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ʿAbd al-Wājid, 149, 258n77
Abioso, Giovanni Battista (Giambattista), 92, 236n41, 241n99
Abū Isḥāq Ibrāhīm al-Zarqālī, 131
Aegidius Romanus, and three-part orbs, 52
Afghānī, Sayyid Jamāl al-Dīn, 258n78
Aiton, E.J., 158, 182
Akhawayn, Muḥyī al-Dīn, 258n77
Albategnius (al-Battānī), 90, 92, 102, 108, 131; mentioned by Brudzewo, 46, 77; Opus Astronomicum, 4
Albert of Saxony: one of moderni 59; questions on De Caelo et Mundo, 54; questions on Posterior Analytics, 67–8
Alberti, Leon Battista, 10, 110–11, 131, 133, 135–7; on beauty, 113, 116–17; De pictura, 112–17, 120–1; 140; and Protagoras, 120; use of a veil, 116
Albertus Magnus, 52, 59, 229n84; Metaphysics, used by Brudzewo, 75, 231–2n119; need for phantasmata in mathematics, 68; and three-part orbs, 52
Aldebaran, occultation, 241n100
Alexander the Great, 37
Alexandria, 38
Alfonsine Tables, 101, 106, 131, 182, 212, 272n2, 278–9n67
Alfonso (king of Aragon and Naples), 34–6, 241n99
Alfonso de Valladolid. See Avner de Burgos
Alfonso X (the Wise) of Castile, 189, 212, 269n86; and corpus of translations from Arabic, 76
Alfraganus (Muḥammad ibn Kathīr al-Farghānī), 93, 151–2, 157, 234n19, 257n67; course on, 132; Latin translation of, 151; lectured on in Padua, 132, 256n63; mentioned by Brudzewo, 46, 77
Almagest, 4, 6, 9, 79–83, 145, 147, 151, 154, 163, 170, 200, 255n51, 255n55, 256n60, 261n108, 272n2, 273n10, 274n17, 279n82, 280n93; asymmetry of second planetary anomaly, 92, 103; book 1, 93; book 12, 103, 238; controversy about, 87; criticisms of, 84–5, 108; lunar model, 84; manuscripts of, 88, 91, 237; planetary anomalies, 102; Regiomontanus’s mastery of, 87; translations of, 88, 94. See also Bessarion; Bianchini; Epitome of the Almagest; George of Trebizond; Ptolemy; Regiomontanus
Almagestum parvum, 89–90
Alpharabius (Abū Naṣr al-Fārābī), Enumeration of the Sciences, 256n57
Amico, Giovanni Battista, 206–7, 208 (fig. 8.5), 209, 277n46, 277n50; De motibus corporum coelestium, 183; and Ṭūsī-couple, 183–5, 190, 196, 266n51
Anatolia, 148–9
Andalò di Negro, 233n15
Andalusian astronomy, 261n103
Andrews, Walter, 41
Angelus, Johannes, 182
anomaly: first, 102; second, 102–5. See also motion
antiqui and moderni (via antiqua, via moderna): compared, 58–67; influence in late-fifteenth-century Cracow, 59
Apollonius of Perga, and alternative explanations of the same observations, 73
appearances: appearances not illusions, 134, 137; beyond appearances, 111, 114, 117, 137; epistemological status of, 111, 138; passive attitude to, 113; problem-atization of, 136; reality of, 137; re-evaluation of, 137; relative to observer’s point of view, 137; saving of appearances, 110; and theories 134; understanding appearances, 111; and the visible, 112. See also phenomena
Aquinas, Thomas, and conceptions of mathematics, 67
Arabic: study of, 30, 41; European and Byzantine knowledge of, 175– 6, 187, 189, 194, 269n80
Arabs: stereotype of, 38; in Bacon’s imaginatio modernorum and Averroes’s moderni Arabes, 230–1n105
Archimedes of Syracuse, 255n51; Cusa and Archimedes, 123, 129, 132; new translation of, 122; On the Measurement of the Circle, 130–1
Argyropoulos, John, 41
Aristarchus, 255n51
Aristotle/Aristotelian philosophy, 85, 88, 196, 260n97, 268–9n78; concentric spheres, 85, 236; cosmology, 261n103; counteracting spheres, 85, 235; De caelo, 84; ethics not a science, 64; metaphysics, 151, 169; physics, 147, 154; Posterior Analytics, 67–9; on principles of natural science, 63; and quies media, 173; seeing and knowing, 115, 122, 134; uniform motion, 84. See also astronomy, concentric/homocentric; Krakovian Aristotelians; Paduan Aristotelians
Aristotle (pseudo-), Mechanics, 60
Asia, 30, 36–9, 41
Asia Minor, 36
astrarium, 93, 100
astrology/astrologers, 5, 10, 87, 93–4, 97, 99; in Bologna, 101–2; in Islam, 144–6, 150, 152, 251n9–14, 251– 2n15, 252n16, 252n18, 252n21, 256nn56–7, 258n80; in Vienna, 81–2. See also ephemerides; Guicciardini; Nihil; Novara; Peurbach; Regiomontanus; tables; zīj
astronomical handbook. See zīj
astronomy: Babylonian, 195; concentric/homocentric, 6, 9, 82–7, 92–3, 96, 146, 149, 151, 155–6, 158, 169, 171–2, 196, 200–2, 206, 208, 211– 12, 214, 261n103, 261n108, 261n115, 271n111, 271n113; epicyclic vs eccentric models, 4–6, 8, 91, 102–5, 154, 156–7, 191, 242– 3n109; Franciscan, 86; Jewish, chapter 8; mathematical vs physical, 8–9, 48, 84–6, 93, 96, 151–2, 157–8, 257n68, 257n72; narrative vs demonstrative, 46; not a fictitious art, 96; as science in process of development, 49, 102; speculative or theoretical, 46; status of, 8–9, chapter 3; two- vs three-dimensional, 83, 96, 99. See also Albategnius; Alfraganus; Aristotle/ Aristotelian philosophy; Averroes; al-Biṭrūjī; Eudoxus of Cnidus; Geber; hayʾa; Ibn al-Haytham; Ibn Naḥmias; Ibn al-Shāṭir; Islamic astronomy; Langenstein; lunar models; Marāgha; Mercury; orb; Padua; Persian Tables; Peurbach; planets; Ptolemy; Qushjī; Regiomontanus; al-Shīrāzī; spheres; Sun; alṬūsī; Ṭūsī-couple; Venus; zīj
Autolycus, 255n51
Averroes (Ibn Rushd), 6, 30, 210–11, 230n105, 279n72; autonomy of scientific disciplines, 50; Averroist critiques of Ptolemy, 216n18; conception of science, 47–8; criticism of epicycles and eccentrics, 77–8; distinction between mathematics and physics 60-1; on logical structure of Aristotle’s arguments, 71; mentioned by Brudzewo, 77; questions purpose of orbs without stars, 71; On the Substance of the Celestial Orbs, 279n75; Talkhīṣ al-Majisṭī (Epitome of the Almagest), 211, 279n74; types of demonstrations, 62
Averroism, 271n111, 271n113; in Padua, 196. See also Paduan Aristotelians
Avicenna (Ibn Sīnā), 30, 253n33; Aqsām al-ʿulūm al-ʿaqliyya, 150; only one species of demonstration, 62
Avignon, 189
Avner de Burgos, 177, 190, 207, 277n51; Meyashsher ʿaqov, 190
Azhar Mosque, 250n4, 254n39
Bābur, Ẓahīr al-Dīn, 258n81
Bacon, Roger, 86, 230–1n105; on conflict between theory and observation, 65–6; on three-part orbs (imaginatio modernorum), 51–2
Banū Mūsā, 255n51
Barbaro, Ermolao, 23
Barbo, Pietro. See Paul II
Barker, Peter, 53, 78, 200–1, 215n1, 216n18, 230n102, 267n61, 268n76, 273n7, 275n25
Basel, Council of, 32, 33, 35, 222n21
Basilian order, 88
al-Battānī. See Albategnius
Bāyazīd I (Ottoman sultan), 148–9
Bāyazīd II (Ottoman sultan), 190, 194, 208–9
Belgrade, 31
Benvoglienti, Leonardo, 223n39
Berkey, Jonathan, 260n99
Bernard of Verdun, 86; Tractatus super totam astrologiam, 51
Bessarion, Basilios (cardinal), 9–10, 30, 39–41, 80, 87, 133, 185, 191, 193, 224n57; advocates crusade, 89, 93; circle of, 89, 93; commis-sions Epitome of the Almagest, 89; controversy with George of Trebizond, 88, 94, 98; and Council of Florence, 88; death, 98; defends Plato, 87; and Defensio Theonis, 95; library of, 88, 91, 93, 101, 237–8n60, 241n99; papal candidate, 93; patron of Regiomontanus, 9, 87–8, 94; in Vienna, 89
Bianchini, Giovanni, 96, 101, 212, 279n82, 279–80nn83–4; correspondence with Regiomontanus, 131, 133; tables, 92
al-Bīrjandī, ʿAbd al-ʿAlī, Sharḥ al-Tadhkira, 192, 264n23
Birkenmajer, L.A., 102, 241n100
al-Bīrūnī, Abū Rayḥān, 145–6; Al-Qānūn al-Masʿūdī, 145, 147; Al-Tafhīm li-awāʾil ṣināʿat al-tanjīm, 145, 252n18
al-Biṭrūjī, Nūr al-Dīn (Alpetragius), 6, 85–7, 96–7, 109, 200–3, 207, 210, 242n102, 274nn19–21, 275n30, 275n32, 278n52; attacked by Guido de Marchia, 86; De motibus celorum, 85–6; On the Principles of Astronomy (Kitāb al-Hayʾa), 200–2, 207, 275n32, 278n52; unorthodox planetary order, 86
Blair, Ann, 22
Bologna, University of, 20, 21, 22, 24, 80, 101–2, 216n18; observation, 241n100
Bonaventure (Giovanni di Fidanza), 23–4
Bonfils, Immanuel, The Six Wings, 212–13
Botticelli, Sandro, 17
Bradwardine, Thomas, on the continuum, 60
Brahe, Tycho, 109, 243n111; cosmography, 4
Bratislava (Pressburg), 89; University of, 94
Brentjes, Sonja, 155, 260–1n102, 273n9
de la Broquière, Bertrand, 222n15
Brudzewo, Albert of, 8, 101, 186–7, 196–7, 268n74, 268n77; citation of Arabic works, 46, 225n9; commentary on Peurbach, Theoricae novae planetarum, 46, 70–6; list of principles for Peurbach, Theoricae novae planetarum, 53; real orbs vs mathematical figures, 231n109; teaching at Cracow, 70–1
Brummett, Palmira, 221n10
Bruni, Leonardo, 26
Buridan, John, and fourteenth-century moderni, 59, 62–3
Burley, Walter, on confidence in science, 62
Bursa, 148–9, 153, 157, 191, 255n46
Byzantium, 30, 37, 40; transmission route for Ṭūsī-couple, 161, 175–6, 187–9, 194
Cairo, 153, 157, 250n4, 254n39, 258n78, 258n80. See also Mamluks
calendars, 144, 251n11
Calippus, 236
Campanus of Novara, 99, 234; Theorica planetarum, 46, 51, 76–7
Capranica, Domenico (cardinal), 35
Capsali, Elijah, 210
Carman, Charles, H., 244n10
Carra de Vaux, 178
Castiglione, Baldassare, 27
Celenza, Christopher, 31
Celoria, Giovanni, 248n95
Central Asia, 148–50, 153
centre: of celestial orbs or spheres, 48; as Earth, 48; of eccentric, 50; of World, 50
Charles VII (king of France), 35
Chaucer, Geoffrey, 233n8
Chen-Morris, Raz, 244n9, 245n27
China, 36
Chioniades, Gregory, 93, 175–6, 187– 8, 190, 213, 281nn100–1; Schemata of the Stars, 176, 188–9, 265n29, 281n99
Christianity, 31–5, 37–9, 41, 224n49
Christmann, Jakob, 213, 270n93, 280n90
Chrysococces, George, 188, 213, 280n90
Chrysococces, Michael, 212
Cicero, Marcus Tullius, 32–3, 244n9
circles, small (at centre of deferents): not real but mathematical, 74; as result of rotation of paired, unequally thick orbs, 74, 231n116
circulation of knowledge, 7. See also scholarly pipelines; travellers
Clagett, Marshall, on Cusa’s methods, 122–3
Collegium Neophytorum, 278n62
Comes, Mercè, 189
Commentariolus, 45–9, 54–5, 102, 108, 110, 136, 183–5, 187, 190, 197, 268n77; criticism of equant, 4–5; epicycles only, 6; manuscripts and translations of, 225n1; similarity to Ibn al-Shāṭir’s models, 4–6, 30, 146, 156, 187, 190, 194–6, 208–9, 214, 216n16, 217n23, 262n1, 268n77, 271n113, 272n1; single centre for each planetary system, 6; symmetry, lack of argument for, 5; written when mathematics of De revolutionibus had not been worked out, 48, 225–6n11. See also Copernicus; De revolutionibus orbium coelestium
computation, 81, 86, 92, 96, 99, 102, 106
Comtino, Mordechai. See Khomṭiano
concentric astronomy. See astronomy
conchoid construction, 190
condemnations at Paris and Oxford in thirteenth century, 65
configuration, 46. See also hayʾa; Ibn al-Haytham, On the Configuration of the World
Constantine (emperor), 89
Constantinople, 9, 31, 33–4, 36, 40, 88–9, 93–4, 191, 193–4, 213, 238n62
Contadini, Anna, 221n10
Copernicus, Nicholas, 17, 18, 19, 20, 21, 22, 27, 28, 29–31, 39–41, 101– 6, 198–201, 207–10, 212, 214, 272n1, 272nn3–4, 273nn7–8, 275n25, 278n54, 279n82; and appearances, 112, 137; and Aristotelian-Averroist homocentrism, 271n113; background to, 3–5, 8, 11; Bologna observation, 241; criticism of Ptolemy, 4, 8, 196, 271n111; and curriculum at Cracow, 67; exceptionalism, 3, 7, 156; heliocentrism, 4, 6–8, 114, 215n1; 217nn20–1; homocentrism, 6, 216n18; influence of Islamic astronomy, 4–9, 216n16, 217n23; influence of/parallels with Islamic astronomy, 146, 156–8, 195–7, 253n25, 255n48, 260n103, 261n108, 267nn60–1, 268n77, 268–9n78; in Italy 121; inversion of eccentric model for second anomaly of inferior planets, 4, 8, 106; latitude theory, 183–4; Letter against Werner, 49, 75; library of, 101; mean Sun as centre of universe, 6, 102–3; Mercury model, 184–5; Mercury observations by Walther, 241; observations by, 137–8; observer’s point of view, 137; origins of heliocentrism, 102–6, 243; planetary order, 5–6, 96–7, 103, 106, 216–17n20; and Proclus, 185–6; and Regiomontanus, 4, 6, 8, 102, 113–14, 130, 134; relative sizes of planetary spheres, 106; solid-sphere astronomy, 4, 6; spherical vs mathematical models, 184; transformation of epicyclic into eccentric models, 4, 8, 191; travels, 101, 185, 189, 197; and Ṭūsī-couple, 161–2, 183–6, 196–7; uniform, circular motion, 4–7, 216–17n20, 217n21; “Uppsala Notes,” 106; visible-invisible relationship, 110– 11, 113, 136–8, 140. See also Commentariolus; Cracow University; De revolutionibus orbium coelestium; Ibn al-Shāṭir; Regiomontanus
cosmography: geocentric, 5–7; Tychonic, 4
cosmological shifts, 3–5
cosmology: alternatives, 84, 87, 96; fluid heavens, 86; stereotype of medieval, 86. See also astronomy; Copernicus; hayʾa
Council of Florence, 88, 133
Council of Trent (Counter-Reformation), 59
Cracow, 12, 67–8, 196
Cracow University, 46, 80, 101, 196; Copernicus, student at, 48, 53, 55, 58–9, 67, 70, 101–2
Crete, 190
critical realism, as opposed to skepticism, 64
Curtze, Maximilian, 247n82, 248n90
Cusa, Nicholas, 10, 33, 35, 93; and Alberti’s project 114, 121, 131; challenge to traditional conception of astronomy, 135; coincidence of opposites, 117, 121, 125, 130; critique by mathematicians, 130, 132– 4; De aequalitate, 127; De arithmeticis complementis, 126; De beryllo, 117– 19, 128; De complementis mathematicis, 126; De docta ignorantia, 117, 119; De geometricis transmutationibus, 122–3, 125, 133; De mathematica perfection, 127; De possest, 117; De visione dei, 139; and diagrams, 120–1, 133; enigma, 117–18, 120, 121; Idiota de mente, 125; intellectual vision, 117, 126–7; isoperimetric methods, 121, 123–4, 133; and Protagoras, 119–20; quadrature of the circle, 113, 121–2, 126–8, 130, 132–3; observer’s point of view, 129, 132, 139–40; and Regiomontanus, 111; social network, 113; visible reality, 119
al-Daftarī, ʿAbd al-Salām. See al-Yahūdī
Damascus, 6, 146, 149, 153, 157, 254n39, 258n80. See also Mamluks
Dank, Johannis, in suis theoricis, 230n98
Darius, 34
Daston, Lorraine, 21, 218n19
De Burgos, Avner. See Avner de Burgos
Defensio Theonis contra Georgium Trapezuntium (Regiomontanus), 94–8, 103–5, 108; conflicting sympathies, 95; critical of Ptolemy, 83; dedication to Matthias Corvinus, 95; defends Ptolemy, 91, 96; printed edition planned, 95; significance and character, 95
deferent (ḥāmil), 163, 165–7, 177–81, 264n16; of the apogee of the eccentric of a planet, 50; of inferior planets, 106–7
Dellākoğlu, Ḥusām, 258n77
Delmedigo, Elijah, 210–12, 214, 278n63, 278nn65–6, 279n72, 279nn75–6
demonstration: a priori and a posteriori, 62; demonstrative science, conceptions of, 60–7; quia and propter quid, 62, 69
De revolutionibus orbium coelestium, 3–6, 24, 27, 78, 102, 108, 111, 138, 183–4, 186, 197, 199–200, 212–13; multiple centres/eccentrics, 5–6, 217n23; symmetry and planet order, 5–6, 216–17n20. See also Commentariolus; Copernicus
Descartes, René, 17
De Valladolid, Alfonso. See Avner de Burgos
diagrams, astronomical, 84, 151–3, 157–8, 234, 242, 257n70
Di Bono, Mario, 5, 183, 185–6, 195– 7, 207, 216n16, 262n2, 268n77
Diels, H., 248n99
Dijksterhuis, E.J., 242n107
Diogenes, Laertius, 249n114
dirigent orb (mudīr), 165, 167
disciplines: boundaries/demarcations of, 7–10, 256nn56–8; overlap of, 146–7; relations of scientific, 64
distance: between Sun and Earth, 49; variation in distance of planets from the observer, 66
Dobrzycki, Jerzy, 158, 182–3, 197, 237–8n60, 271n111, 279n77
Dondi, Giovanni, 93, 100
Doukas, 40, 233n39
Droppers, Garrett, 177–8, 179 (fig. 7.10), 180, 265–6n39
Duhem, Pierre, 244n8, 274n20
Duran, Profiat, 275n22
Durandus de Sancto Porciano, and three-part orbs, 52
Earth: centrality, 4, 48–9, 78, 87, 107, 200–1; configuration (hayʾa) of, 152–3; possible motion of, 4, 6–8, 12, 45, 49, 80, 90, 102–6, 110–14, 121, 133, 136–40, 147, 154, 268– 9n78, 272n3; stationary, 4, 60, 85, 243n1
East, the, 38
eccentrics, 49; Copernicus on, 54, 217n23; eccentric model of second anomaly, 91–2, 103, 105 (fig. 4.2), 106, 242–3n109; eccentric models for Mercury and Venus, 191, 272n3; motion due to eccentric or epicycle indistinguishable, 71–2, 231n115; rejection of, 84–5, 108, 261n103, 274n20. See also anomaly; astronomy; fictionalism; Ptolemy; realism
eclipses, knowledge of, 61
Egypt, 148, 258n74. See also Mamluks
Egyptians, 38
eighth sphere/orb, of fixed stars, 46, 49, 85; Averroes on, 71; rotation of, one degree per century, 50–2. See also precession; trepidation
Elisha the Greek, 280n95
enclosing/maintaining sphere/orb (muḥīṭa). See Ṭūsī-couple
England, 34, 36, 38
ephemerides, 82; Regiomontanus’s, 98–100
epicycles, 49, 163, 165, 167, 172, 177–82, 186, 196–7; Copernicus on, 5–6, 54; diameters of, 169–70, 173, 175; doubts about reality, 236n47; epicyclic model for second anomaly, 103–7; of inferior planets, 91–2; rejection of, 84–5, 108; of superior planets, 97, 106; Theon of Smyrna’s preference for, 91. See also anomaly; astronomy; Copernicus; fictionalism; Langenstein; realism; Regiomontanus
Epitome of the Almagest (Peurbach and Regiomontanus), 6, 79–81, 89–91, 94–5, 114, 157, 191, 200, 211, 261n108, 270nn95–6, 272n2; and Almagestum parvum, 90; book 5, 91, 241n100; book 9, 242n103; book 12, 92, 102–3, 106–8, 238n69; as breviarium, 98; copied in Ferrara, 101; manuscripts, 241n99; preface, 92; printing, 101–2. See also Regiomontanus
equant points or circles, 4–5, 58, 70, 75, 80, 84, 99, 135, 231n117; Copernicus on, 55; equant problem, 78, 162–3, 196, 264n16, 271nn110–11; in Ibn al-Haytham, 57; not physically real but imaginary, 64, 74, 77; in Peurbach, 57. See also Brudzewo; Głogów; John of Sicily
equivalence proof of epicyclic and eccentric models, 80, 91–2, 103–4, 107–8, 242n105, 242–3n109. See also anomaly; Qushjī; Regiomontanus
Erasmus, Desiderius, 27
Erfurt, 98, 240n79
Erhardus Cremonensis. See Gerard of Cremona
Esztergom, 94
Euclid, 116, 126, 132; Elements, 147, 154, 255n51; parallels postulate, 189; pseudo-Ṭūsī’s Commentary on Euclid’s Elements, 189–90
Eudoxus of Cnidus, 85, 235n28, 236n47, 275n32; hippopede, 235n28, 264n19; homocentric orbs, 169. See also Ibn al-Haytham, Eudoxan-couple and latitude theory
Eugenius IV (pope), 33, 35
Eurocentrism, 5, 155–7, 193, 216n16, 249–50n2, 260nn96–7, 261n110
Europe, 29–39, 41, 223n27, 223n38, 224n49
experience, as basis for knowledge of principles, 49
Fakhr al-Dīn al-ʿAjamī, 258n77
al-Fanārī, Muḥammad Shāh, latitude problem in Unmūdhaj al-ʿulūm, 269n92
al-Fanārī, Mullā Shams al-Dīn, circle of, 148–9, 255n46
al-Fārābī. See Alpharabius
al-Farghānī. See Alfraganus
al-Fārisī, ʿUmar b. Daʾūd, Takmīl al-Tadhkira, 192
Fārs, 249n1
Fazlıoğlu, İhsan, 194
Felix V (anti-pope Amedeo of Savoy), 35, 223n31
Ferrara, 92; University of, 101
Ferrara-Florence, Council of, 224n58
Ficino, Marsilio, 21, 22, 41
fictionalism, 80, 96, 152, 236n47. See also astronomy; realism
Field, J.V., 245n18
figures (theoricae): artificial properties in Theoricae novae planetarum, 72; in manuscripts of Ibn al-Haytham’s On the Configuration, 232nn124–5, 257n70. See also diagrams, astronomical
Filelfo, Francesco, 38, 224n48
Finzi, Mordechai, 190, 212, 269n90, 278n67, 279n83
fixed stars, sphere of. See eighth sphere/orb
Florence, 19, 23, 33, 125. See also Council of Florence
Folkerts, Menso, 240n79
Fracastoro, Girolamo, 206–7, 209; Homocentrica, 183; and Ṭūsī-couple, 183, 185
France, 34, 36, 38
Francis I (king of France), 222n15
Frederick III of Habsburg (emperor), 32–5, 81
Gal, Ofer, 244n9, 245n27
Galeano, Moses ben Judah (Mūsā Jālīnūs), 156, 190, 208–11, 213–14, 270n102, 278n53; Puzzles of Wisdom (Taʿalumot ḥokmah), 208–9
Geber (Jābir ibn Aflaḥ), 46, 94, 97, 211, 238n63, 239n75; mentioned by Brudzewo, 46, 77
genre: of astronomical writing, 45–6; narrative, 53; of Peurbach, Theoricae novae planetarum, 46; shared by Ibn al-Haytham’s On the Configuration, 77. See also hayʾa
George of Trebizond (Georgius Trapezuntius), 41, 87; attacks Plato, 87; attacks Theon, 88, 95; biography, 87–8; dedicates translation and commentary to King Matthias Corvinus, 94; defends Aristotle, 88; letters to Mehmed II, 94; translates and comments on Almagest, 88; travel to Constantinople, 94, 238n62; Commentary on Almagest, 88, 94; on book 9 of Almagest, 97; on book 12 of Almagest, 103.
Gerard of Cremona (Erhardus Cremonensis), 88, 230n98, 230n100
Germany, 38
Gersonides (Levi ben Gerson), 84, 189–90, 210, 235n26, 237n56, 275n22, 277n46, 278n67; apparent size of Moon, 91
al-Ghazālī, AbūḤāmid Muḥammad, 249n2
Glasner, Ruth, 67
Głogów, John of, 8, 81; on equants as imaginary, 70, 230n98; on mathematics vs physics in astronomy, 70; on the Posterior Analytics, 67–9; purpose or final cause in astronomy, 69; on Sacrobosco’s Sphere, 69–70
God: His divine will, 145; glorification via His creation, 153–4, 259n87; man’s knowledge of, 118–19, 128– 9. See also Cusa
Goddu, André, 5, 217n21, 228n46, 244n7, 273n7; interpretation of Oresme, 177–8, 180, 266n39, 266n41; as skeptic of Islamic influence on Copernicus, 186–7, 195–7, 267n61, 268n77, 268–9n78
Goldstein, Bernard, 6, 201, 217n21, 272n3, 275–6n32, 277n46, 278n67
Grant, Edward, 51–2, 155, 226n17, 226–7n23, 260nn96–7
Greece, 38
Grosseteste, Robert, levels of scientific knowledge, 61
Guarino da Verona, 87
Guicciardini, Francesco, 21–2, 219n21; Ricordi, 21
Habermas, Jürgen, 23
Habsburgs, 39, 81
Ḥall-i mushkilāt-i Muʿīniyya. See Muʿīniyya Treatise
Haly (ʿAlī ibn Riḍwān), mentioned by Brudzewo, 46, 77
handbooks, practical astronomical. See zīj
Harries, Karsten, 244n10
Hartner, Willy, 158, 267n61
Ha-Separdi, Isaac al-Ḥadīb, The Paved Way, 213
Hay, Denys, 38
hayʾa (configuration): connection with theorica tradition, 6, 46–7, 51– 2, 56–8, 77; ʿilm al-hayʾa as discipline/genre, 146, 148, 150–4, 163, 217n22, 255nn53–4, 255–6n55, 256nn56–8, 259n87. See also Hebrew translations; Latin translations of hayʾa works
Heath, Thomas, 248n99
Hebrew translations: of Ibn al-Haytham, On the Configuration, 55, 76, 232n125, 257n70; of Jaghmīnī, Al-Mulakhkhaṣ, 153, 209; of Kharaqī, Al-Tabṣira, 258n74. See also Judeo-Arabic
Henry of Hesse. See Langenstein
Hipparchus of Nicaea, 91, 195, 248n101
hippopede. See Eudoxus of Cnidus
Hofmann, Joseph, 122–3, 127
Holy Roman Empire, 32–3, 35, 39
Homer, 34, 37
homocentric astronomy. See astronomy
Huff, Toby, 155–6, 260n97, 261n110
Humām al-Ṭabīb, 258n77
Hungary, 34–5, 38, 82, 86, 100; political rifts, 97; Regiomontanus in, 94– 5, 97. See also Ladislaus Posthumus; Matthias Corvinus
Hus, Jan, 224n46
hypothesis (aṣl)/hypotheses, 45, 49, 162, 174, 198–9, 264n24, 273n10; derived from experience, 49; need for better, 47; in title of Commentariolus, 53. See also principles
Hypsicles, 255n51
Ibn Aflaḥ, Jābir. See Geber
Ibn al-Akfānī, 148, 254n37
Ibn al-Haytham, AbūʿAlī al-Ḥasan, 8, 46, 84, 211, 279n77; Almagest commentary, 256n60; alternative models (Maqāla fīḥarakat al-iltifāf), 151, 256n61; On the Configuration of the World (Maqāla fī hayʾat alʿālam), 8, 46, 50–2, 57, 76, 83, 152, 157–8, 257n67; criticisms of Ptolemy (Al-Shukūk ʿalā Baṭlamyūs), 151, 195, 211, 271n111, 279n74; Eudoxan-couple and latitude theory, 163, 169, 171–2, 174–5 (figs 7.8, 7.9), 176, 182, 186–8, 190, 196, 205 (fig. 8.3), 264n19; influence of, 152, 158, 257nn68–70, 257n72; Optics, intromission and extromission theories in, 66; orbs of, 53; as source for Peurbach’s Theoricae novae planetarum, 228n44; translations to Hebrew, 55, 76; translations to Latin, 55–6
Ibn al-Shāṭir, ʿAlāʾ al-Dīn, 4–6, 30, 146, 149, 156, 182, 187, 190, 194–5, 208–9, 214, 216n16, 217n23, 254n39, 255n48, 260–1n102, 261n114, 262n1, 268n77, 271n113, 272n1, 278n54, 281n99; epicycleonly models, 196
Ibn Jubayr, 221n15
Ibn Naḥmias, Joseph, 8, 162, 182, 190, 200–2, 204–10, 264n19, 274n18, 274n21, 275n22, 275nn30–1, 275–6n32, 276n40, 277n45, 277n49, 277n51, 278n62; double-circle hypothesis, 205–7, 277n45, 277nn48–9, 277n51; The Light of the World, 182, 199–204, 206–9, 214, 273n10, 274n18, 275nn31–2, 277n49, 278n62
Ibn Riḍwān, ʿAlī. See Haly
Ibn Rushd. See Averroes
Ibn Sīnā. See Avicenna
Ikhwān al-Ṣafāʾ, Rasāʾil, epistle 3, 256n57
Īlkhānids, 149, 165, 189, 194
ʿilm aḥkām al-nujūm (science of judgments of the stars), 146. See also astrology/astrologers, in Islam; ʿilm al-nujūm
ʿilm al-hayʾa. See hayʾa
ʿilm al-mīqāt. See time reckoning
ʿilm al-nujūm (science of the stars), 150, 256n57. See also astrology/ astrologers, in Islam
ʿilm al-zījāt (science of astronomical handbooks with tables), 146. See also zīj
imaginatio modernorum (Bacon’s label for three-part orbs), 52, 230–1n105
imitatio, 90, 236n44
inclined orb, 166–8
Indian astronomy, 153, 258n81
induction, senses of term, 63
insight, following experience, 64
institutions, 10; Islamic, 146, 154–8, 250nn3–4, 251n14, 254n39, 260nn96–7, 260n99. See also madrasa; Marāgha, Observatory
instruments, 100, 144–5, 240, 252nn20–1, 253n31, 258n80. See also astrarium; sundial; volvelles
intelligence, 75; as celestial mover, 52; in each orb of Peurbach’s Theoricae novae planetarum, 53
internal logic of parallel scientific innovation, 186, 195–7, 267n61, 271n107
Iran, 143, 149, 189, 249n1
Isidore of Seville, mentioned by Brudzewo, 46
Islam, 32, 38
“Islamic,” definition of, 250n6
Islamic astronomy, 87, 90; connections with Copernicus, 144, 146, 156–8, 253n25, 255n48, 260n97, 261n108; practical vs theoretical, 144–8, 252n20, 253n31; subject matter of, 144–8, 150–4, 251n9, 252nn20–1, 258n80. See also astrology/ astrologers, in Islam; hayʾa
Islamic Scientific Manuscripts Initiative (ISMI), 269n91
Italy, 34, 36, 38, 81–2, 87, 89, 92, 98, 101
al-Jabartī, ʿAbd al-Raḥmān, 250n4
al-Jabartī, Ḥasan, 250n4
Jābir ibn Aflaḥ. See Geber
Jacobus Cremonensis, 95, 122, 131
al-Jaghmīnī, Maḥmūd ibn Muḥammad ibn ʿUmar, Al-Mulakhkhaṣ fī al-hayʾa al-basīṭa (Epitome of Plain Hayʾa), 147–8, 150, 153, 157–60, 209, 250n4, 254n37, 258n77; commentaries on, 149, 153–4, 250n4, 254n37, 254n44, 254–5n45, 258n58, 258nn77–8; Hebrew version of, 153, 209
Jālīnūs, Mūsā. See Galeano
Jarzombek, Mark, 245n18
Jews as scientific intermediaries/ transmitters, 57, 156, 190, 194, chapter 8, 260n101. See also Hebrew translations
Johannes de Fundis, 233n15
John Duns Scotus, and three-part orbs, 52
John Marsilius Inguen (pseudo Marsilius of Inghen), on thick orbs, 77
John of Jandun, on embedding epicycles within deferents, 77
John of Sicily, Scriptum super canones, 50; equant as imaginary, 77
Johns, Adrian, 22
Joseph ibn Naḥmias. See Ibn Naḥmias
Judeo-Arabic, 182, 199, 209
Julmann, 186
Jupiter, 102, 235n28
al-Jurjānī, al-Sayyid al-Sharīf, 147, 254n37, 254n44, 254–5n45, 255n46, 258n77; Sharḥ al-Tadhkira al-Naṣīriyya, 192
Kalpaklı, Mehmet, 41
Kāshān, 143
al-Kāshī, Jamshīd Ghiyāth al-Dīn, 143– 4, 147, 249n1, 250n7, 254n45, 259n92
Kemp, Martin, 245n18 Kennedy, Edward S., 251n9, 267n61, 275–6n32
Kepler, Johannes, 20, 25, 109, 231n117; Astronomia nova, 25; and unification of mathematical and physical astronomy, 58
al-Khafrī, Shams al-Dīn, 173, 264n18; Al-Takmila fī sharḥ al-Tadhkira, 192
al-Kharaqī, ʿAbd al-Jabbār: hayʾa works, 149–50, 152–3, 258n74, 259n87; on solid-sphere astronomy, 257n68
Khomṭiano (Comtino), Mordechai, 213
Khurāsān, 148–9
Khwārizm, 148, 153
Khwārizm-Shāhs, 150
Khwārizmī, AbūʿAbd Allāh, Mafātīḥ al-ʿulūm, 256n57
King, David A., 146, 251n10, 258n80
Kircher, Timothy, 245n18
Klosterneuburg, 82
knowledge: concepts of, 7–10; possibility of new, 68
Koenigsberger, Dorothy, 244n10
Koerner, Joseph Leo, 249n118
Koestler, Arthur, 3, 10, 215n2
Krakovian Aristotelians, 5
Kremer, Richard, 158, 182, 197, 237–8n60, 247n8, 271n111
Kren, Claudia, 177–9, 266n41
Kritoboulos, Michael, 40, 223n39
Kubnawī, al-Ḥaqq, 258n77
Kugler, Franz, 195
Kuhn, Thomas, The Copernican Revolution, 3, 215–16n11
külliyyes, 250n3. See also institutions, Islamic
Labowski, Lotte, 248n94
Ladislaus Posthumus, 82
Laird, Walter, Scientiae mediae, 228n51
Langenstein, Henry of (Henry of Hesse), 99, 186–8, 271n111; apparent size of Moon, 91; copied by Regiomontanus, 84, 99, 240n87; nonuniformly moving homocentric spheres, 84–5
Langermann, Y. Tzvi, 156, 177, 190, 194, 208, 257n67, 257n72, 264n22, 269n86, 277n51
Latin translations of hayʾa works: Farghānī, Jawāmiʿ, 151; Ibn al-Haytham, On the Configuration, 55– 6, 232n125, 257n70
latitude theory, 151, 234. See also Copernicus; Ibn al-Haytham; Ptolemy; al-Ṭūsī
Leipzig, University of, 81–2
Leonardo da Vinci, 17
Lepanto, 31
Lerner, Michel-Pierre, 216n16
Levao, Ronald, 249n120
Levi ben Gerson. See Gersonides
Lévy, Tony, 189
links, genealogical, between Ibn al-Haytham’s On the Configuration and Peurbach’s Theoricae novae planetarum, 47. See also Ibn al-Haytham; Peurbach
Lithuania, 36
Lloyd, G.E.R., 244n8
Locke, John, 19
Lodi, Peace of, 35
Lombard, Peter, 23–4
“long fifteenth century,” definition of, 17–18, 25–7, 144
“long sixteenth century,” definition of, 18
Ludlam, Ivor, 244n9
lunar models: Ptolemy’s, 84, 235n34; Sandivogius of Czechel’s, 186, 268n74; Ṭūsī’s, 163, 165–8, 176, 187–8. See also Almagest; Moon
Lunbeck, Elizabeth, 243n3
Machiavelli, Niccolò, 17, 27
Macrobius, 236n44
madrasa, teaching sciences, 143, 146– 9, 153–7, 250nn3–4, 253–4n36, 259nn92–3, 260nn96–7; under the Ottomans, 148–9, 154, 156–8, 250n4, 254n42, 260n99. See also institutions, Islamic; Samarqand
Magna Carta, 18
Makdisi, George, 155, 253–4n36, 260nn96–7
Malpangotto, Michela, 53, 78
Mamluks, 153, 251n10, 252n20, 258n80
Mancha, José Luis, 186–7
Manilius, Marcus, 98–9
Mantua, Congress of, 223n38
Maqāla fīḥarakat al-iltifāf. See Ibn al-Haytham
Maqāla fī hayʾat al-ʿālam. See Ibn al-Haytham
Marāgha: influence on Latin West, 158, 253n25, 255n46, 255n48, 257n68; models, 182, 184, 270– 1n106; Observatory, 149–50, 153, 156, 199, 251n15, 255n46, 255n50, 257n68; School, 149–50, 153, 156, 172
Marchia, Guido de, 86
Mars, 4, 92, 97; variation in apparent size, 237n56
Marsilius of Inghen, and moderni, 59
Martianus Capella, 97
Martin Bylica of Ilkusch, 93–4, 101, 241n99
Masaccio, 17
Masolino da Panicale, 17
Matar, Nabil, 222n11, 222n15
mathematics: certainty of, 69; deals with mental concepts, 67; and reasoning from observation to theory, 73
Matthias Corvinus (king of Hungary), 94–5, 97; library of, 241n99
Mavrogonato, David, 274n14
McKitterick, David, 22
Medici Press, 189
Mehmed II (Ottoman sultan), 37, 38, 88–9, 156, 193–4, 209; as dedicatee, 154; letters from George of Trebizond to, 94
Menelaus, 255n51
Mercury, 4, 86, 99, 106–7, 216n16, 217n23; Copernicus’s model for, 183–5; as hermaphrodite, 97; observations by Walther, 241n97; order inverted, 239nn74–5; oval trajectory, 234n17; parallax, 239n74; “recorded” below Venus, 239n74; Ṭūsī’s lack of solution, 163–4
Merv, 150, 153
meteorology, hypotheses at least possible for, 64, 229n64
“Middle Books,” 255n51
Milan, 222n19
Mizraḥi, Elijah, 213, 280n93
models, planetary. See astronomy
Mohaçs, 31
Monfasani, John, 89
Mongols, 143, 149, 172, 189, 251n15
month, synodic, 195
Moon: apparent size, 84, 87, 91, 241; full and new, 81; homocentric models for, 84; lunar months, 144; lunar stations, 145; occultation of Aldebaran, 241n100; orbs of, 160 (fig. 6.3); parallax, 241n100; Ptolemaic model, 235n34; spheres required for motion of, 83. See also Almagest; Gersonides; lunar models; Regiomontanus
More, Thomas, 27
Morrison, Robert, 156, 182, 190, 194
Moses Ben Judah Galeano (Mūsā Jālīnūs). See Galeano
mosques, 146, 156, 250n3. See also Azhar Mosque; institutions, Islamic; Umayyad Mosque
motion: of access and recess (Babylonian), 71; contrary, 85–6, 108; of fixed stars, 49; reciprocal, 202–4, 208, 276n34, 276n37; retrograde, 49; of Sun, 499; uniform vs nonuniform, 4–5, 7, 84, 99, 103–5, 216–17n20, 217n21, 235n27. See also Earth, possible motion of; spheres
mover, celestial (intelligence, separate substance), 52
Mughal Empire, 258n81
Muhammad (Prophet), 38, 88, 224n46
Muḥammad ʿAbduh, 258n78
Muḥyī al-Dīn al-Maghribī, 149, 269n86
Muʿīniyya Treatise, 150, 257n68, 163– 4; appendix to (i.e., Dhayl or Ḥall), 164–7, 170, 188, 190, 192, 206, 262n6, 281n99; dedicated to Muʿīn al-Dīn, 164; and Ibn al-Haytham’s latitude theory, 169, 188; source for Chioniades, 176, 187–8
Al-Mulakhkhaṣ fīʿilm al-hayʾa al-basīṭa. See al-Jaghmīnī
Müller von Königsberg, Johannes. See Regiomontanus
Muntahā al-idrāk fī taqāsīm al-aflāk. See al-Kharaqī, hayʾa works
Murad II (Ottoman sultan), 223n33
Mūsā Jālīnūs. See Galeano
Naples, 34–5, 234n22, 241n99
nature, praeter nature (neither natural nor violent), 53
Nederman, Cary, 32
Negroponte, 31
Neugebauer, Otto, 3–4, 30, 108, 183–4, 186, 189, 194, 253n25, 255n48, 265n27, 267n61, 272n1, 272n4
Nicholas of Erfurt, 234n22
Nicholas V (pope), 87, 122
Nicolle, Jean-Marie, 126–7, 246n49, 246nn52–4
Nicopolis, Battle of, 31
Nihāyat al-idrāk fī dirāyat al-aflāk. See al-Shīrāzī
Nihil (Nitzka), Johann, 82
Niksārī, Muḥyī al-Dīn, 258n77
al-Nīsābūrī, Niẓām al-Dīn, 147, 258n77; Tawḍīḥ al-Tadhkira, 192
Nitzka, Johann. See Nihil
Novara, Domenico Maria, 20, 101–2
Nuremberg, 82, 98–101, 241n97
obliquity of ecliptic, variation of, 172, 183–4
observation/s, 80, 84, 90–1, 98, 100– 1, 108–9, 241; astronomical, importance of, 76; facts of, should not be denied, 65; improvements/new values of, 149–50, 153–4, 250n7, 251–2n15. See also Marāgha, Observatory; Samarqand, Madrasa and Observatory
Ockham, William of: and conceptions of mathematics, 67; and moderni, 59
orb (shell of aether): aetherial, 48–9; axes of, 30; cavity of, containing epicycle or planet, 52; deferent, 50; of Earth (“our orb”), 49; falak in Arabic, 52; lower orb obeys higher orb, 53; ninth orb (posited by Ptolemy), 71; on the number in Albert of Saxony and Pierre d’Ailly, 54; partial, 83–4, 238n72 (“monstrosity of”); physical (three-dimensional), 47; relative sizes in Copernicus, 106; rigid, 51–2; solid, 164, 171–2, 174; three-part, in Peurbach’s Theoricae novae planetarum, 50, 74; unequal thickness, 50; uniform circular motion of, 163, 195. See also astronomy; deferent; dirigent orb; eccentrics; epicycles; inclined orb; parecliptic orb; spheres; Ṭūsī-couple, enclosing/ maintaining orb in
Oresme, Nicole, 165, 177, 186–7, 190; physicality of planet, 266n39; Ṭūsī-couple in Questiones de spera, 177–81
Osiander, Andreas, 137–8; introduction to De revolutionibus, 58
Otranto, 31
Ottoman Empire, 29, 31–41, 221nn6–7. See also Ottomans; scholarly pipelines
Ottomans, 88–9, 94, 148–9, 154, 156–7, 190–1, 193–4, 221n10, 222n11, 222n14, 224n48, 250n4, 254n37, 258n81. See also Bāyazīd I; Bāyazīd II; madrasa, under the Ottomans; Mehmed II; Murad II; Ottoman Empire; Suleyman the Magnificent
Oxford, 86
Padua, 5–6, 206, 208–10, 256n63, 278n62; University of, 93, 210, 279n68. See also Aristotle/ Aristotelian philosophy; Averroism; Paduan Aristotelians
Paduan Aristotelians, 5
Palatine collection, 270n93
Panofsky, Erwin, 245n29
Papal Schism, 35
parallels postulate. See Euclid
parecliptic orb (mumaththal), 166–7
Paris, University of, 20
Park, Katherine, 111–12
Parmenides, and denial of motion, 65
Paul II (pope), 87, 94
Paul III (pope), 24
Pavia, 93
Peckham, John, 86
Persian as language of astronomy, 163, 165, 175–6, 187
Persian Tables, 93, 213, 280n90, 281n101
Persians, 39; refusal to teach astronomy to foreigners, 188, 265n30
Perspectiva communis, 87
petitiones. See postulates; principles
Petrarch, Francesco, 17, 25, 26, 221n7, 236n44
Petreius, Johannes, 100
Peurbach, Georg, 8, 39–41, 45–6, 51, 58, 81, 111, 131, 133, 135, 182, 186, 191, 271n111, 272n2, 279n77; astrologer to Nihil, 82; cited as vir dignus by Głogów, 230n100; commissioned to write an epitome of Almagest, 89; principles of Theoricae novae planetarum according to Brudzewo, 53; theoricae descended from Ibn al-Haytham’s On the Configuration, 55; theoricae (figures) as principles in Theoricae novae planetarum, 49–50; Theoricae novae planetarum, 1, 6, 57–8, 82–4, 96, 98, 159 (fig. 6.2), 234n17, 234n19, 234n22, 261n108; Theoricae novae planetarum printed by Regiomontanus, 84, 98; travel in Italy, 82. See also Epitome of the Almagest
phenomena, 111–12, 116, 120, 135, 140
Piccolomini, Aeneas Silvius. See Pius II
Pico della Mirandola, Giovanni, 23, 30, 221n6, 210, 278n67
Pierre d’Ailly, questions on the Sphere,
Pingree, David, 189, 281n99
Pius II (Aeneas Silvius Piccolomini), 32–41, 93, 193
Planetary Hypotheses. See Ptolemy
planets: apparent size, 84, 92; brightness, 85–7, 108; criteria for order, 97, 106; distances, 84–7, 92, 102, 106, 108; inferior, 86, 92, 97, 102– 4, 106–7; linkage to Sun, 97; order, 86, 96–7, 102, 106–7, 239nn74–5, 239–40n78; sex of, 97; speed-distance relation, 239n74; superior, 92, 97, 102–3, 106. See also Copernicus; De revolutionibus orbium coelestium; Regiomontanus; individual planets
Plato, 34, 68, 87–9, 235n37, 244n9; Platonic notions, 67, 122, 244n9, 246n44
Pletho, George Gemistos, 88, 94, 213, 224n57, 280n94, 280–1n95
Poland, 36, 101, 210
Poliziano, Angelo, 17, 23, 26–7
Pomata, Gianna, 111–12
Pomponazzi, Pietro, 21
Possevino, Antonio, 20
possibility: natural vs supernatural, 65; physical vs logical, 65
Postel, Guillaume, 30, 221n6 postulates (petitiones), in the Commentariolus, 48–9, 55
precession, 84–6, 92, 98, 100, 108, 172, 182–4. See also eighth sphere/ orb; trepidation
predictions, 145, 251–2n15. See also tables
Pressburg. See Bratislava
principles, 48; based on experience, 53, 61–2, 228n44; in Commentariolus, 48–9; in determinations of scholastic questions, 54; for Ibn al-Haytham’s On the Configuration, 227n27; Ibn al-Haytham on reconsideration of in optics, 66; proper vs common, 68–9; search for new, 54–5. See also postulates
printing: Epitome of the Almagest, 101; printing prospectus, 89, 92, 95, 98, 237n54, 240n82; Ratdolt’s compendia, 84; Regiomontanus’s press, 84, 97–100; techniques of, 99–100
Proclus, 91–2, 237n49, 239n75, 248n98; commentary on Euclid’s Elements, 185; and Ṭūsī-couple, 184–6
Prosdocimo de’ Beldomandi, 239n76
prosneusis point, 168, 172, 187, 196, 264n18
Protagoras, 119–20
Protestant Reformation, 39
Prowe, Leopold, 185
Ptolemy, Claudius, 29, 30, 39, 46, 114–15, 131, 135, 137–9, 195, 199–201, 205, 210–11, 214, 275n25, 279n82, 280n93; alternatives to Ptolemaic models, 4, 6, 8, 146, 149, 151, 161–2, 165–6, 185, 194–5, 197, 216n18; astronomical tradition, 6; Copernicus on, 54; criticism of, 163, 195–6, 271n111; influence on Islamic astronomers, 151–4, 157–60; latitude theory, 163, 168–70, 187, 264n16, 264n19; longitude models, 163, 166, 182; mathematical astronomy in, 47; and ninth orb, 71; not source of Peurbach’s Theoricae novae planetarum, 55–6; physicalization of models, 8–9, 215–16n11; Planetary Hypotheses, 6, 46, 51, 83, 151–2, 163; violations of accepted physics, 4–6, 8, 217n21. See also Alfraganus; Almagest; equant points or circles; hayʾa; Ibn al-Haythām; al-Jaghmīnī; Regiomontanus; al-Ṭūsī
Qāḍīzāde al-Rūmī, 147–9, 154, 191, 253n31, 254n44, 254–5n45, 255n46, 259n92; definition of “astronomy,” 150; Mulakhkhaṣ commentary, 154, 160 (fig. 6.3), 250n4, 254n37, 254n44, 258n77, 259n85, 259n87
Al-Qānūn al-Masʿūdī. See al-Bīrūnī
qibla, 144–5
Qūhistān, 163–4
quies media, 172–4, 177, 181, 264n22. See also Aristotle/Aristotelian philosophy
Quintilian, 25, 220n42, 236n44
al-Qūnawī, Ṣadr al-Dīn, 250n4
Qushjī, ʿAlī, 8, 30, 103, 191, 242n105, 259n92, 270n94, 272n3; and Aristotelian physics, 146–7, 154; on possibility of Earth’s rotation, 146–7, 154; transforming epicyclic into eccentric models, 154, 156–7
Ragep, F. Jamil, 30, 103, 198, 205, 242n105, 247n87; on Planetary Hypotheses and On the Configuration, 56
Randall, John H., Jr, 5
Ratdolt, Erhard, 84, 240n83
realism, 80, 83, 96. See also fictionalism
referencing practices, 271n112
Regiomontanus, Johannes (Johannes Müller von Königsberg), 8–10, 29, 39–41, chapter 4, 186, 190–1, 200, 202–3, 204 (fig. 8.2), 207–8, 211– 12, 264n19, 271n111, 272n2, 275n23, 276n34, 276n37, 280n84; astrarium, 100; astrologer, 82; and Bianchini, 92, 96, 101, 131, 133, 212; calendars, 100; and Copernicus, 135; copied Peurbach’s Theoricae novae planetarum, 83; crisis in astronomy, 96–7; critical outlook, 96–7; criticizes Almagest as two-dimensional, 108; criticizes partial orbs, 238n72; critique of Cusa, 123, 125, 130, 132–3; Disputationes, 82, 236n45; eccentric models, 4; Ephemerides, 98–100; ephemerides of 1448, 82; experiential observer, 111; his Dialogus cited by Głogów, 230n100; and homocentric astronomy, 78, 83, 85–7, 93–6, 108, 216n18, 238n72, 261n115; in Hungary, 94, 97, 100; inquiry into foundations, 97; letter on al-Biṭrūjī, 202; “Letter to Vitéz,” 86, 91, 96; nonuniform homocentric Sun, 235n27; Nuremberg press, 84, 98– 100; observations, 100–1, 131–2; Oratio, 93, 132; planetary order uncertain, 97, 102; and “positive mathematics,” 133; as printer, 99– 100; printing prospectus, 89, 92, 95, 98, 237n54, 240n82; Problemata Almagesti, 92, 236n46, 237n58, 241n97; quadrature of the circle, 129, 131; reformer, 80; relation to Qushjī, 242n105; reprehends Gerard of Cremona, 230n100; social network, 113, 120, 134; Tabula primi mobilis, 97, 132, 134; Tabulae directionum, 97; and Toscanelli, 129–30; university studies, 81; university teaching, 87, 132, 256n63; unresolved tensions in astronomical modelling, 96–7. See also Bessarion; Defensio Theonis contra Georgium Trapezuntium; Epitome of the Almagest; Walther
regressus, in demonstration, 62
retrograde motion, 97, 102, 107–8. See also anomaly, second
Rheticus, Georg Joachim, 22, 48, 80, 108, 185, 233n4, 241n97
Rhodes, 31
Richard of Wallingford, on work of astronomers, quoted by Brudzewo, 47
Rivier, Petrus, 278n62
Roder, Christian, 132, 240n79
Rogier van der Weyden, 139
Roman Catholic Church, 35, 37, 39, 221n6
Roman Empire, 34–5, 37
Rome, 9–10, 93–4, 100, 133, 189, 210, 270n93
Rose, Paul L., 245n13
Rosen, Edward, 3–4, 185, 244n7
Sabra, A.I., 39–40, 201, 251n15, 255n53, 259n93, 260–1n102, 261n103
Saccheri, Giovanni, 189
Sacrobosco, Johannes de, 81, 234n22; On the Sphere of the World, 51, 177; questions of John of Głogów on, 69–70
Saliba, George, 251n12, 255n53, 256n56, 261n110, 263n13, 270n93
Salisbury, John of, 25
Samarqand, 38; astronomical works produced at, 147, 153, 160 (fig. 6.3); Madrasa and Observatory, 143–4, 147–9, 153–7, 249n1, 250n7, 252n17, 253n33, 255n46, 255n50, 259n92
Samarqandī, Shams al-Dīn, Ashkāl al-taʾsīs, 149
Sandivogius of Czechel, 186, 268n74
Sanskrit, translation into, 258n81
Santinello, Giovanni, 244n10
Saturn, 235n28, 242–3n109
saving the phenomena, 58, 110–11, 114, 152. See also appearances; fictionalism; realism
Saxony, 36
Sayyid AbūṬālib, 147
Scandinavia, 34
Schemata of the Stars. See Chioniades
Schoener, Johannes, 100, 247n86
scholarly pipelines: between Islam and Europe, 253–4n36, 260n101, 261n103; within Islamic lands, 143, 147–50, 156–7, 254n39, 255n46; between Ottoman court and Italy, 156–7. See also Jews as scientific intermediaries/transmitters; travellers
scholastic form, and lists of suppositions for determinations, 53, 66
schools, Vienna citizens’ school, 82. See also madrasa
science: antiqui and moderni, 58–67; a priori and a posteriori, 62; autonomy of scientific disciplines in Aristotle and Averroes, 47–8; fallibility of, 68–9; quia and propter quid, 62
science of configuration. See hayʾa
science of the stars. See ʿilm al-nujūm
Scot, Michael, 85
Segonds, Alain-Philippe, 216n16
Seneca, Lucius Annaeus, 26
Serbia, 35
sex as criterion for planetary order, 97
Shams Bukharos. See Shams al-Dīn al-Bukhārī
Shams al-Dīn al-Bukhārī (Shams Bukharos, Shams al-Dīn al-Wābkanawī), 176, 187
Shams al-Dīn al-Wābkanawī. See Shams al-Dīn al-Bukhārī
Shank, Michael, 200, 216n15, 239n78, 275nn23–4
Sharbiṭ ha-Zahab, 213, 280n90
al-Shīrāzī, Quṭb al-Dīn, 172–3, 177, 181, 195, 264n22; Faʿalta fa-lā talum, 192; hayʾa works, 147–50, 154; Ikhtiyārāt-i Muẓaffarī, 192; Nihāyat al-idrāk fī dirāyat al-aflāk, 192, 270n94; Al-Tuḥfa al-shāhiyya fī al-hayʾa, 172, 192, 270n94; view of discipline of hayʾa, 259n87
al-Shīrwānī, Fatḥ Allāh, 147–8, 258n77; Sharḥ al-Tadhkira, 192
Al-Shukūk ʿalā Baṭlamyūs. See Ibn al-Haytham
Sibṭ al-Māridīnī, 157, 254n39
Siena, 32
sign, arguments from, in Głogów on Sacrobosco’s Sphere, 69
Simonetto da Camerino (fra), 35
Simplicius of Cilicia, 134
Sinān Pāshā, 258n77
Sinisgalli, Rocco, 245n24
skepticism, vs critical realism, 64
Smith, Adam, 19; Wealth of Nations, 19
Soncino, Gershom, 209
Spain, 38, 87, 250n6; Christian, 189, 194, 199; route for Ṭūsī-couple, 189–90
species, sensible and intelligible, 68
spheres (kura), 82–3, 162; vs circles, 96, 108; collisions impossible, 93, 164, 262n9; concentric, 52, 82, 84, 86, 92–3; contrary, 85–6, 108; counteracting, 84, 235n28; in homocentric system, 86; large (al-kabīra) and small (al-ṣaghīra) of Ṭūsī-couple, 165, 167–8, 172; motion in same direction, 85; order of, 86, 96–7, 102, 106–7, 239nn74–5, 239–40n78; physical, 83–5, 99, 234n19; reality of, 83, 236n47; sizes of, 102, 106, 234n19; uniform vs nonuniform motion of, 84, 99. See also Aristotle/Aristotelian philosophy; astronomy; al-Biṭrūjī; Campanus of Novara; Copernicus; eighth sphere/orb; Langenstein; orb; Peurbach; Regiomontanus; Sacrobosco; Sun
stars, twinkling of, 49
subalternation, of sciences to each other, 60, 68; astronomy not subalternate to natural philosophy for moderni, 60, 228n51
Suger of St Denis (abbot), 117–18, 245n24
Suleyman the Magnificent (Ottoman sultan), 222n15
Summers, David, 245n18
Sun: imbedded in its sphere, 83; linked with features of planetary models, 97; mean, 97, 102–8; order among planets, 97, 102, 106–7; parallax, 235n34; relation to retrograde motion, 102; uniform vs nonuniform motion of its sphere, 102, 104, 235n27. See also Copernicus; distance; motion; planets
sundial, 100
Swerdlow, Noel, 4, 7, 30, 45–6, 86, 90, 102–3, 106, 108, 114, 131–2, 183–5, 189, 191, 194, 199, 202–3, 206, 215–16n11, 216–17n20, 241n100, 243n111, 243n1, 253n25, 255n48, 262n2, 267n61, 272n4, 276nn34–5, 277n50
Syria, 38, 149. See also Mamluks
tables, 86, 100; Bianchini’s, 92; Tabulae directionum, 97, 101; Tabulae eclypsium, 233n9; Tabula primi mobilis, 97, 132, 238n72; Toledan, 50, 269n90. See also Alfonsine Tables; ephemerides; Persian Tables; zīj
Tabrīz, 153, 172, 187, 189, 199, 213
Al-Tabṣira fīʿilm al-hayʾa. See al-Kharaqī, hayʾa works
Al-Tadhkira fīʿilm al-hayʾa (Memoir on Astronomy), 51, 147–50, 153, 157, 164–5, 176, 187–8, 204, 206, 256n58, 258n77, 261n108, 270n93, 276n40, 279n77; lunar model in, 165–8; Ṭūsī-couple in, 166–7, 169, 171, 178, 181–3, 192
Al-Tafhīm li-awāʾil ṣināʿat al-tanjīm. See al-Bīrūnī
Taḥrīr al-Majisṭī (Recension of the Almagest). See al-Ṭūsī
Tajrīd al-ʿaqāʾid. See al-Ṭūsī
Tannenberg, Battle of, 36
Ṭāshkubrīzāde, Aḥmad ibn Muṣṭafā, 148, 254n37
Taub, Liba, 245n17
Teutonic Knights, 36
Thābit ibn Qurra, 131, 182, 255n51; mentioned by Brudzewo, 77
Theodosius, 255n51
Theon of Alexandria, 88, 91, 94–5; Bessarion conflates with Theon of Smyrna, 237n50. See also Defensio Theonis contra Georgium Trapezuntium; Regiomontanus
Theon of Smyrna, 91, 239n75; Bessarion conflates with Theon of Alexandria, 237n50
theoricae (figures): of axes and poles, 56; complementary, 47; connotations of term, 56; mathematical (circles and lines), 47, 57; used as principles or postulates, 49–50
Theorica planetarum, 99, 108; genre of, 76; old, 51; Theorica planetarum communis (anon.), 82–4, 90, 93, 96, 98–9, 234n19, 234n22. See also Brudzewo; Campanus of Novara; intelligence; orb; Peurbach, Theoricae novae planetarum; Ptolemy
Tignosi, Niccolò, 41
timekeeper (muwaqqit), 146, 254n39. See also time reckoning
time reckoning, science of (ʿilm almīqāt), 144–6, 253n31, 258n80. See also timekeeper (muwaqqit)
Tīmūrids, 154, 250n3, 258n81, 259n92
Toruń, 197
Toscanelli, Paolo, 10, 111; critique of Cusa, 126, 129–30, 133; observations, 131; social network, 113, 121, 125
translations: from Arabic to Latin, cessation of, 47; from Persian to Greek, 176, 187. See also Hebrew translations; Latin translations of hayʾa works
transmission: skeptics, 267n60. See also Alfonso X (the Wise) of Castile; Byzantium; Hebrew translations; Ibn al-Haytham; Jews as scientific intermediaries/transmitters; Latin translations of hayʾa works; scholarly pipelines; translations; travellers; Ṭūsī-couple
Transoxiana, 148
Transylvania, 35
Trapezuntius, Georgius. See George of Trebizond
travellers: between Europe and Islamdom, 187, 190, 194, 221n10, 222n11, 222nn14–15, 270nn101– 2; travelling scholars, 9–10. See also scholarly pipelines
Trebizond, 87–8, 188, 191. See also George of Trebizond
trepidation, 172, 182–3. See also precession
trigonometry, history of, 193
Tucci, Roberta, 244n7
Al-Tuḥfa al-shāhiyya fī al-hayʾa. See al-Shīrāzī
Tūn, 164, 197, 262n8
al-Turkmānī, Kamāl al-Dīn, 254n37
Turks. See Ottoman Empire
al-Ṭūsī, Naṣīr al-Dīn, 8, 30, 149–50, 158, 161, 163–6, 194–6, 199, 205, 207, 255n45, 272n1, 277n50, 281n101; definition of “discipline of hayʾa,” 255n54; and eccentrics vs concentrics with epicycles, 73, 231n115; and latitude theory, 163, 168–72, 269n92; recensions (taḥārīr) project, 150, 253n33; Taḥrīr al-Majisṭī (Recension of the Almagest), 151, 157, 169, 176, 192, 263n13, 277n49; Tajrīd al-ʿaqāʾid, 146–7; Zīj-i Īlkhānī, 213; Al-Zubda, 150. See also Euclid, pseudo-Ṭūsī’s Commentary on Euclid’s Elements; hayʾa; lunar models; Mercury; Muʿīniyya Treatise; Muʿīniyya Treatise, appendix to (i.e., Dhayl or Ḥall); Al-Tadhkira fīʿilm al-hayʾa; Ṭūsī-couple
Ṭūsī-couple, 8, 20, 25, 28, 149, 156, 161, 173–4, 182, 198–9, 205–7, 214, 217n21, 261n114, 272n1, 273n7, 274n11, 276n40, 277n49, 277n51, 281n101; curvilinear versions with inclined (oblique) axes, 162, 168–73, 182–4, 196–7, 199, 204, 264n18, 276n40, 277n49; enclosing/maintaining orb in, 162, 165, 167, 172, 179, 184, 266n51; evolution of, 165–6, 168–9, 171–4, 196; hypothesis of the large and small spheres, 174; manuscript evidence of, 191–2; “motion along the width of a circle,” 185, 197; physicalized versions of, 164–6, 171–2, 178–81, 184, 197, 266n41; planar, 277n51; Sanskrit translation of, 264n23; transmission to other cultural contexts, 174–6, 193–7; two-equal-circle version (rectilinear with parallel axes), 162, 168–71, 182–4, 197, 263n13, 268n77; two-unequal-circle version (rectilinear with parallel axes), 162–6, 170, 172, 177–8, 187–8; versions of, 161–72, 262n2. See also Amico; Byzantium; Copernicus; Fracastoro; Ibn Naḥmias, double-circle hypothesis; Oresme; Proclus; Spain; spheres; Al-Tadhkira; Werner
al-ʿUbaydī, Jalāl al-Dīn Faḍl Allāh, Bayān al-Tadhkira wa-tibyān al-tabṣira, 192, 254n37
ʿulamāʾ, 250n4. See also madrasa
Ulugh Beg, 38, 143–5, 147, 149, 153– 4, 249n1, 250n3, 251–2n15, 255n50, 259n92. See also Samarqand; zīj
Umayyad Mosque, 146, 254n39
ʿUmda li-ūlī al-albāb. See al-Kharaqī, hayʾa works
al-ʿUrḍī, Muʾayyad al-Dīn, 148–9, 195, 253n33, 270n94
Uzielli, Gustavo, 248n95
Uzun Hasan, 37, 223n36, 224n48
vacuum, 57, 65, 93, 227n27, 239n74
Valla, Georgio, 244n7
Varna, Crusade of, 31, 36, 222n21, 223n33
Venice/Veneto, 32, 84, 88–9, 100, 102, 190, 203, 209; Biblioteca Nazionale Marciana, 88; Senate, 185
Venus, 4, 92, 97, 106–7, 157, 191; large epicycle, 235n34; order inverted, 86, 239nn74–5, 239n77; parallax, 239nn74–5; “recorded” above Mercury, 239n74; variation in brightness, 235n34
Versor, John, his questions on Posterior Analytics, 68
Vesel, Matjaž, 267n61
Veselovsky, Ivan Nikolayevich, 184–5
Vienna, 31, 39, 40, 81, 84, 86–7, 89, 92, 99–101, 191, 193; citizens’ school, 83; University of, 81–2, 84
Vitéz, János, 86, 94, 97–8, 233–4n16; letter to, 91, 96
Vladislas IV (king of Hungary), 223n33
volvelles, 100, 240n88
Wājidiyya Madrasa (Kütahya), 149. See also madrasa Wallerstein, Immanuel, 18
Walther, Bernard, 100–1, 111, 241n97
Werner, Johannes, 241n97; linear harmonic motion, 183; On the Motion of the Eighth Sphere, 49, 182; and Ṭūsī-couple, 182–3
West, the, 38
Westman, Robert, 5–6, 25, 110, 216n16, 217n21, 239–40n78, 270–1n106
Wittenburg interpretation, 58
Wolack, Gottfried, 240n79
Xerxes, 34
al-Yahūdī, Ibrāhīm (ʿAbd al-Salām al-Daftarī), 209, 278n58
year, 106; sidereal, 108; tropical, 108. See also Sun
Yemen, 258n74
Zabarella, Giacomo, on regressus, 62
Al-Zīj al-Sanjarī (The Sanjarī Astronomical Handbook), 213
zīj (astronomical handbook), 144–6, 251nn9–10; Shārḥ-i Zīj-i Ulugh Beg, 154; Ulugh Beg’s Zīj, 144, 153–4, 251n11
Al-Zubda. See al-Ṭūsī