**Autolycus of Pitane** (Greek : Αὐτόλυκος ὁ Πιταναῖος; c. 360 – c. 290 BC) was a Greek astronomer, mathematician, and geographer. The lunar crater Autolycus was named in his honour.

Autolycus was born in Pitane, a town of Aeolis within Ionia, Asia Minor. Of his personal life nothing is known, although he was a contemporary of Aristotle and his works seem to have been completed in Athens between 335–300 BC. Euclid references some of Autolycus' work, and Autolycus is known to have taught Arcesilaus. Autolycus' surviving works include a book on spheres entitled *On the Moving Sphere* (Περὶ κινουμένης σφαίρας) and another *On Risings and Settings* (Περὶ ἐπιτολῶν καὶ δύσεων) of celestial bodies. Autolycus' works were translated by Maurolycus in the sixteenth century.

*On the Moving Sphere* is believed to be the oldest mathematical treatise from ancient Greece that is completely preserved. All Greek mathematical works prior to Autolycus' *Sphere* are taken from later summaries, commentaries, or descriptions of the works.^{ [1] } One reason for its survival is that it had originally been a part of a widely used collection called "Little Astronomy",^{ [2] } which was preserved by translation into Arabic in the 9th century. In Europe it was lost, but was brought back during the Crusades in the 12th century, and translated back into Latin.^{ [3] }^{ [4] } In his *Sphere*, Autolycus studied the characteristics and movement of a sphere. The work is simple and not exactly original, since it consists of only elementary theorems on spheres that would be needed by astronomers, but its theorems are clearly enunciated and proved. Its prime significance, therefore, is that it indicates that by his day there was a thoroughly established textbook tradition in geometry that is today regarded as typical of classical Greek geometry. The theorem statement is clearly enunciated, a figure of the construction is given alongside the proof, and finally a concluding remark is made. Moreover, it gives indications of what theorems were well known in his day (around 320 BC).^{ [2] } Two hundred years later Theodosius' wrote *Sphaerics*, a book that is believed to have a common origin with *On the Moving Sphere* in some pre-Euclidean textbook, possibly written by Eudoxus.

In astronomy, Autolycus studied the relationship between the rising and the setting of the celestial bodies in his treatise in two books entitled *On Risings and Settings*. The second book is actually an expansion of his first book and of higher quality. He wrote that "any star which rises and sets always rises and sets at the same point in the horizon." Autolycus relied heavily on Eudoxus' astronomy and was a strong supporter of Eudoxus' theory of homocentric spheres.

- ↑ Boyer (1991). "The age of Plato and Aristotle".
*A History of Mathematics*. p. 97.A few years after Dinostratus and Menaechmus there flourished a mathematician who has the distinction of having written the oldest surviving Greek mathematical treatise. We have described rather fully the work of earlier Hellenic mathematicians, but it must be borne in mind that the accounts have been based no on original work but on later summaries, commentaries, or description. Occasionally a commentator appears to be copying from an original work extant at the time, as when Simplicius in the sixth century of our era is describing the quadrature of lines by Hippocrates. But not until we come to Autolycus of Pitane, a contemporary of Aristotle, do we find a Greek author one of whose works has survived.

- 1 2 Boyer (1991). "The age of Plato and Aristotle".
*A History of Mathematics*. pp. 97–98.One reason for the survival of little treatise,

*On the Moving Sphere*, is that it formed a part of a collection, known as the "Little Astronomy," widely used by ancient astronomers.*On the Moving Sphere*is not a profound and probably not a very original work, for it includes little beyond elementary theorems on the geometry of the sphere that would be needed in astronomy. Its chief significance lies in the fact that it indicates that Greek geometry evidently had reached the form that we regard as typical of the classical age. Theorems are clearly enunciated and proved. Moreover, the author uses without proof or indication of source other theorems that he regards as well known; we conclude, therefore, that there was in Greece in his day, about 320 B.C., a thoroughly established textbook tradition in geometry. - ↑ "Theodosius of Bithynia" . Retrieved 2 May 2015.
- ↑ Theodosius of Bithynia

**Euclid**, sometimes called **Euclid of Alexandria** to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I. His *Elements* is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from the time of its publication until the late 19th or early 20th century. In the *Elements*, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour.

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In astronomy and navigation, the **celestial sphere** is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location.

**Eudoxus of Cnidus** was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. *Sphaerics* by Theodosius of Bithynia may be based on a work by Eudoxus.

**Aristarchus of Samos** was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the known universe, with the Earth revolving around the Sun once a year and rotating about its axis once a day. He was influenced by Philolaus of Croton, but Aristarchus identified the "central fire" with the Sun, and he put the other planets in their correct order of distance around the Sun. Like Anaxagoras before him, he suspected that the stars were just other bodies like the Sun, albeit farther away from Earth. His astronomical ideas were often rejected in favor of the geocentric theories of Aristotle and Ptolemy. Nicolaus Copernicus attributed the heliocentric theory to Aristarchus. Aristarchus also estimated the sizes of the Sun and Moon as compared to Earth's size, and the distances to the Sun and Moon.

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The * Elements* is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines.

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**Geminus** of Rhodes, was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the *Introduction to the Phenomena*, still survives; it was intended as an introductory astronomy book for students. He also wrote a work on mathematics, of which only fragments quoted by later authors survive.

**Francesco Maurolico** was a mathematician and astronomer from Sicily. He made contributions to the fields of geometry, optics, conics, mechanics, music, and astronomy. He edited the works of classical authors including Archimedes, Apollonius, Autolycus, Theodosius and Serenus. He also composed his own unique treatises on mathematics and mathematical science.

**Theodosius of Bithynia** was a Greek astronomer and mathematician who wrote the *Sphaerics*, a book on the geometry of the sphere.

**Eudemus of Rhodes** was an ancient Greek philosopher, considered the first historian of science, who lived from c. 370 BCE until c. 300 BCE. He was one of Aristotle's most important pupils, editing his teacher's work and making it more easily accessible. Eudemus' nephew, Pasicles, was also credited with editing Aristotle's works.

**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.

**Qusta ibn Luqa** (820–912) was a Syrian Melkite Christian physician, philosopher, astronomer, mathematician and translator. He was born in Baalbek. Travelling to parts of the Byzantine Empire, he brought back Greek texts and translated them into Arabic.

This is a **timeline of ancient Greek mathematicians**.

This is a timeline of pure and applied mathematics history. It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic" stage, in which comprehensive notational systems for formulas are the norm.

* Sphaerics* was a set of three volumes on spherical geometry written by Theodosius of Bithynia in the 2nd century BC. These proved essential in the restoration of Euclidean geometry to Western civilization, when brought back from the Islamic world during the crusades and translated back from Arabic into Latin.

Wikisource has the text of the 1911 Encyclopædia Britannica article . Autolycus of Pitane |

- Boyer, Carl B. (1991).
*A History of Mathematics*(2nd ed.). John Wiley & Sons, Inc. ISBN 0-471-54397-7. - Huxley, G. L. (1970). "Autolycus of Pitane".
*Dictionary of Scientific Biography*.**1**. New York: Charles Scribner's Sons. pp. 338–39. ISBN 0-684-10114-9. on line at "Autolycus of Pitane".*HighBeam Research*. Retrieved 26 March 2015. - O'Connor, John J.; Robertson, Edmund F. (April 1999), "Autolycus of Pitane",
*MacTutor History of Mathematics archive*, University of St Andrews .

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