201:) held that the stars, Sun, Moon, and planets are all made of fire. But whilst the stars are fastened on a revolving crystal sphere like nails or studs, the Sun, Moon, and planets, and also the Earth, all just ride on air like leaves because of their breadth. And whilst the fixed stars are carried around in a complete circle by the stellar sphere, the Sun, Moon and planets do not revolve under the Earth between setting and rising again like the stars do, but rather on setting they go laterally around the Earth like a cap turning halfway around the head until they rise again. And unlike Anaximander, he relegated the fixed stars to the region most distant from the Earth. The most enduring feature of Anaximenes' cosmos was its conception of the stars being fixed on a crystal sphere as in a rigid frame, which became a fundamental principle of cosmology down to Copernicus and Kepler.
579:
closer to the apparent sense of the Qur'anic verses regarding the celestial orbits." However, al-Razi mentions that some, such as the
Islamic scholar Dahhak, considered them to be abstract. Al-Razi himself, was undecided, he said: "In truth, there is no way to ascertain the characteristics of the heavens except by authority ." Setia concludes: "Thus it seems that for al-Razi (and for others before and after him), astronomical models, whatever their utility or lack thereof for ordering the heavens, are not founded on sound rational proofs, and so no intellectual commitment can be made to them insofar as description and explanation of celestial realities are concerned."
388:
110:, they presumed that each planetary sphere was exactly thick enough to accommodate them. By combining this nested sphere model with astronomical observations, scholars calculated what became generally accepted values at the time for the distances to the Sun: about 4 million miles (6.4 million kilometres), to the other planets, and to the edge of the universe: about 73 million miles (117 million kilometres). The nested sphere model's distances to the Sun and planets differ significantly from modern measurements of the distances, and the
761:'s tabulated distances of the comet of 1577, which passed through the planetary orbs, led Tycho to conclude that "the structure of the heavens was very fluid and simple." Tycho opposed his view to that of "very many modern philosophers" who divided the heavens into "various orbs made of hard and impervious matter." Edward Grant found relatively few believers in hard celestial spheres before Copernicus and concluded that the idea first became common sometime between the publication of Copernicus's
708:
244:
Eudoxus and
Callippus qualitatively describe the major features of the motion of the planets, they fail to account exactly for these motions and therefore cannot provide quantitative predictions. Although historians of Greek science have traditionally considered these models to be merely geometrical representations, recent studies have proposed that they were also intended to be physically real or have withheld judgment, noting the limited evidence to resolve the question.
270:
258:
whereas in the models of
Eudoxus and Callippus each planet's individual set of spheres were not connected to those of the next planet. Aristotle says the exact number of spheres, and hence the number of movers, is to be determined by astronomical investigation, but he added additional spheres to those proposed by Eudoxus and Callippus, to counteract the motion of the outer spheres. Aristotle considers that these spheres are made of an unchanging fifth element, the
36:
821:
487:, he recalculated the distance of the planets using parameters which he redetermined. Taking the distance of the Sun as 1,266 Earth radii, he was forced to place the sphere of Venus above the sphere of the Sun; as a further refinement, he added the planet's diameters to the thickness of their spheres. As a consequence, his version of the nesting spheres model had the sphere of the stars at a distance of 140,177 Earth radii.
375:. In antiquity the order of the lower planets was not universally agreed. Plato and his followers ordered them Moon, Sun, Mercury, Venus, and then followed the standard model for the upper spheres. Others disagreed about the relative place of the spheres of Mercury and Venus: Ptolemy placed both of them beneath the Sun with Venus above Mercury, but noted others placed them both above the Sun; some medieval thinkers, such as
660:
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781:, which accounted for the spheres' measured astronomical distance. In Kepler's mature celestial physics, the spheres were regarded as the purely geometric spatial regions containing each planetary orbit rather than as the rotating physical orbs of the earlier Aristotelian celestial physics. The eccentricity of each planet's orbit thereby defined the
681:). Although Copernicus does not treat the physical nature of the spheres in detail, his few allusions make it clear that, like many of his predecessors, he accepted non-solid celestial spheres. Copernicus rejected the ninth and tenth spheres, placed the orb of the Moon around the Earth, and moved the Sun from its orb to the center of the
608:, a historian of science, has provided evidence that medieval scholastic philosophers generally considered the celestial spheres to be solid in the sense of three-dimensional or continuous, but most did not consider them solid in the sense of hard. The consensus was that the celestial spheres were made of some kind of continuous fluid.
412:, used the Ptolemaic model of nesting spheres to compute distances to the stars and planetary spheres. Al-Farghānī's distance to the stars was 20,110 Earth radii which, on the assumption that the radius of the Earth was 3,250 miles (5,230 kilometres), came to 65,357,500 miles (105,182,700 kilometres). An introduction to Ptolemy's
631:
such as motive souls or impressed forces. Most of these models were qualitative, although a few incorporated quantitative analyses that related speed, motive force and resistance. By the end of the Middle Ages, the common opinion in Europe was that celestial bodies were moved by external intelligences, identified with the
877:
1484:
Bk1.10 Copernicus claimed the empirical reason why Plato's followers put the orbits of
Mercury and Venus above the Sun's was that if they were sub-solar, then by the Sun's reflected light they would only ever appear as hemispheres at most and would also sometimes eclipse the Sun, but they do neither.
578:
about whether the celestial spheres are real, concrete physical bodies or "merely the abstract circles in the heavens traced out… by the various stars and planets." Setia points out that most of the learned, and the astronomers, said they were solid spheres "on which the stars turn… and this view is
475:
sought to explain the complex motions of the planets without
Ptolemy's epicycles and eccentrics, using an Aristotelian framework of purely concentric spheres that moved with differing speeds from east to west. This model was much less accurate as a predictive astronomical model, but it was discussed
182:
wholly encompassing the Earth, which had disintegrated into many individual rings. Hence, in
Anaximanders's cosmogony, in the beginning was the sphere, out of which celestial rings were formed, from some of which the stellar sphere was in turn composed. As viewed from the Earth, the ring of the Sun
177:
in the early 6th century BC. In his cosmology both the Sun and Moon are circular open vents in tubular rings of fire enclosed in tubes of condensed air; these rings constitute the rims of rotating chariot-like wheels pivoting on the Earth at their centre. The fixed stars are also open vents in such
331:
embedded in the deferent, with the planet embedded in the epicyclical sphere/slice. Ptolemy's model of nesting spheres provided the general dimensions of the cosmos, the greatest distance of Saturn being 19,865 times the radius of the Earth and the distance of the fixed stars being at least 20,000
630:
Medieval astronomers and philosophers developed diverse theories about the causes of the celestial spheres' motions. They attempted to explain the spheres' motions in terms of the materials of which they were thought to be made, external movers such as celestial intelligences, and internal movers
243:
modified this system, using five spheres for his models of the Sun, Moon, Mercury, Venus, and Mars and retaining four spheres for the models of
Jupiter and Saturn, thus making 33 spheres in all. Each planet is attached to the innermost of its own particular set of spheres. Although the models of
105:
are viewed as the paths of those planets through mostly empty space. Ancient and medieval thinkers, however, considered the celestial orbs to be thick spheres of rarefied matter nested one within the other, each one in complete contact with the sphere above it and the sphere below. When scholars
942:
vividly portrays the celestial spheres as a "great machine of the universe" constructed by God. The explorer Vasco da Gama is shown the celestial spheres in the form of a mechanical model. Contrary to Cicero's representation, da Gama's tour of the spheres begins with the
Empyrean, then descends
257:
developed a physical cosmology of spheres, based on the mathematical models of
Eudoxus. In Aristotle's fully developed celestial model, the spherical Earth is at the centre of the universe and the planets are moved by either 47 or 55 interconnected spheres that form a unified planetary system,
929:, employed the same motif. He drew the spheres in the conventional order, with the Moon closest to the Earth and the stars highest, but the spheres were concave upwards, centered on God, rather than concave downwards, centered on the Earth. Below this figure Oresme quotes the
222:
proposed that the body of the cosmos was made in the most perfect and uniform shape, that of a sphere containing the fixed stars. But it posited that the planets were spherical bodies set in rotating bands or rings rather than wheel rims as in
Anaximander's cosmology.
776:
considered the distances of the planets and the consequent gaps required between the planetary spheres implied by the Copernican system, which had been noted by his former teacher, Michael Maestlin. Kepler's Platonic cosmology filled the large gaps with the five
319:, his geometrical model achieved greater mathematical detail and predictive accuracy than had been exhibited by earlier concentric spherical models of the cosmos. In Ptolemy's physical model, each planet is contained in two or more spheres, but in Book 2 of his
121:
Albert Van Helden has suggested that from about 1250 until the 17th century, virtually all educated Europeans were familiar with the Ptolemaic model of "nesting spheres and the cosmic dimensions derived from it". Even following the adoption of Copernicus's
685:. The planetary orbs circled the center of the universe in the following order: Mercury, Venus, the great orb containing the Earth and the orb of the Moon, then the orbs of Mars, Jupiter, and Saturn. Finally he retained the eighth sphere of the
623:, which maintained that all physical effects were caused directly by God's will rather than by natural causes. He maintained that the celestial spheres were "imaginary things" and "more tenuous than a spider's web". His views were challenged by
494:
began to address the implications of the rediscovered philosophy of Aristotle and astronomy of Ptolemy. Both astronomical scholars and popular writers considered the implications of the nested sphere model for the dimensions of the universe.
363:. In more detailed models the seven planetary spheres contained other secondary spheres within them. The planetary spheres were followed by the stellar sphere containing the fixed stars; other scholars added a ninth sphere to account for the
888:
Some late medieval figures noted that the celestial spheres' physical order was inverse to their order on the spiritual plane, where God was at the center and the Earth at the periphery. Near the beginning of the fourteenth century
434:
presented independent calculations of the distances to the planets on the model of nesting spheres, which he thought was due to scholars writing after Ptolemy. His calculations yielded a distance of 19,000 Earth radii to the stars.
554:, that it would take 8,000 years to reach the highest starry heaven. General understanding of the dimensions of the universe derived from the nested sphere model reached wider audiences through the presentations in Hebrew by
178:
wheel rims, but there are so many such wheels for the stars that their contiguous rims all together form a continuous spherical shell encompassing the Earth. All these wheel rims had originally been formed out of an original
789:, the cause of planetary motion became the rotating Sun, itself rotated by its own motive soul. However, an immobile stellar sphere was a lasting remnant of physical celestial spheres in Kepler's cosmology.
126:
of the universe, new versions of the celestial sphere model were introduced, with the planetary spheres following this sequence from the central Sun: Mercury, Venus, Earth-Moon, Mars, Jupiter and Saturn.
570:
Philosophers were less concerned with such mathematical calculations than with the nature of the celestial spheres, their relation to revealed accounts of created nature, and the causes of their motion.
704:, and the Moon, and expanding the sphere of stars infinitely to encompass all the stars and also to serve as "the court of the Great God, the habitacle of the elect, and of the coelestiall angelles."
98:), like gems set in orbs. Since it was believed that the fixed stars did not change their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.
2849:
751:
indicated that the comet was beyond Saturn, while the absence of observed refraction indicated the celestial region was of the same material as air, hence there were no planetary spheres.
627:(1339–1413), who maintained that even if the celestial spheres "do not have an external reality, yet they are things that are correctly imagined and correspond to what in actuality".
651:, who was identified with God. Each of the lower spheres was moved by a subordinate spiritual mover (a replacement for Aristotle's multiple divine movers), called an intelligence.
431:
138:
continued to discuss celestial spheres, although he did not consider that the planets were carried by the spheres but held that they moved in elliptical paths described by
527:
cited Al-Farghānī's distance to the stars of 20,110 Earth radii, or 65,357,700 miles (105,183,000 km), from which he computed the circumference of the universe to be
239:
for all the planets, with three spheres each for his models of the Moon and the Sun and four each for the models of the other five planets, thus making 26 spheres in all.
454:, al-Haytham's presentation differs in sufficient detail that it has been argued that it reflects an independent development of the concept. In chapters 15–16 of his
943:
inward toward Earth, culminating in a survey of the domains and divisions of earthly kingdoms, thus magnifying the importance of human deeds in the divine plan.
869:, which included a discussion of the various schools of thought on the order of the spheres, did much to spread the idea of the celestial spheres through the
2000:(Frankfurt a. d. Oder, 1576), quoted in Peter Barker and Bernard R. Goldstein, "Realism and Instrumentalism in Sixteenth Century Astronomy: A Reappraisal",
909:
Heaven, where he comes face to face with God himself and is granted understanding of both divine and human nature. Later in the century, the illuminator of
2958:
861:
describes an ascent through the celestial spheres, compared to which the Earth and the Roman Empire dwindle into insignificance. A commentary on the
307:(fl. c. 150 AD) developed geometrical predictive models of the motions of the stars and planets and extended them to a unified physical model of the
409:
335:
The planetary spheres were arranged outwards from the spherical, stationary Earth at the centre of the universe in this order: the spheres of the
671:
drastically reformed the model of astronomy by displacing the Earth from its central place in favour of the Sun, yet he called his great work
2784:
The General History of Astronomy: Volume 2 Planetary astronomy from the Renaissance to the rise of astrophysics Part A Tycho Brahe to Newton
503:, used the model of nesting spheres to compute the distances of the various planets from the Earth, which he gave as 22,612 Earth radii or
700:(1576). Here he arranged the "orbes" in the new Copernican order, expanding one sphere to carry "the globe of mortalitye", the Earth, the
541:
miles (661,148,316.1 km). Clear evidence that this model was thought to represent physical reality is the accounts found in Bacon's
799:"Because the medieval universe is finite, it has a shape, the perfect spherical shape, containing within itself an ordered variety....
801:"The spheres ... present us with an object in which the mind can rest, overwhelming in its greatness but satisfying in its harmony."
2852:
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Duhem, Pierre. "History of Physics." The Catholic Encyclopedia. Vol. 12. New York: Robert Appleton Company, 1911. 18 Jun. 2008 <
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142:. In the late 1600s, Greek and medieval theories concerning the motion of terrestrial and celestial objects were replaced by
139:
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Johannes Kepler's diagram of the celestial spheres, and of the spaces between them, following the opinion of Copernicus (
673:
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2638:
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are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element (
3456:
2944:
757:'s investigations of a series of comets from 1577 to 1585, aided by Rothmann's discussion of the comet of 1585 and
1011:
701:
2530:
2126:
transl. by William Harris Stahl, New York: Columbia Univ. Pr., 1952; on the order of the spheres see pp. 162–165.
905:, described God as a light at the center of the cosmos. Here the poet ascends beyond physical existence to the
480:
232:
3356:
2653:
At the Threshold of Exact Science: Selected Writings of Annaliese Maier on Late Medieval Natural Philosophy
1317:"The final cause, then, produces motion by being loved, but all other things move by being moved" Aristotle
2039:
Bernard R. Goldstein and Peter Barker, "The Role of Rothmann in the Dissolution of the Celestial Spheres",
1410:
1406:
364:
2171:
edited and translated by A, D. Menut and A. J. Denomy, Madison: Univ. of Wisconsin Pr., 1968, pp. 282–283.
3466:
786:
624:
574:
Adi Setia describes the debate among Islamic scholars in the twelfth century, based on the commentary of
439:
582:
Christian and Muslim philosophers modified Ptolemy's system to include an unmoved outermost region, the
2868:
1847:
259:
95:
1879:
3153:
648:
372:
323:
Ptolemy depicted thick circular slices rather than spheres as in its Book 1. One sphere/slice is the
115:
615:
Adud al-Din al-Iji (1281–1355) rejected the principle of uniform and circular motion, following the
26:"Heavenly spheres" redirects here. For the album by the Studio de musique ancienne de Montréal, see
2629:
Lloyd, G. E. R., "Heavenly aberrations: Aristotle the amateur astronomer," pp. 160–183 in his
1018:
1758:
3148:
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550:
368:
249:
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3168:
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1851:
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1390:
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491:
472:
187:
131:
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1759:"Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey"
719:
In the sixteenth century, a number of philosophers, theologians, and astronomers—among them
3402:
3143:
3093:
3013:
2988:
2433:
1891:
720:
575:
387:
111:
216:
all held that the universe was spherical. And much later in the fourth century BC Plato's
150:, which explain how Kepler's laws arise from the gravitational attraction between bodies.
8:
3173:
3078:
3028:
3003:
2930:
2295:
926:
811:
668:
443:
286:
147:
2437:
2274:
Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds
1895:
1502:, 7.159–65, trans. Bernard R. Goldstein, vol. 1, pp. 123–5. New Haven: Yale Univ. Pr.
590:
and all the elect. Medieval Christians identified the sphere of stars with the Biblical
450:
in terms of nested spheres. Despite the similarity of this concept to that of Ptolemy's
421:
3407:
3321:
2918:
2449:
1923:
1915:
1593:
968:
828:
740:
643:, which moved with the daily motion affecting all subordinate spheres, was moved by an
496:
236:
218:
123:
2505:
743:—abandoned the concept of celestial spheres. Rothmann argued from observations of the
594:
and sometimes posited an invisible layer of water above the firmament, to accord with
3163:
3068:
3023:
2860:
2809:
2743:
2697:
2680:
2663:
2634:
2619:
2598:
2581:
2563:
2557:
2546:
2515:
2495:
2453:
2424:
Grasshoff, Gerd (2012). "Michael Maestlin's Mystery: Theory Building with Diagrams".
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2140:
1993:
1927:
1907:
1855:
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1503:
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that "The heavens declare the Glory of God and the firmament showeth his handiwork."
870:
728:
424:, presented minor variations of Ptolemy's distances to the celestial spheres. In his
67:
2280:, translated and edited by Roger Ariew, Chicago: University of Chicago Press, 1987
1439:
3428:
3381:
3351:
3341:
3290:
3265:
2894:
2441:
2323:
Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance,
1899:
1585:
1469:
Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance,
895:
858:
758:
555:
447:
340:
91:
27:
20:
2655:, edited by Steven Sargent, Philadelphia: University of Pennsylvania Press, 1982.
1440:"The Structure and Function of Ptolemy's Physical Hypotheses of Planetary Motion,"
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3311:
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3178:
3108:
2843:
2691:
2672:
2592:
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of the inner and outer limits of its celestial sphere and thus its thickness. In
773:
736:
595:
559:
183:
was highest, that of the Moon was lower, and the sphere of the stars was lowest.
135:
2202:, in 'The Basic Works of Aristotle' Richard McKeon (Ed) The Modern Library, 2001
1017:
The references used may be made clearer with a different or consistent style of
832:
3239:
3118:
3053:
3033:
2882:
2611:
2472:. Great Books of the Western World. Vol. 16. Chicago, Ill: William Benton.
2445:
2267:
Le Système du Monde: Histoire des doctrines cosmologiques de Platon à Copernic,
1022:
983:
920:
778:
732:
546:
456:
179:
170:
158:
Further information on the causes of the motions of the celestial spheres:
83:
40:
2836:
2830:
2789:
Thoren, Victor E., "The Comet of 1577 and Tycho Brahe's System of the World,"
2052:
Michael A. Granada, "Did Tycho Eliminate the Celestial Spheres before 1586?",
2026:
Michael A. Granada, "Did Tycho Eliminate the Celestial Spheres before 1586?",
1880:"Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science"
102:
3450:
3361:
3346:
3326:
2259:
1911:
978:
973:
958:
910:
901:
837:
693:
644:
640:
327:, with a centre offset somewhat from the Earth; the other sphere/slice is an
263:
2156:
Nicole Oreseme, "Le livre du Ciel et du Monde", 1377, retrieved 2 June 2007.
2137:
The Discarded Image: An Introduction to Medieval and Renaissance Literature,
173:
the ideas of celestial spheres and rings first appeared in the cosmology of
3209:
3058:
2906:
2543:
The Discarded Image: An Introduction to Medieval and Renaissance Literature
1146:
1913/97 Oxford University Press/Sandpiper Books Ltd; see p. 11 of Popper's
724:
707:
605:
2936:
1214:
Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 677–85.
3048:
2993:
2314:
Eastwood, Bruce, "Astronomy in Christian Latin Europe c. 500 – c. 1150,"
938:
806:
754:
524:
483:
proposed a radical change to Ptolemy's system of nesting spheres. In his
379:, placed the sphere of Venus above the Sun and that of Mercury below it.
273:
Ptolemaic model of the spheres for Venus, Mars, Jupiter, and Saturn with
269:
262:. Each of these concentric spheres is moved by its own god—an unchanging
174:
130:
Mainstream belief in the theory of celestial spheres did not survive the
87:
2338:
Planetary Diagrams for Roman Astronomy in Medieval Europe, ca. 800–1500,
1576:
Rosen, Edward (1985). "The Dissolution of the Solid Celestial Spheres".
765:
in 1542 and Tycho Brahe's publication of his cometary research in 1588.
460:, Ibn al-Haytham also said that the celestial spheres do not consist of
35:
3366:
3183:
3128:
3088:
3018:
1597:
663:
Thomas Digges' 1576 Copernican heliocentric model of the celestial orbs
636:
616:
612:
519:
468:
376:
213:
209:
205:
79:
1919:
876:
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3123:
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3043:
3038:
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866:
591:
316:
254:
240:
107:
71:
59:
2806:
Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley
2536:
Great Books of the Western World : 16 Ptolemy Copernicus Kepler
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Great Books of the Western World : 16 Ptolemy Copernicus Kepler
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820:
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1903:
906:
748:
682:
583:
328:
324:
299:
278:
274:
659:
266:, and who moves its sphere simply by virtue of being loved by it.
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3138:
3133:
3083:
3073:
2241:
Theories of the World from Antiquity to the Copernican Revolution
620:
356:
304:
75:
2761:
The Philosophy of the Commentators, 200–600 AD: Volume 2 Physics
3386:
3336:
3285:
3158:
3008:
2831:
Working model and complete explanation of the Eudoxus's Spheres
1616:. Vol. 1. New Haven: Yale University Press. pp. 40–5.
1274:
Larry Wright, "The Astronomy of Eudoxus: Geometry or Physics,"
1184:
For Xenophanes' and Parmenides' spherist cosmologies see Heath
930:
847:
782:
696:, delineated the spheres of the new cosmological system in his
599:
360:
308:
282:
408:
A series of astronomers, beginning with the Muslim astronomer
1979:
Nicholas Jardine, "The Significance of the Copernican Orbs",
1890:(Science in Theistic Contexts: Cognitive Dimensions): 55–57.
1487:
Great Books of the Western World 16 Ptolemy–Copernicus–Kepler
890:
744:
632:
586:
heaven, which came to be identified as the dwelling place of
461:
344:
63:
2594:
From Eudoxus to Einstein—A History of Mathematical Astronomy
2184:, translated by Landeg White. Oxford University Press, 2010.
1842:
The Rise of Early Modern Science: Islam, China, and the West
565:
2468:
Hutchins, Robert Maynard; Adler, Mortimer J., eds. (1952).
2383:
The Scientific Enterprise in Antiquity and the Middle Ages,
686:
392:
352:
336:
2901:
2377:
Grant, Edward, "Celestial Orbs in the Latin Middle Ages,"
545:
of the time needed to walk to the Moon and in the popular
2397:
Planets, Stars, and Orbs: The Medieval Cosmos, 1200–1687,
1998:
Propositiones Cosmographicae de Globi Terreni Dimensione,
587:
426:
348:
2618:
pp. 133–153, Cambridge: Cambridge Univ. Pr., 1968.
114:
is now known to be inconceivably large and continuously
2693:
Early Physics and Astronomy: A Historical Introduction
2381:
78(1987): 153–73; reprinted in Michael H. Shank, ed.,
2297:
History of the Planetary Systems from Thales to Kepler
1543:
1541:
1421:
1419:
231:
Instead of bands, Plato's student Eudoxus developed a
2866:
226:
164:
2754:
Philoponus and the Rejection of Aristotelian Science
2480:
Oxford University Press/Sandpiper Books Ltd. 1913/97
2411:
The Foundations of Modern Science in the Middle Ages
2808:. Chicago and London: University of Chicago Press.
2616:
Aristotle: The Growth and Structure of his Thought,
2341:
Transactions of the American Philosophical Society,
1538:
1454:Francis R. Johnson, "Marlowe's "Imperiall Heaven,"
1416:
371:, and even an eleventh to account for the changing
2660:Astronomies and Cultures in Early Medieval Europe,
2555:
1563:Ibn al Haytham's on the Configuration of the World
1073:
1071:
792:
558:, in French by Gossuin of Metz, and in Italian by
2848:Henry Mendell, Vignettes of Ancient Mathematics:
2791:Archives Internationales d'Histoire des Sciences,
1188:chapter 7 and chapter 9 respectively, and Popper
919:, a translation of and commentary on Aristotle's
3448:
476:by later European astronomers and philosophers.
2863:– Depiction of celestial spheres in a 1613 book
1565:. New York: Garland Publishing. pp. 11–25.
1222:
1220:
1068:
391:The Earth within seven celestial spheres, from
2837:Animated Ptolemaic model of the nested spheres
2545:, Cambridge: Cambridge University Press 1964
2511:From the Closed World to the Infinite Universe
2139:Cambridge: Cambridge Univ. Pr., 1964, p. 116.
2041:The British Journal for the History of Science
1877:
2952:
2113:, vol. 1, book 4.2.3, pp. 514–15 (1630).
884:Paris, BnF, Manuscrits, Fr. 565, f. 69 (1377)
698:Perfit Description of the Caelestiall Orbes …
82:, and others. In these celestial models, the
2733:The Tychonic and Semi-Tychonic World Systems
2677:A History of Ancient Mathematical Astronomy,
1308:Richard McKeon, ed., The Modern Library 2001
1276:Studies in History and Philosophy of Science
1217:
914:
2966:
679:On the Revolutions of the Celestial Spheres
403:
2959:
2945:
2590:
2360:. Chicago: Chicago University Press, 1988
2260:http://www.newadvent.org/cathen/12047a.htm
2228:On the Revolutions of the Heavenly Spheres
1614:Al-Bitrūjī: On the Principles of Astronomy
1560:
1377:
1332:History of Ancient Mathematical Astronomy,
1237:History of Ancient Mathematical Astronomy,
490:About the same time, scholars in European
2772:Translator's Introduction to the Almagest
2696:. Cambridge: Cambridge University Press.
2597:. Cambridge: Cambridge University Press.
2494:(translator Mepham) Harvester Press 1977
2423:
2413:, Cambridge: Cambridge Univ. Pr., 1996.
2237:
2065:Grant, "Celestial Orbs," pp. 185–86.
1756:
1611:
1427:History of Ancient Mathematical Astronomy
1396:Translator's Introduction to the Almagest
1362:
1041:Learn how and when to remove this message
566:Philosophical and theological discussions
479:In the thirteenth century the astronomer
467:Near the end of the twelfth century, the
2562:. Chicago: University of Chicago Press.
2244:. Mineola, NY: Dover Publications, Inc.
2087:Grasshoff, "Michael Maestlin's Mystery".
1878:Ragep, F. Jamil; Al-Qushji, Ali (2001).
1873:
1871:
1831:
1287:G. E. R. Lloyd, "Saving the Phenomena,"
875:
819:
706:
658:
386:
268:
34:
2207:Science of Mechanics in the Middle Ages
1203:Plato's Cosmology: The Timaeus of Plato
517:miles (118,106,130.55 km). In his
499:'s introductory astronomical text, the
438:Around the turn of the millennium, the
58:, were the fundamental entities of the
3449:
2662:Cambridge: Cambridge Univ. Pr., 1998.
2633:Cambridge: Cambridge Univ. Pr., 1996.
2580:Chicago: Univ. of Chicago Pr., 1978.
2399:Cambridge: Cambridge Univ. Pr., 1994.
2043:, 28 (1995): 385–403, pp. 390–91.
1226:Lloyd, "Heavenly aberrations," p. 173.
936:The late-16th-century Portuguese epic
367:, a tenth to account for the supposed
2940:
2504:
2385:Chicago: Univ. of Chicago Pr., 2000.
2374:, University of California Press 1966
2316:Journal for the History of Astronomy,
2054:Journal for the History of Astronomy,
2028:Journal for the History of Astronomy,
1981:Journal for the History of Astronomy,
1868:
1750:
1575:
1443:Journal for the History of Astronomy,
964:History of the center of the Universe
446:presented a development of Ptolemy's
144:Newton's law of universal gravitation
2786:Cambridge: Cambridge Univ. Pr., 1989
2766:
2726:The Physical World of Late Antiquity
2679:3 vols., New York: Springer, 1975.
2464:, American Institute of Physics 1993
2426:Journal for the History of Astronomy
2343:vol. 94, pt. 3, Philadelphia, 2004.
2167:Ps. 18: 2; quoted in Nicole Oresme,
2004:6.3 (1998): 232–58, pp. 242–23.
1837:
1395:
994:
16:Elements of some cosmological models
2538:, Encyclopædia Britannica Inc. 1952
2336:Eastwood, Bruce and Gerd Graßhoff,
2216:University of California Press 1999
2056:37 (2006): 126–45, pp. 132–38.
2030:37 (2006): 126–45, pp. 127–29.
1983:13 (1982): 168–94, pp. 177–78.
831:gaze upon the highest Heaven; from
674:De revolutionibus orbium coelestium
13:
2861:M. Blundevile his exercises, p 282
2775:
2689:
2467:
2209:University of Wisconsin Press 1959
2124:Commentary on the Dream of Scipio,
1345:
747:of 1585 that the lack of observed
689:, which he held to be stationary.
227:Emergence of the planetary spheres
165:Early ideas of spheres and circles
14:
3478:
2824:
2782:R. Taton & C. Wilson (eds.),
2559:The Beginnings of Western Science
2485:The contemporaries of Tycho Brahe
2221:The Cambridge Companion to Newton
186:Following Anaximander, his pupil
160:Dynamics of the celestial spheres
140:Kepler's laws of planetary motion
2924:
2912:
2900:
2888:
2876:
2735:in Taton & Wilson (eds) 1989
2728:Routledge & Kegan Paul, 1962
2290:
2234:Encyclopædia Britannica Inc 1952
1402:History of the Planetary Systems
1401:
1250:History of the Planetary Systems
999:
598:. An outer sphere, inhabited by
2591:Linton, Christopher M. (2004).
2531:Epitome of Copernican Astronomy
2487:in Taton & Wilson (eds)1989
2269:10 vols., Paris: Hermann, 1959.
2191:
2174:
2161:
2150:
2129:
2116:
2111:Epitome of Copernican Astronomy
2103:
2090:
2081:
2068:
2059:
2046:
2033:
2020:
2007:
1986:
1973:
1960:
1947:
1934:
1818:
1805:
1792:
1779:
1737:
1724:
1711:
1698:
1685:
1672:
1659:
1646:
1633:
1620:
1605:
1578:Journal of the History of Ideas
1569:
1554:
1525:
1512:
1492:
1474:
1471:(Leiden: Brill) 2007, pp. 36–45
1461:
1448:
1432:
1384:
1369:
1354:
1337:
1324:
1311:
1304:1073b1–1074a13, pp. 882–883 in
1294:
1281:
1268:
1255:
1242:
1229:
1208:
1195:
1178:
793:Literary and visual expressions
667:Early in the sixteenth century
2803:
2534:(Bks 4 & 5), published in
2358:Kepler's geometrical cosmology
2212:Cohen, I.B. & Whitman, A.
1612:Goldstein, Bernard R. (1971).
1500:On the Principles of Astronomy
1291:28 (1978): 202–222, at p. 219.
1172:See chapter 5 of Heath’s 1913
1166:
1153:
1136:
1123:
1110:
1097:
1084:
1055:
925:produced for Oresme's patron,
654:
382:
39:Geocentric celestial spheres;
1:
3357:Inferior and superior planets
2169:Le livre du ciel et du monde,
1813:Beginnings of Western Science
1800:Beginnings of Western Science
1079:Beginnings of Western Science
882:Le livre du Ciel et du Monde,
602:, appeared in some accounts.
191:
3462:Early scientific cosmologies
2098:Kepler's geometric cosmology
1561:Langermann, Y. Tzvi (1990).
1306:The Basic Works of Aristotle
916:Le livre du Ciel et du Monde
787:Kepler's celestial mechanics
420:, believed to be written by
369:trepidation of the equinoxes
7:
2804:Van Helden, Albert (1985).
2756:London & Ithaca NY 1987
2556:Lindberg, David C. (1992).
2470:Ptolemy, Copernicus, Kepler
1346:Early Physics and Astronomy
946:
692:The English almanac maker,
365:precession of the equinoxes
10:
3483:
3434:Medieval Islamic astronomy
3231:On the Sizes and Distances
2800:in Taton & Wilson 1989
2719:Three Copernican Treatises
2631:Aristotelian Explorations,
2578:Science in the Middle Ages
2576:Lindberg, David C. (ed.),
2446:10.1177/002182861204300104
2238:Crowe, Michael J. (1990).
1848:Cambridge University Press
611:Later in the century, the
315:. By using eccentrics and
291:Theoricae novae planetarum
157:
153:
25:
18:
3424:Medieval European science
3416:
3395:
3304:
3253:
3192:
3154:Sosigenes the Peripatetic
2974:
2742:London: Duckworth, 1988
2076:Planets, Stars, and Orbs,
1968:Planets, Stars, and Orbs,
1955:Planets, Stars, and Orbs,
1942:Planets, Stars, and Orbs,
1826:Planets, Stars, and Orbs,
1787:Planets, Stars, and Orbs,
1641:Planets, Stars, and Orbs,
1458:, 12 (1945): 35–44, p. 39
1142:See chapter 4 of Heath's
373:obliquity of the ecliptic
2842:8 September 2006 at the
2752:Sorabji, Richard, (ed.)
2740:Matter, Space and Motion
2690:Pederson, Olaf (1993) .
2646:The Science of Mechanics
2300:. New York, NY: Cosimo.
2219:Cohen & Smith (eds)
1667:Planets, Stars, and Orbs
1654:Planets, Stars, and Orbs
1378:From Eudoxus to Einstein
1105:Planets, Stars, and Orbs
1063:Planets, Stars, and Orbs
990:
835:'s illustrations to the
770:Mysterium Cosmographicum
713:Mysterium Cosmographicum
473:al-Bitrūjī (Alpetragius)
444:Ibn al-Haytham (Alhacen)
404:Astronomical discussions
19:Not to be confused with
3457:Ancient Greek astronomy
3149:Sosigenes of Alexandria
2968:Ancient Greek astronomy
2776:Hutchins (1952, pp.1–4)
2712:The World of Parmenides
2658:McCluskey, Stephen C.,
2292:Dreyer, John Louis Emil
2002:Perspectives on Science
1148:The World of Parmenides
702:four classical elements
641:outermost moving sphere
551:South English Legendary
101:In modern thought, the
3221:On Sizes and Distances
2768:Taliaferro, R. Catesby
2325:Leiden: Brill, 2007.
1745:Measuring the Universe
1732:Measuring the Universe
1706:Measuring the Universe
1693:Measuring the Universe
1680:Measuring the Universe
1549:Measuring the Universe
1533:Measuring the Universe
1520:Measuring the Universe
1429:, vol. 2, pp. 917–926.
1131:Measuring the Universe
1118:Measuring the Universe
1092:Measuring the Universe
954:Angels in Christianity
915:
885:
843:
842:Canto 28, lines 16–39.
803:
716:
664:
400:
294:
134:. In the early 1600s,
47:
3332:Deferent and epicycle
3261:Antikythera mechanism
2370:Golino, Carlo (ed.),
2226:Copernicus, Nicolaus
2015:From the Closed World
1992:Hilderich von Varel (
1363:Theories of the World
879:
823:
797:
710:
662:
390:
272:
132:Scientific Revolution
103:orbits of the planets
38:
3403:Babylonian astronomy
3094:Hippocrates of Chios
2478:Aristarchus of Samos
2180:Luiz Vaz de Camões,
1289:Classical Quarterly,
1174:Aristarchus of Samos
1144:Aristarchus of Samos
865:by the Roman writer
723:, Andrea Cisalpino,
576:Fakhr al-Din al-Razi
452:Planetary Hypotheses
321:Planetary Hypotheses
313:Planetary hypotheses
264:divine unmoved mover
112:size of the universe
62:models developed by
3174:Theon of Alexandria
2796:Thoren, Victor E.,
2514:. Forgotten Books.
2438:2012JHA....43...57G
2372:Galileo Reappraised
2278:Le Système du Monde
2205:Clagett, Marshall
1896:2001Osir...16...49R
1838:Huff, Toby (2003).
1763:Islam & Science
1719:The Discarded Image
1498:al-Biţrūjī. (1971)
1467:Bruce S. Eastwood,
1366:, pp.45, 49–50, 72,
1278:, 4 (1973): 165–72.
1239:vol. 2, pp. 677–85.
812:The Discarded Image
669:Nicolaus Copernicus
501:Theorica planetarum
399:, late 11th century
287:Georg von Peuerbach
148:Newtonian mechanics
3467:Physical cosmology
3408:Egyptian astronomy
3322:Circle of latitude
2759:Sorabji, Richard,
2738:Sorabji, Richard,
2651:Maier, Annaliese,
2528:Kepler, Johannes,
2490:Koyré, Alexandre,
2318:28(1997): 235–258.
1757:Adi Setia (2004),
969:Musica universalis
886:
844:
779:Platonic polyhedra
741:Christoph Rothmann
735:, Jerónimo Muñoz,
717:
665:
497:Campanus of Novara
401:
295:
237:concentric spheres
204:After Anaximenes,
124:heliocentric model
106:applied Ptolemy's
48:
3442:
3441:
3317:Celestial spheres
2850:Eudoxus of Cnidus
2815:978-0-226-84882-2
2793:29 (1979): 53–67.
2703:978-0-521-40340-5
2604:978-0-521-82750-8
2569:978-0-226-48231-6
2521:978-1-60620-143-5
2462:The Eye of Heaven
2331:978-90-04-16186-3
2321:Eastwood, Bruce,
2307:978-1-60206-441-6
2251:978-0-486-26173-7
2109:Johannes Kepler,
2017:, pp. 28–30.
1861:978-0-521-52994-5
1482:De Revolutionibus
1438:Andrea Murschel,
1252:, pp. 90–1, 121–2
1192:Essays 2 & 3.
1051:
1050:
1043:
871:Early Middle Ages
763:De revolutionibus
739:, Jean Pena, and
729:Robert Bellarmine
721:Francesco Patrizi
448:geocentric models
440:Arabic astronomer
418:Tashil al-Majisti
303:, the astronomer
52:celestial spheres
3474:
3429:Indian astronomy
3382:Sublunary sphere
3352:Hipparchic cycle
3291:Mural instrument
3266:Armillary sphere
3245:
3235:
3225:
3215:
3205:
2961:
2954:
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2938:
2937:
2929:
2928:
2927:
2917:
2916:
2915:
2905:
2904:
2893:
2892:
2891:
2881:
2880:
2879:
2872:
2819:
2779:
2707:
2673:Neugebauer, Otto
2648:Open Court 1960.
2608:
2573:
2525:
2506:Koyré, Alexandre
2473:
2460:Gingerich, Owen
2457:
2311:
2276:, excerpts from
2272:Duhem, Pierre.
2265:Duhem, Pierre.
2255:
2185:
2178:
2172:
2165:
2159:
2154:
2148:
2133:
2127:
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2114:
2107:
2101:
2094:
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2085:
2079:
2078:pp. 345–48.
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2018:
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2005:
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1445:26(1995): 33–61.
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859:Scipio Africanus
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759:Michael Maestlin
715:, 2nd ed., 1621)
556:Moses Maimonides
540:
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535:
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422:Thābit ibn Qurra
200:
196:
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84:apparent motions
28:Heavenly Spheres
21:Celestial sphere
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3377:Spherical Earth
3312:Callippic cycle
3300:
3281:Equatorial ring
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3179:Theon of Smyrna
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2875:
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2844:Wayback Machine
2827:
2822:
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2731:Schofield, C.,
2724:Sambursky, S.,
2717:Rosen, Edward,
2704:
2612:Lloyd, G. E. R.
2605:
2570:
2522:
2492:Galileo Studies
2483:Jarrell, R.A.,
2476:Heath, Thomas,
2409:Grant, Edward,
2395:Grant, Edward,
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1010:has an unclear
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988:
949:
880:Nicole Oresme,
863:Dream of Scipio
853:Dream of Scipio
818:
805:
800:
795:
774:Johannes Kepler
737:Michael Neander
657:
568:
560:Dante Alighieri
537:
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397:De natura rerum
385:
233:planetary model
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2763:Duckworth 2004
2757:
2750:
2736:
2729:
2722:
2721:Dover 1939/59.
2715:
2714:Routledge 1996
2710:Popper, Karl,
2708:
2702:
2687:
2670:
2656:
2649:
2642:
2627:
2609:
2603:
2588:
2574:
2568:
2553:
2541:Lewis, C. S.,
2539:
2526:
2520:
2502:
2488:
2481:
2474:
2465:
2458:
2421:
2407:
2393:
2375:
2368:
2351:
2334:
2319:
2312:
2306:
2288:
2270:
2263:
2256:
2250:
2235:
2224:
2217:
2210:
2203:
2195:
2193:
2190:
2187:
2186:
2173:
2160:
2149:
2128:
2115:
2102:
2089:
2080:
2067:
2058:
2045:
2032:
2019:
2006:
1994:Edo Hildericus
1985:
1972:
1959:
1946:
1933:
1904:10.1086/649338
1886:. 2nd Series.
1867:
1860:
1830:
1817:
1804:
1791:
1778:
1749:
1736:
1723:
1710:
1697:
1684:
1671:
1658:
1645:
1632:
1619:
1604:
1568:
1553:
1537:
1524:
1511:
1491:
1473:
1460:
1447:
1431:
1415:
1383:
1368:
1353:
1336:
1323:
1310:
1293:
1280:
1267:
1254:
1241:
1228:
1216:
1207:
1194:
1177:
1165:
1152:
1150:Routledge 1998
1135:
1122:
1109:
1096:
1083:
1067:
1053:
1052:
1049:
1048:
1012:citation style
1007:
1005:
998:
992:
989:
987:
986:
984:Sphere of fire
981:
976:
971:
966:
961:
956:
950:
948:
945:
927:King Charles V
796:
794:
791:
733:Giordano Bruno
656:
653:
567:
564:
547:Middle English
485:Kitāb al-Hayáh
469:Spanish Muslim
457:Book of Optics
405:
402:
384:
381:
228:
225:
180:sphere of fire
166:
163:
155:
152:
56:celestial orbs
15:
9:
6:
4:
3:
2:
3479:
3468:
3465:
3463:
3460:
3458:
3455:
3454:
3452:
3445:
3435:
3432:
3430:
3427:
3425:
3422:
3421:
3419:
3415:
3409:
3406:
3404:
3401:
3400:
3398:
3394:
3388:
3385:
3383:
3380:
3378:
3375:
3373:
3370:
3368:
3365:
3363:
3362:Metonic cycle
3360:
3358:
3355:
3353:
3350:
3348:
3347:Heliocentrism
3345:
3343:
3340:
3338:
3335:
3333:
3330:
3328:
3327:Counter-Earth
3325:
3323:
3320:
3318:
3315:
3313:
3310:
3309:
3307:
3303:
3297:
3294:
3292:
3289:
3287:
3284:
3282:
3279:
3277:
3274:
3272:
3269:
3267:
3264:
3262:
3259:
3258:
3256:
3252:
3246:
3242:
3238:
3236:
3234:(Aristarchus)
3232:
3228:
3226:
3222:
3218:
3216:
3212:
3208:
3206:
3202:
3198:
3197:
3195:
3191:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3127:
3125:
3122:
3120:
3117:
3115:
3112:
3110:
3107:
3105:
3102:
3100:
3097:
3095:
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3075:
3072:
3070:
3067:
3065:
3062:
3060:
3057:
3055:
3052:
3050:
3047:
3045:
3042:
3040:
3037:
3035:
3032:
3030:
3027:
3025:
3022:
3020:
3017:
3015:
3012:
3010:
3007:
3005:
3002:
3000:
2997:
2995:
2992:
2990:
2987:
2985:
2982:
2981:
2979:
2977:
2973:
2969:
2962:
2957:
2955:
2950:
2948:
2943:
2942:
2939:
2932:
2922:
2920:
2910:
2908:
2903:
2898:
2896:
2886:
2884:
2874:
2873:
2870:
2862:
2859:
2857:
2856:
2851:
2847:
2845:
2841:
2838:
2835:Dennis Duke,
2834:
2832:
2829:
2828:
2817:
2811:
2807:
2802:
2799:
2795:
2792:
2788:
2785:
2781:
2777:
2773:
2769:
2765:
2762:
2758:
2755:
2751:
2749:
2748:0-7156-2205-6
2745:
2741:
2737:
2734:
2730:
2727:
2723:
2720:
2716:
2713:
2709:
2705:
2699:
2695:
2694:
2688:
2686:
2685:0-387-06995-X
2682:
2678:
2674:
2671:
2669:
2668:0-521-77852-2
2665:
2661:
2657:
2654:
2650:
2647:
2644:Mach, Ernst,
2643:
2640:
2639:0-521-55619-8
2636:
2632:
2628:
2625:
2624:0-521-09456-9
2621:
2617:
2613:
2610:
2606:
2600:
2596:
2595:
2589:
2587:
2586:0-226-48233-2
2583:
2579:
2575:
2571:
2565:
2561:
2560:
2554:
2552:
2551:0-521-09450-X
2548:
2544:
2540:
2537:
2533:
2532:
2527:
2523:
2517:
2513:
2512:
2507:
2503:
2501:
2500:0-85527-354-2
2497:
2493:
2489:
2486:
2482:
2479:
2475:
2471:
2466:
2463:
2459:
2455:
2451:
2447:
2443:
2439:
2435:
2431:
2427:
2422:
2420:
2419:0-521-56762-9
2416:
2412:
2408:
2406:
2405:0-521-56509-X
2402:
2398:
2394:
2392:
2391:0-226-74951-7
2388:
2384:
2380:
2376:
2373:
2369:
2367:
2366:0-226-24823-2
2363:
2359:
2355:
2352:
2350:
2349:0-87169-943-5
2346:
2342:
2339:
2335:
2332:
2328:
2324:
2320:
2317:
2313:
2309:
2303:
2299:
2298:
2293:
2289:
2287:
2286:0-226-16923-5
2283:
2279:
2275:
2271:
2268:
2264:
2261:
2257:
2253:
2247:
2243:
2242:
2236:
2233:
2229:
2225:
2222:
2218:
2215:
2211:
2208:
2204:
2201:
2197:
2196:
2183:
2177:
2170:
2164:
2158:
2153:
2146:
2145:0-521-09450-X
2142:
2138:
2135:C. S. Lewis,
2132:
2125:
2119:
2112:
2106:
2099:
2093:
2084:
2077:
2071:
2062:
2055:
2049:
2042:
2036:
2029:
2023:
2016:
2010:
2003:
1999:
1995:
1989:
1982:
1976:
1969:
1963:
1956:
1950:
1943:
1937:
1929:
1925:
1921:
1917:
1913:
1909:
1905:
1901:
1897:
1893:
1889:
1885:
1881:
1874:
1872:
1863:
1857:
1853:
1849:
1844:
1843:
1834:
1827:
1821:
1814:
1808:
1802:, pp. 249–50.
1801:
1795:
1788:
1782:
1768:
1764:
1760:
1753:
1746:
1740:
1733:
1727:
1720:
1714:
1707:
1701:
1694:
1688:
1681:
1675:
1668:
1662:
1656:, pp. 433–43.
1655:
1649:
1642:
1636:
1629:
1623:
1615:
1608:
1599:
1595:
1591:
1587:
1584:(1): 13–31 .
1583:
1579:
1572:
1564:
1557:
1550:
1544:
1542:
1534:
1528:
1521:
1515:
1509:
1508:0-300-01387-6
1505:
1501:
1495:
1488:
1483:
1477:
1470:
1464:
1457:
1451:
1444:
1441:
1435:
1428:
1422:
1420:
1412:
1408:
1404:
1403:
1398:
1397:
1392:
1387:
1380:
1379:
1372:
1365:
1364:
1357:
1351:
1348:
1347:
1340:
1333:
1327:
1320:
1314:
1307:
1303:
1297:
1290:
1284:
1277:
1271:
1264:
1258:
1251:
1245:
1238:
1232:
1223:
1221:
1211:
1204:
1198:
1191:
1187:
1181:
1175:
1169:
1162:
1156:
1149:
1145:
1139:
1133:, pp. 37, 40.
1132:
1126:
1119:
1113:
1106:
1100:
1093:
1087:
1080:
1074:
1072:
1064:
1058:
1054:
1045:
1042:
1034:
1024:
1020:
1014:
1013:
1008:This article
1006:
997:
996:
985:
982:
980:
979:Seven heavens
977:
975:
974:Primum Mobile
972:
970:
967:
965:
962:
960:
959:Body of light
957:
955:
952:
951:
944:
941:
940:
934:
932:
928:
924:
923:
917:
912:
911:Nicole Oresme
908:
904:
903:
902:Divine Comedy
898:
897:
892:
883:
878:
874:
872:
868:
864:
860:
856:
854:
849:
841:
839:
838:Divine Comedy
834:
830:
826:
822:
817:
814:
813:
808:
802:
790:
788:
784:
780:
775:
771:
768:In his early
766:
764:
760:
756:
752:
750:
746:
742:
738:
734:
730:
726:
722:
714:
709:
705:
703:
699:
695:
694:Thomas Digges
690:
688:
684:
680:
676:
675:
670:
661:
652:
650:
646:
645:unmoved mover
642:
638:
634:
628:
626:
622:
618:
614:
609:
607:
603:
601:
597:
593:
589:
585:
580:
577:
572:
563:
561:
557:
553:
552:
548:
544:
526:
522:
521:
502:
498:
493:
488:
486:
482:
477:
474:
470:
465:
463:
459:
458:
453:
449:
445:
442:and polymath
441:
436:
433:
429:
428:
423:
419:
415:
411:
398:
394:
389:
380:
378:
374:
370:
366:
362:
358:
354:
350:
346:
342:
338:
333:
332:Earth radii.
330:
326:
322:
318:
314:
310:
306:
302:
301:
292:
288:
284:
280:
276:
271:
267:
265:
261:
256:
252:
251:
245:
242:
238:
234:
224:
221:
220:
215:
211:
207:
202:
189:
184:
181:
176:
172:
161:
151:
149:
145:
141:
137:
133:
128:
125:
119:
117:
113:
109:
104:
99:
97:
93:
89:
85:
81:
77:
73:
69:
65:
61:
57:
53:
45:
42:
41:Peter Apian's
37:
33:
29:
22:
3444:
3316:
3240:
3230:
3224:(Hipparchus)
3220:
3211:Catasterismi
3210:
3200:
3059:Eratosthenes
2931:Solar System
2854:
2805:
2797:
2790:
2783:
2771:
2760:
2753:
2739:
2732:
2725:
2718:
2711:
2692:
2676:
2659:
2652:
2645:
2630:
2615:
2593:
2577:
2558:
2542:
2535:
2529:
2510:
2491:
2484:
2477:
2469:
2461:
2432:(1): 57–73.
2429:
2425:
2410:
2396:
2382:
2378:
2371:
2357:
2354:Field, J. V.
2340:
2337:
2322:
2315:
2296:
2277:
2273:
2266:
2240:
2231:
2227:
2220:
2213:
2206:
2199:
2192:Bibliography
2181:
2176:
2168:
2163:
2152:
2136:
2131:
2123:
2118:
2110:
2105:
2097:
2092:
2083:
2075:
2070:
2061:
2053:
2048:
2040:
2035:
2027:
2022:
2014:
2009:
2001:
1997:
1988:
1980:
1975:
1967:
1962:
1954:
1949:
1941:
1936:
1887:
1883:
1841:
1833:
1825:
1820:
1812:
1807:
1799:
1794:
1786:
1781:
1770:, retrieved
1766:
1762:
1752:
1744:
1743:Van Helden,
1739:
1731:
1730:Van Helden,
1726:
1718:
1713:
1705:
1704:Van Helden,
1700:
1692:
1691:Van Helden,
1687:
1679:
1678:Van Helden,
1674:
1669:, pp. 434–8.
1666:
1661:
1653:
1648:
1640:
1635:
1627:
1622:
1613:
1607:
1581:
1577:
1571:
1562:
1556:
1548:
1547:Van Helden,
1532:
1531:Van Helden,
1527:
1522:, pp. 29–31.
1519:
1518:Van Helden,
1514:
1499:
1494:
1486:
1481:
1476:
1468:
1463:
1455:
1450:
1442:
1434:
1426:
1425:Neugebauer,
1400:
1394:
1386:
1376:
1371:
1361:
1356:
1344:
1339:
1331:
1330:Neugebauer,
1326:
1318:
1313:
1305:
1301:
1296:
1288:
1283:
1275:
1270:
1262:
1257:
1249:
1244:
1236:
1235:Neugebauer,
1231:
1210:
1202:
1197:
1189:
1185:
1180:
1173:
1168:
1160:
1155:
1147:
1143:
1138:
1130:
1129:Van Helden,
1125:
1117:
1116:Van Helden,
1112:
1107:, pp. 437–8.
1104:
1099:
1094:, pp. 28–40.
1091:
1090:Van Helden,
1086:
1078:
1062:
1057:
1037:
1028:
1009:
937:
935:
921:
900:
894:
887:
881:
862:
851:
845:
836:
833:Gustave Doré
810:
804:
798:
769:
767:
762:
753:
718:
712:
697:
691:
678:
672:
666:
629:
619:doctrine of
610:
606:Edward Grant
604:
581:
573:
569:
549:
542:
518:
500:
492:universities
489:
484:
478:
466:
455:
451:
437:
425:
417:
413:
407:
396:
334:
320:
312:
298:
296:
290:
277:, eccentric
248:
246:
230:
217:
203:
199: 528/4
185:
168:
129:
120:
100:
96:quintessence
60:cosmological
55:
51:
49:
44:Cosmographia
43:
32:
3342:Geocentrism
3254:Instruments
3244:(Aristotle)
3049:Cleostratus
3014:Aristarchus
2994:Anaximander
2976:Astronomers
2919:Outer space
2798:Tycho Brahe
2200:Metaphysics
2182:The Lusiads
2122:Macrobius,
1970:pp. 526–45.
1828:pp. 328–30.
1747:, pp. 37–9.
1721:, pp. 97–8.
1682:, pp. 33–4.
1626:Goldstein,
1551:, pp. 31–2.
1319:Metaphysics
1302:Metaphysics
1300:Aristotle,
939:The Lusiads
807:C. S. Lewis
755:Tycho Brahe
725:Peter Ramus
655:Renaissance
649:Prime Mover
529:410,818,517
525:Roger Bacon
471:astronomer
410:al-Farghānī
383:Middle Ages
250:Metaphysics
175:Anaximander
88:fixed stars
3451:Categories
3417:Influenced
3396:Influences
3367:Octaeteris
3296:Triquetrum
3184:Timocharis
3169:Theodosius
3129:Posidonius
3089:Hipparchus
3079:Heraclides
3019:Aristyllus
3004:Apollonius
2999:Andronicus
2198:Aristotle
1850:. p.
1811:Lindberg,
1798:Lindberg,
1789:pp. 382–3.
1643:pp. 563–6.
1628:Al-Bitrūjī
1485:(See p521
1391:Taliaferro
1343:Pedersen,
1205:, pp. 54–7
1077:Lindberg,
1023:footnoting
857:the elder
840:, Paradiso
637:revelation
625:al-Jurjani
613:mutakallim
543:Opus Majus
520:Opus Majus
505:73,387,747
432:Al-Battānī
377:al-Bitruji
214:Parmenides
210:Xenophanes
206:Pythagoras
197: – c.
195: 585
188:Anaximenes
80:Copernicus
3271:Astrolabe
3204:(Ptolemy)
3124:Philolaus
3114:Oenopides
3099:Hypsicles
3044:Cleomedes
3039:Callippus
3029:Autolycus
2984:Aglaonice
2895:Astronomy
2853:Ptolemy,
2454:117056401
2294:(2007) .
2214:Principia
1928:142586786
1912:0369-7827
1815:, p. 250.
1265:, p. 150.
1263:Aristotle
1081:, p. 251.
1065:, p. 440.
893:, in the
867:Macrobius
592:firmament
317:epicycles
255:Aristotle
241:Callippus
116:expanding
108:epicycles
72:Aristotle
3372:Solstice
3305:Concepts
3201:Almagest
3144:Seleucus
3104:Menelaus
3064:Euctemon
2855:Almagest
2840:Archived
2770:(1946).
2508:(1957).
2223:CUP 2002
1734:, p. 38.
1708:, p. 35.
1695:, p. 36.
1535:, p. 31.
1375:Linton,
1248:Dreyer,
1031:May 2023
1019:citation
947:See also
922:De caelo
907:Empyrean
896:Paradiso
829:Beatrice
815:, p. 99.
749:parallax
683:universe
584:empyrean
481:al-'Urḍi
464:matter.
414:Almagest
329:epicycle
325:deferent
300:Almagest
279:deferent
275:epicycle
3276:Dioptra
3139:Pytheas
3134:Ptolemy
3084:Hicetas
3074:Geminus
3069:Eudoxus
3024:Attalus
2989:Agrippa
2883:History
2869:Portals
2434:Bibcode
2096:Field,
2074:Grant,
2013:Koyre,
1966:Grant,
1957:p. 527.
1953:Grant,
1944:p. 541.
1940:Grant,
1892:Bibcode
1824:Grant,
1785:Grant,
1772:2 March
1717:Lewis,
1665:Grant,
1652:Grant,
1639:Grant,
1630:, p. 6.
1598:2709773
1480:In his
1360:Crowe,
1321:1072b4.
1261:Lloyd,
1159:Heath
1120:, p. 3.
1103:Grant,
1061:Grant,
899:of his
621:atomism
617:Ash'ari
596:Genesis
536:⁄
512:⁄
357:Jupiter
341:Mercury
311:in his
305:Ptolemy
297:In his
293:, 1474.
285:point.
247:In his
219:Timaeus
154:History
92:planets
86:of the
76:Ptolemy
68:Eudoxus
3387:Zodiac
3337:Equant
3286:Gnomon
3164:Thales
3159:Strabo
3009:Aratus
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1884:Osiris
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1407:pp.160
1163:pp26–8
931:Psalms
848:Cicero
647:, the
639:. The
633:angels
600:angels
416:, the
361:Saturn
359:, and
309:cosmos
283:equant
260:aether
235:using
136:Kepler
3193:Works
3109:Meton
3054:Conon
2907:Stars
2774:. In
2450:S2CID
2379:Isis,
2262:>.
2230:, in
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1916:JSTOR
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991:Notes
891:Dante
825:Dante
783:radii
745:comet
687:stars
462:solid
345:Venus
64:Plato
54:, or
3034:Bion
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1774:2010
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1021:and
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353:Mars
337:Moon
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2442:doi
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1900:doi
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