page_title: Ancient Greek astronomy
section_title: Eudoxan astronomy
hierarchical_section_title: Ancient Greek astronomy / Eudoxan astronomy
caption_attribution_description: From Petrus Apianus&#59; Gemma Frisius&#32;(1539)&#32;Petri Apiani cosmographia, per Gemmam Phrysium, apud Louanienses medicum ac mathematicum insignem, restituta: additis de adem re ipsius Gemmae Phry. libellis, ut sequens pagina docet, Antwerp&#58; In pingui gallina Arnoldo Berckma[n]no [Arnold Birckmann], OCLC 1113627241. Schema huius præmiʃʃæ diuiʃionis Sphærarum. COELVM EMPIREVM HABITACVLVM DEI ET OMNIVM ELECTORVM Ⅰ0 &#160; ♌ &#166; Decimŭm Cœlŭm ♋ &#166; Primŭ Mobile ♊ &#166; &#160; ♉ &#166; &#160; ♈ &#166; &#160; ♓ &#166; &#160; ♒ &#166; &#160; ♑ &#166; &#160; ♐ &#166; &#160; ♏ &#166; &#160; ♎ &#166; &#160; ♍ &#166; 9 &#160; ♋ &#166; Nonŭ Cœlŭm ♊ &#166; Criʃtallinŭm ♉ &#166; &#160; ♈ &#166; ⊕ &#160; ♓ &#166; &#160; ♒ &#166; &#160; ♑ &#166; &#160; ♐ &#166; &#160; ♏ &#166; &#160; ♎ &#166;⊕ &#160; ♍ &#166; &#160; ♌ &#166; 8 ••••••★ ♋ &#166; (•) Octaŭum •• ♊ &#166; (•) Firmamentŭ • ♉ • &#166; •••••• ♈ &#166; ••★••★••• ♓ &#166; •••★• ♒ • &#166; ••••••••• ♑ &#166; •••★ ♐ &#166; ••••••• ♏ &#166; ★•★ ♎ &#166; ••••••• ♍ &#166; ••★•••• ♌ &#166; 7 COELÛ &#160; ♃ SATVRNI &#160; ★ 6 ♄ IOVIS &#160; ★ 5 ♂ MARTIS &#160; ★ 4 ☉ SOLIS &#160; ☼ 3 ♀VENERIS &#160; ★ Z ☿ MERCVRII &#160; ★ Ⅰ ☾ LVNÆ &#160; ◯ &#160; ☽ &#160; ◯ (•) Star aligned with following word; only two sizes of stars are used, relative positions ignored English: The scheme of the aforementioned division of spheres. · The empyrean (fiery) heaven, dwelling of God and of all the selected · 10 Tenth heaven, first cause · 9 Ninth heaven, crystalline · 8 Eighth heaven of the firmament · 7 Heaven of Saturn · 6 Jupiter · 5 Mars · 4 Sun · 3 Venus · 2 Mercury · 1 Moon Latina: Schema huius praemissae divisionis sphaerarum. · Coelum empireum habitaculum dei et omnium electorum · 10 Decimum coelum primu mobile · 9 Nonu coelum cristallinum · 8 Octavum [coelum] firmamentu · 7 Coelu saturni · 6 [Coelu] Iovis · 5 [Coelu] Martis · 4 [Coelu] Solis · 3 [Coelu] Veneris · 2 [Coelu] Mercurii · 1 [Coelu] Lunae Compare to: Sacrobosco's De sphaera mundi
context_page_description: Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.
  The development of astronomy by the Greek and notably Hellenistic astronomers is considered to be a major phase in the history of astronomy. Greek astronomy is characterized by seeking a geometrical model for celestial phenomena.
context_section_description: In classical Greece, astronomy was a branch of mathematics; astronomers sought to create geometrical models that could imitate the appearances of celestial motions. This tradition began with the Pythagoreans, who placed astronomy among the four mathematical arts (along with arithmetic, geometry, and music). The study of number comprising the four arts was later called the Quadrivium.
  Although he was not a creative mathematician, Plato (427–347 BC) included the quadrivium as the basis for philosophical education in the Republic. He encouraged a younger mathematician, Eudoxus of Cnidus (c. 410 BC–c. 347 BC), to develop a system of Greek astronomy. According to a modern historian of science, David Lindberg:
  
  "In their work we find (1) a shift from stellar to planetary concerns, (2) the creation of a geometrical model, the "two-sphere model," for the representation of stellar and planetary phenomena, and (3) the establishment of criteria governing theories designed to account for planetary observations".
  The two-sphere model is a geocentric model that divides the cosmos into two regions, a spherical Earth, central and motionless (the sublunary sphere) and a spherical heavenly realm centered on the Earth, which may contain multiple rotating spheres made of aether.
  Plato's main books on cosmology are the Timaeus and the Republic. In them he described the two-sphere model and said there were eight circles or spheres carrying the seven planets and the fixed stars.
  According to the "Myth of Er" in the Republic, the cosmos is the Spindle of Necessity, attended by Sirens and spun by the three daughters of the Goddess Necessity known collectively as the Moirai or Fates.
  According to a story reported by Simplicius of Cilicia (6th century), Plato posed a question for the Greek mathematicians of his day: "By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?" (quoted in Lloyd 1970, p. 84). Plato proposed that the seemingly chaotic wandering motions of the planets could be explained by combinations of uniform circular motions centered on a spherical Earth, apparently a novel idea in the 4th century.
  Eudoxus rose to the challenge by assigning to each planet a set of concentric spheres. By tilting the axes of the spheres, and by assigning each a different period of revolution, he was able to approximate the celestial "appearances." Thus, he was the first to attempt a mathematical description of the motions of the planets. A general idea of the content of On Speeds, his book on the planets, can be gleaned from Aristotle's Metaphysics XII, 8, and a commentary by Simplicius on De caelo, another work by Aristotle. Since all his own works are lost, our knowledge of Eudoxus is obtained from secondary sources. Aratus's poem on astronomy is based on a work of Eudoxus, and possibly also Theodosius of Bithynia's Sphaerics. They give us an indication of his work in spherical astronomy as well as planetary motions.
  Callippus, a Greek astronomer of the 4th century, added seven spheres to Eudoxus' original 27 (in addition to the planetary spheres, Eudoxus included a sphere for the fixed stars). Aristotle described both systems, but insisted on adding "unrolling" spheres between each set of spheres to cancel the motions of the outer set. Aristotle was concerned about the physical nature of the system; without unrollers, the outer motions would be transferred to the inner planets.
caption: Renaissance woodcut illustrating the two-sphere model.
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