.
[1] Grammar gets its name from the letters of the alphabet, as the derived character of the word itself shows.95 Sixteen of these letters are said to have been invented by Cadmus, who handed them down to the studious Greeks, who in turn supplied the rest by their liveliness of mind. On the positions and worth of the letters Helenus has written a subtle treatise in Greek and Priscian another in Latin.96 Grammar is skill in the art of cultivated speech—skill acquired from famous writers of poetry and of prose; its function is the creation of faultless prose and verse; its end is to please through skill in finished speech and blameless writing. But although such authors of earlier times as Palaemon, Phocas, Probus, and Censorinus have written on the art of grammar with variety of method and have been highly esteemed in their own day,97 nevertheless, for the good of all we intend to quote from Donatus, who is considered to be especially appropriate for boys and suitable for novices; we have left you his twofold treatise in order that a twofold explanation may make even clearer him who is already clear.98 We have also discovered that St. Augustine has written a short course of instruction on the same topic for the simple brothers; and we have left you this work to read, lest anything seem to be lacking to the inexperienced who are being made ready for high achievement in this great study.
[2] In the second part of his work Donatus discusses the following topics: the spoken word, the letter, the syllable, feet, accentuation, punctuation and proper phrasing, the eight parts of speech (for the second time), figures of speech, etymologies, and orthography. . . .
[3] Let these words, which concern brief definitions alone, suffice. But let him who desires wider and fuller knowledge of these matters read both preface and body of the codex which I have had written on the art of grammar, in order that the careful reader may find the facts which he knows are considered to belong to the subject.99 Let us now come to the divisions and definitions of the art of rhetoric; as its extensiveness and richness deserve, it has been amply treated by many illustrious writers.
[1] Rhetoric is said to be derived apo tou rhetoreuein, (“from speaking in public”) that is, from skill in making a set speech. The art of rhetoric, moreover, according to the teaching of professors of secular letters, is expertness in discourse on civil questions. The orator, then, is a good man skilled, as has just been said, in discoursing on civil questions.100 The function of an orator is speaking suitably in order to persuade; his purpose is to persuade, by speaking on civil questions, to the extent permitted by the nature of things and persons. Let us now, therefore, take up a few matters briefly in order that we may understand the main points of almost the entire art and the excellence of the art from a description of several of its parts. According to Fortunatianus, a modern writer on rhetoric, civil questions are questions “which can fall within the range of common understanding, that is, questions which everyone can comprehend, since they concern what is fair and good.”101
[2] Rhetoric has five parts: invention, arrangement, proper expression, memorization, delivery.102 Invention is the devising of arguments which are true or which resemble true arguments to make a case appear credible. Arrangement is the excellent distribution in regular order of the arguments devised. Proper expression is the adaptation of suitable words to the arguments. Memorization is a lasting comprehension by the mind of the arguments and the language. Delivery is the harmonious adjustment of voice and gesture in keeping with the dignity of the arguments and the language. . . .
[1] Writers of secular letters have meant to convey the idea that arithmetic is the first among the mathematical sciences, inasmuch as music and geometry and astronomy, which follow it, require it for explanation of their own potentialities. Music, for example, requires it because music deals, among other things, with the relationship between a simple number and its double; geometry, likewise requires it, because geometry deals with the triangle, the quadrangle, and the like; astronomy too requires it, because astronomy deals with the reckoning of the changing positions of the heavenly bodies; arithmetic, however, depends for its existence neither upon geometry nor upon astronomy. On that account arithmetic is recognized as being the origin and source of the others, and Pythagoras is known to have praised this science to such a degree as to state that all things were created by God on the basis of number and measure, saying that some things were fashioned in motion, and other things at rest, but that all things were fashioned in such a way that nothing had any substance beyond the substratum mentioned above; I believe that this explanation is correct, and I derive my belief in the origin of things, as many philosophers have done, from that prophetic statement which says that God ordered all things in measure, and number, and weight. [Wisdom of Solomon 11: 21]
[2] The present study, therefore, consists of separate quantity, which produces varieties of number that do not possess a common boundary. For 5 is not united to 10 by any common boundary; nor is 6 thus united to 4; nor 7 to 3. Our study is called arithmetic because it has numbers as its special province. Now a number is a quantity made up of units: for example, 3, 5, 10, 20, and so forth. The purpose of arithmetic is to teach us the nature of abstract number and its accidents; for example, evenness, oddness, and so forth. . . .103
[10] Most pleasant and useful, then, is the branch of learning which leads our understanding to heavenly things and soothes our ears with sweet harmony. Among Greek writers Alypius, Euclid, Ptolemy, and others have instructed us in it with excellent elementary treatises; among Latin writers Albinus, a man of distinction, has written a compendious work on this subject, which we recall having had in the library at Rome and having read carefully. If perchance this work has been destroyed by the barbarian assault, you still have Gaudentius; and if you read him punctiliously, he will open the entrance halls of this science to you. Apuleius of Madaura is also said to have written an elementary treatise on this subject in Latin.104 Father Augustine too has written a work in six books entitled On Music, in which he has pointed out that the human voice can by reason of its nature utter rhythmical sounds and melodious harmony in long and short syllables.105 Censorinus too has discussed accents, which are most necessary to our voice, in subtle fashion, and he states that they have to do with musical science; I have left you a copy of his work among others. . . .
[1] Geometry is rendered into Latin as the measuring of the earth, because, according to some, Egypt was at first divided among its own lords by means of the various forms of this science; and those who taught it used to be called measurers. But Varro, the greatest of Latin writers in practical knowledge, explains the origin of the name as follows: at first, when the existing boundaries were unsettled and conflicting, measuring of the earth brought the people the benefits of tranquility; thereafter, the circle of the entire year was divided by the number of the months and consequently the months themselves, so called because they measure the year, were established. But after these things were discovered, learned men, incited to learn about intangible objects, began to seek the distance between the moon and the earth, and between the sun itself and the moon, and the distance to the very top of the sky; he relates that the most skillful geometers arrived at these facts. He then gives an excellent account of the measuring of the entire earth; and it was for this reason that this science happened to be called geometry, a name which it has guarded for many generations. And consequently Censorinus has carefully described the size of the circumferences of heaven and earth in stades in the book which he has written and dedicated to Quintus Cerellius; and if anyone desires to examine this book, he will not read long before learning many secrets of the philosophers.106
[2] Geometry is the science of immovable magnitude and of figures. Geometry has the following divisions: plane figures, numerable magnitude, rational and irrational magnitude, and solid figures. Plane figures are those which possess length and breadth. A numerable magnitude is one which can be [expressed in numbers.] Rational and irrational magnitudes are, respectively, commensurable and incommensurable. Solid figures are those which possess length, breadth, and thickness.
[3] The science of geometry is treated in its entirety in these parts and divisions, and the multiplicity of the figures which exists in earthly and heavenly objects is comprehended in the above description. Among the Greeks Euclid, Apollonius, Archimedes,107 and other excellent writers have been conspicuous for their books on this science; the work of one of these men, Euclid, has been translated into Latin by the previously mentioned Boethius, a man of distinction. If this work be read carefully, the matter which has been set forth in the divisions mentioned above will be distinctly and clearly understood. . . .
[1] Astronomy, accordingly, is rendered into Latin as “the law of the stars” (the literal meaning of the word108), inasmuch as the stars can neither remain fixed nor move in any way other than that in which they have been arranged by their Creator; except perchance when they are changed at the will of the Divinity on the occasion of some miracle, as Joshua is said to have obtained his request that the sun stand still upon Gibeon [Joshua 10: 12], and as a star announcing to the world the coming of the Lord for its salvation is said to have been shown to the three wise men [Matthew 2: 2]; and in the passion of the Lord Christ as well the sun was darkened for three hours [Luke 23: 44]; and so forth. These events are called miracles because they concern unexpected matters that deserve wonder. For, according to the astronomers the stars which are fixed in the sky are supported without motion; the planets, however, that is, “the wanderers,” do move, though the boundaries of the courses which they traverse are fixed.
[2] Astronomy, then, as has already been stated, is the science which surveys the movements of heavenly bodies and all their forms and investigates the accustomed state of the stars in relation to themselves and to the earth.
Isidore of Seville (c. 560–636) was orphaned soon after his birth and educated in a monastery in Seville, Spain. In about 600 his brother, the bishop of Seville, died, and Isidore was elected to succeed him. During the subsequent decades, Isidore played a significant role in several national councils held by the Spanish Church, and led the most important one, convened at Toledo in 633, which declared toleration of the Jews and the union of church and state. While serving as an ecclesiastical leader, Isidore read and wrote prolifically and contributed to scholarship largely by compiling and transmitting the residue of classical learning that was preserved in his extensive library at Seville. His writings include manuals on Christian worship and morals, treatises on natural science and cosmology, a chronicle of the Goths, Vandals, and Sueves, to whom he proselytized, and a history of the world from the time of creation. He died in Seville in 636.
Selection #11 is drawn from his best known work, a 20-volume encyclopedia covering all branches of knowledge and employing a method of explaining his topics by accounting for their origins or etymology. This widely used and cited work survives in about one thousand manuscripts in libraries across Europe. Although many of Isidore’s etymologies are fanciful and much of his encyclopedia is uncritical borrowing, chiefly from Augustine and Cassiodorus, he became the author most read during the next five centuries; and the first three books of his encyclopedia, describing the seven liberal arts, became the most frequently cited of his writings.109 In these three books the distribution of text devoted to the separate, liberal arts in the standard Latin edition is: 62 pages to grammar in Book I, 42 pages to rhetoric and dialectic in Book II, and 37 pages to the four mathematical disciplines in Book III.110 These three books have not yet been entirely translated into English, and the following translation of his descriptions of each of the seven arts is published here for the first time.
1. On Discipline [or Science] and Art. The word disciplina [discipline] comes from Latin, discere (learning). A discipline can also be called a “science,” because scire [to know] gets its name from discere, since none of us is a knower unless he is a learner. The other half of disciplina gets its name from plena (full), because what is learned is something complete or total. The word ars gets its name on the grounds of consisting of the precepts and rules of “art,” of course. Others say this word was derived by the Greeks from areté (virtue, excellence), which they have termed a science.
Plato and Aristotle have proposed the following difference between “art” and “discipline,” saying that art resides in those things which are capable of being otherwise than as they are; but discipline is assuredly what addresses those things which cannot turn out otherwise than as they are. Thus, whenever something is the subject of disquisitions that are true, there will prove to be discipline; but whenever something verisimilar and subject to opinion is what is being treated, the term “art” will apply.
2. On the Seven Liberal Disciplines. The disciplines of the liberal arts are seven in number. The first is grammar; that is, competence in speaking. The second is rhetoric which is reckoned as necessary most of all in those inquiries proper to citizens, due to the glamour of extemporaneous eloquence. Third is dialectic (or “logic” by another name), which separates the true from the false by reasonings of the greatest subtlety. Fourth is arithmetic, which contains the causes and divisions of numbers. Fifth is music, which consists in songs and chants. Sixth is geometry, which embraces the measurements and dimensions of the earth. Seventh is astronomy, which contains the law of the stars. . . .112
4. On the Latin letters. The Italian maiden Carmentis first devised the Latin letters. She was called Carmentis because she sang songs [carmina] of things to come. By others [the Greeks] she was called Nicostrata.113 The term “letters,” in fact, may be used in a common or a liberal sense. Letters are common in the sense that many people use them commonly to write and read. They are liberal in the sense that those know them who compose books and know the principle of speaking and writing correctly. . . .
5. On Grammar. Grammar is the science of speaking correctly, and is both source and foundation of liberal letters.114 Among the disciplines this one was discovered right after the alphabet, in order that those who had learned to spell might straightway learn by it the technique of speaking correctly. . . . The divisions within grammatical art are counted by some up to thirty; that is, the eight parts of speech, plus: articulate voice, letter, syllable, metric feet, accents, word location, punctuation, orthography, analogy, etymology, glosses, difference, barbarisms, solecisms, mistakes, metaplasms, outlines, tropes, prose, meters, stories and histories. . . .115
1. On Rhetoric and its Name. Rhetoric is the science of speaking well in those inquiries proper to citizens, with the purpose of convincing people of just and good causes. Rhetoric is so called after the Greek work, rhetorizein, that is, from “abundance of speech.” Rhesis is the word for “expression” in Greek, rhetor is the word for “orator.” Rhetoric, moreover, is joined to the art of grammar. For it is in Grammar that we learn the science of speaking correctly; after all, it is in Rhetoric that we learn how to enunciate the things that we have learned.
2. On the Discoverers of the Art of Rhetoric. . . .
3. On the Word, Orator, and the Parts of Rhetoric. So the orator is a good man, skilled at speaking.116 A man becomes good through nature, character and arts. A man becomes skilled at speaking through technical eloquence which consists of five parts: intention, arrangement, style, memory, and delivery;117 and includes the purpose of the function which is to bring about persuasion. Skill at speaking, moreover, in itself consists in three parts: nature, doctrine, practice. Nature is in talent; doctrine, in science; practice, in assiduity. For these are technical expectations not only of an orator, but of each and every human being for him to accomplish anything. . . .
22. On Dialectic. Dialectic is the discipline ordered towards explicating the causes of things. It is a part of that philosophy which is called Logic; that is, the reasoning part capable of defining, inquiring and explicating.118 For it teaches how truth and falsity are distinguished by distribution in many kinds of inquiries. Certain of the first philosophers applied it in their discussions; but they did not constitute it as an art to be acquired by practice. After them, Aristotle brought the argumentation characteristic of this doctrine within the scope of certain rules, and he named it Dialectic because, within its discussion is conducted concerning utterances as such. For an utterance is called lekton. So dialectic comes next after Rhetoric as a discipline, because in many instances both turn out to be involved in common.
23. On the Difference between the Art of Dialectic and that of Rhetoric. Varro, in Book 9 of his work on the disciplines, defined Dialectic and Rhetoric by means of the following likeness: “Dialectic and Rhetoric are like a man’s hand being a formed fist and then a spread-out palm: the former contracting words; the latter distending.”119 Dialectic is certainly sharper when the task is to explicate matters. Rhetoric is more inventive when the task is teaching those things which it strives for. The former comes to schools on occasion; the latter is perpetually on its way into the forum. The former requires students of rare application; the latter frequently requires actual populations. Philosophers, moreover, before they get to the exposition of the Introduction120 are wont to provide a definition of philosophy, in order to demonstrate more easily the properties that pertain to it.
24. On the Definition of Philosophy. Philosophy is the understanding of matters both human and divine joined to the study of the good life. It clearly consists of two things, science and opinion. There is science when something is perceived with a reasoning that is certain; but there is opinion when the thing still lurks in uncertainty and it isn’t seen with any firm reasoning—as, for example whether the sun is just as large as it seems, or is larger than the whole earth; and likewise whether the moon is spherical, or concave; and whether the stars stick to the sky, or are carried through the air on a free course; and how large the heavens themselves are and what matter they are made of; whether they are quiet and immobile, or revolve with incredible speed; how thick is the earth, or on what foundations does it stay balanced and suspended. The very name “philosophy,” moreover, means “love of wisdom” translated into Latin. For the Greeks call “love” philo and “wisdom” sophia. The appearance of philosophy is tripartite: the first is “natural” which is named “Physics” in Greek, treating of inquiry into nature. The second is “moral” which is called “Ethics” in Greek, dealing with character. The third is “Rational,” which is named by the Greek term “logic,” disputing of the way truth itself is sought in the causes of things or in character as it is relevant to life. So physics is concerned with inquiry into cause; Ethics, with the order of living; Logic, with the reason for understanding.121 . . .
I can assure you that it is within these three classifications of philosophy that those speeches which are divine take their shape. For they are wont to have as their subject either nature, as in Genesis and Ecclesiastes; or morality, as in Proverbs and scattered through all the other books; or logic, on behalf of which our people claim theoretical philosophy for themselves, as in the Song of Songs and in the Gospels. Similarly, other learned men have defined philosophy in its name and parts as follows . . .
Mathematics is said in Latin to be the doctrinal science which considers abstract quantity.122 That quantity is abstract which separates it from matter or from other accidental properties like equal and unequal or from others of this sort, within our thinking alone. It has four kinds: Arithmetic, Music, Geometry and Astronomy. Arithmetic is the discipline ordered to countable quantity in itself. Music is the discipline which speaks of those numbers which are found in sounds. Geometry is the discipline ordered to size and shapes. Astronomy is the discipline which contemplates the orbits and figure of heavenly bodies as a whole, and the habits of the stars. We proceed to point out these disciplines at somewhat greater length so that their causes may be shown adequately.
1. On the Name of the Discipline of Arithmetic. Arithmetic is the discipline ordered to numbers. For the Greeks call number arithmus. And the authors of secular literature have wished that it be first among the mathematical disciplines for the reason that it needs no other discipline in order to exist. Music, Geometry and Astronomy, however, which come next, need the aid of it, in order to be and subsist. . . .
10. On the Discoverers of Geometry and Its Name. The discipline of geometry is said first to have been come upon by Egyptians because, upon the overflowing of the Nile and the covering of all possessions by mud, the beginning was made in dividing the earth by lines and measures, and a name was given to that art. And that art proceeded next to the point where people measure the spaces of sea, heavens and sky, thanks to the acuity of wise men. For driven as they were by zeal, they began to seek the spaces of the heavens, after measuring the earth: at how great a distance is the moon from the earth? The sun from the moon? And by how great a measurement is it to the top of the heavens? And thus they distinguished the very spaces of the heavens and the circumference of the orb down to a number of stades which had some probability. But because this discipline began with the measuring out of earth, it has retained the name from its origin; thus, geometry has been named from “earth” and from “measure.” For “earth” is called ge in Greek, and “measure” is metron. The art of this discipline contains within itself lines, intervals, magnitudes and figures; and within figures it contains dimensions and numbers.
15. On Music and Its Name.123 Music is the skill consisting of modulating in sound and in song. . . . So no discipline can be complete without music, since nothing can be, without it. For the very world itself is said to have been composed by a certain harmony, and the very heavens are said to revolve at the modulating effected by harmony. . . .
24. On the Name Astronomy. Astronomy is the law of stars which pervades the courses of heavenly bodies and the shapes and regularities of stars [moving] around one another and around the earth, obeying a rationale which cannot be discerned. . . .
27. On the Differences between Astronomy and Astrology.124 There is, however, some difference between astronomy and astrology. For astronomy contains the rotation of the heavens, and the risings, settings and movements of heavenly bodies and the reasons why this terminology is as it is. Astrology is actually partly natural and partly superstitious. It is natural as long as it is following out the courses of the sun and moon, or the definite stopping-points in time of the stars. But it is actually superstitious in that part done by the so-called “mathematicals,” who do augury on the basis of stars and even correlate the twelve constellations of the heavens with individual organs of the soul or body, and attempt to predict the births and characters of human beings by the course of heavenly bodies.