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.One reason for its survival is that it had originally been a part of a widely used collection called "Little Astronomy", 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. 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). 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.
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.
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.
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.
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.
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.
Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sphere" are used for the surface together with its 3-dimensional interior.
The cosmological model of concentricspheres, developed by Eudoxus, Callippus, and Aristotle, employed celestial spheres all centered on the Earth. In this respect, it differed from the epicyclic and eccentric models with multiple centers, which were used by Ptolemy and other mathematical astronomers until the time of Copernicus.
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. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.
Pappus of Alexandria was one of the last great Greek mathematicians of antiquity, known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.
Greek mathematics refers to mathematics texts written during and ideas stemming from the Archaic through the Hellenistic periods, extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the Ancient Greek: μάθημα, romanized: máthēmaAttic Greek: [má.tʰɛː.ma]Koine Greek: [ˈma.θi.ma], meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations.
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 .|