Eudoxus

Cnidus Eudoxus

(. b Cnidus, around 400 BC; d Cnidus, BC 347 years.)

astronomy, mathematics .

Eudoxus was a Greek mathematician and astronomer who contributed to Euclid's element . He drew stars and compiled a map of the known world. His philosophy influenced Aristotle.

As an outstanding scholar and scientist, Eudoxus is the son of a certain Aischines. He has contributed to the development of astronomy, mathematics, geography and philosophy and provided for his hometown The law. When he was young, he studied geometry with Archytas in Tarentum, and he probably became interested in number theory and music from them. In medicine, he was under the guidance of Dr. Feliston; his philosophical inquiry was inspired by Plato ,He attended Plato's lectures as a poor student during his first visit to Athens. Later, his friends in Cnidus paid for the visit to Egypt, where he appeared to represent spartan and Agsilius II had diplomatic contacts with the king Nekhtanibef II.

Eudoxos spent more than a year in Egypt, some of which time was spent in the company of priests of Heliopolis . It is said that he created his Oktaeteris , or eight-year calendar cycle during his stay with them. Next, he settled in Cyzicus in northwest Asia Minor and founded a school. He also visited the Mossolas dynasty in Cartier. Some of his students followed him on their second visit to Athens, which brought him closer to Plato, but it was not easy to determine that their thinking on ethical and scientific issues interacted with each other. Plato is unlikely to have any influence on the development of Odos' planetary theory, nor is it likely to have any influence on Cnidian's formal philosophy, which is reminiscent of Anaxagora . But it is possible that Plato's Philebos is written in Eudokian hedonism (correct understanding, happiness is the highest good).

Back to Cnidus, Eudoxus teaches theology, cosmology and meteorology ,Write textbooks and be respected by compatriots. In terms of mathematics, his thinking lags behind many of Euclid's elements , especially the fifth, sixth and twelfth volumes. Eudoxus studied mathematical proportions, the method of exhaustion, and the method of axioms-the "Euclidean" expression of axioms and propositions was probably the first to be systematized by him. The importance of his theory of proportion is that it contains incommensurable abilities.

It is difficult to exaggerate the importance of this theory, because it is equivalent to a strict definition of real numbers. After Pythagoras imposed the discovery of irrational number on number theory, number theory was developed again, bringing inestimable benefits to all subsequent mathematics. In fact, as TL Heath declared ( Greek history of mathematics , I [Oxford, 1921], 326-327), "When remembering the definition of equal ratio in Eucl, the greatness of the new theory itself is not Need further argumentation. V, definition. 5 is fully in line with modern irrational number theory due to Dedekin, and it is exactly the same as Weilstrass's definition of equal numbers."

Eudoxus also attacked the so-called "Delian problem", the traditional problem of copying cubes; that is, he tried to find two average proportions of consecutive proportions between two given quantities. His exact geometric solution has been lost, and he may have constructed a device describing the approximate mechanical solution; The “curved lines” were used to solve Tyrian’s problem: this may mean an “organic” presentation.Plato is said to object to the use of such devices by Eudoxus (and Archytas), believing that they devalue pure or ideal geometry. Proclus refers to Eudoxus' "general theorems"; they are missing, but may contain all the concepts of size, including the theory of proportions. The element V) is his exhaustion method for calculating the volume of solids. This method is an important step towards the development of integral calculus.

Archimedes pointed out that Eudoxus proved that the volume of pyramid is one-third of the volume of a prism with a constant base and a cone, and the volume of a cone is the volume of a cylinder with a constant base and constant height. (These propositions may have been known by Democritus, but Eudoxus seems to be the first to prove them). Archimedes also implied that Eudoxus showed that the areas of circles between each other are the squares of their respective diameters, and the volumes between spheres are cubes of their diameters between each other. All four propositions can be found in Elements XII , which is closely related to his work. It is said that Eudoxus also added another two to the first three types of mathematical averages (arithmetic, geometry and harmony), the opposite of harmony and geometry, but his attribution is not very certain.

Perhaps the most important and, of course, the most influential part of Eudoxus's life is his application of spherical geometry to astronomy. In his book "On velocity" he described a geocentric, concentric rotating sphere system, which aims to explain the irregularity of planetary motion seen from the earth.Eudoxus might treat his system as simply an abstract geometric model, but Aristotle thought it was a description of the physical world and made it complicated by adding more spheres; fourth century BC In the later period, Calyps also added more spheres through the appropriate combination of spheres, which can approximately represent the periodic motion of the planets, but due to the hippo or "horse fetters", the system also has inherent value as a geometry. The curve, Eudox represents the apparent motion of the planet in latitude and its retrograde motion.

Eudoxus' model assumes that the distance between the planet and the center remains the same, but in fact, as critics quickly pointed out, the brightness of the planets varies, so it appears to be at a different distance from the Earth. Another objection is that, according to the model, each retrograde of the planet has the same curve shape as the previous retrograde, which does not conform to the facts. Therefore, although the Eudosi system proved its author's geometric skills, it could not be accepted as deterministic by serious astronomers, and the current round of theories was developed in time. However, due in part to Aristotle’s blessing, Eudoxus’ influence on popular astronomical ideas lasted into ancient times and the Middle Ages. In explaining this system, Eudoxus had an effect on Saturn, Jupiter, Mars, Mercury, and Venus. The rendezvous period is approximated (hence the title of this book is On Speeds ). Only the estimate of Mars is seriously wrong, and the texts given here worthy of Simplisius are almost certainly wrong (Eudoxus, Frag. 124 in Lasserre).

Eudoxus is an observer who carefully observes the stars, both during his visit to Egypt and at his home in Knidos, where he has an observatory. His research results are published in two books, Enoptron ("Zhizhitongjian") and Phaenomena .Two centuries later, the great astronomer Hipparchus criticized these works based on excellent knowledge, but they were groundbreaking compendiums that have long proven useful. Hipparchus quoted Eudoxus verbatim in his comment on Aratus's astronomical poems and titled "Phenomena" ( Phaenomena) . A book by Eudoxus is called "The Disappearance of the Sun" may have been concerned about solar eclipse , perhaps also concerned about rising and sunset. Suda Lexicon 's statement He wrote an astronomy poem may be due to confusion with Aratus, but in the Hesiodic tradition, the true six-meter star astronomy _em8 spanem is possible 3 . Oktaeteris may include the seasonal rise of the constellation and setting calendar, as well as weather signs. His observation instruments include sundial (Vitruvius, De architectura 9.8.1).