# Hippocrates of Chios

Hippocrates of Chios

▪ Greek mathematician
flourished c. 440 BC

Greek geometer who compiled the first known work on the elements of geometry nearly a century before Euclid. Although the work is no longer extant, Euclid may have used it as a model for his Elements.

According to tradition, Hippocrates was a merchant whose goods had been captured by pirates. He went to Athens to prosecute them but met with little success in recovering his property. He remained in Athens, however, where he attended lectures on mathematics and finally took up teaching geometry to support himself. Aristotle (384–322 BC) recounts a different story, claiming that Hippocrates was cheated by customs officers in Byzantium; he purportedly did so to show that, although Hippocrates was a good geometer, he was incompetent to handle the ordinary affairs of life.

Hippocrates' Elements is known only through references made in the works of later commentators, especially the Greek philosophers Proclus (c. AD 410–485) and Simplicius Of Cilicia (fl. c. AD 530). In his attempts to square the circle, Hippocrates was able to find the areas of certain lunes, or crescent-shaped figures contained between two intersecting circles. He based this work upon the theorem that the areas of two circles have the same ratio as the squares of their radii. A summary of these quadratures of lunes, written by Eudemus Of Rhodes (c. 335 BC), with elaborate proofs, has been preserved by Simplicius.

The third of the achievements attributed to Hippocrates was the discovery that, given a cube of side a, a cube with double its volume can be constructed if two mean proportionals, x and y, can be determined such that a:x = x:y = y:2a. It is also generally thought that Hippocrates introduced the tactic of reducing a complex problem to a more tractable or simpler problem. His reduction of the problem of “doubling the cube” (a three-dimensional quantity) to finding two lengths (one-dimensional quantities) certainly fits this description.

* * *

Universalium. 2010.

### Look at other dictionaries:

• Hippocrates of Chios — was an ancient Greek mathematician (geometer) and astronomer, who lived c. 470 c. 410 BCE. He was born on the isle of Chios, where he originally was a merchant. After some misadventures (he was robbed by either pirates or fraudulent customs… …   Wikipedia

• Hippocrates of Chios — See Greek arithmetic, geometry and harmonics …   History of philosophy

• Hippocrates (disambiguation) — Hippocrates was an ancient Greek physician of the Age of Pericles, considered one of the most outstanding figures in the history of medicine.Hippocrates may also refer to:*Hippocrates of Chios, ancient Greek geometer who wrote the first known… …   Wikipedia

• Chios Island National Airport — Κρατικός Αερολιμένας Χίου IATA: JKH – ICAO: LGHI …   Wikipedia

• Hippocrates — Unter dem Namen Hippokrates gab es in der Antike acht bekannte Persönlichkeiten: Hippokrates von Kos, berühmtester Arzt der Antike Hippokrates von Chios, Mathematiker und Astronom Hippokrates (Gesandter Hannibals) Hippokrates, lakedaimonischer… …   Deutsch Wikipedia

• Greek arithmetic, geometry and harmonics: Thales to Plato — Ian Mueller INTRODUCTION: PROCLUS’ HISTORY OF GEOMETRY In a famous passage in Book VII of the Republic starting at Socrates proposes to inquire about the studies (mathēmata) needed to train the young people who will become leaders of the ideal… …   History of philosophy

• mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

• Squaring the circle — Squaring the circle: the areas of this square and this circle are equal. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized compass and straightedge …   Wikipedia

• Oenopides — is also the name of a lunar crater Oenopides of Chios (Greek: Οἰνοπίδης) was an ancient Greek mathematician (geometer) and astronomer, who lived around 450 BCE. He was born shortly after 500 BCE on the island of Chios, but mostly worked in Athens …   Wikipedia

• Lune (mathematics) — In geometry, a lune is either of two figures, both shaped roughly like a crescent Moon. The word lune derives from luna, the Latin word for Moon. Contents 1 Plane geometry 2 Spherical geometry 3 Lune of Hippocrates …   Wikipedia