Carpus of Antioch

Antioch

Antioch on the Orontes was an ancient city on the eastern side of the Orontes River. It is near the modern city of Antakya, Turkey.Founded near the end of the 4th century BC by Seleucus I Nicator, one of Alexander the Great's generals, Antioch eventually rivaled Alexandria as the chief city of the...

was an ancient Greek

Greeks

The Greeks, also known as the Hellenes , are a nation and ethnic group native to Greece, Cyprus and neighboring regions. They also form a significant diaspora, with Greek communities established around the world....

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

. It is not certain when he lived; he may have lived any time between the 2nd century BC and the 2nd century AD. He wrote on mechanics

Mechanics

Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

, astronomy

Astronomy

Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

, and geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

. Proclus

Proclus

Proclus Lycaeus , called "The Successor" or "Diadochos" , was a Greek Neoplatonist philosopher, one of the last major Classical philosophers . He set forth one of the most elaborate and fully developed systems of Neoplatonism...

 quotes from an Astronomical Treatise by Carpus concerning whether problems should come before theorems, in which Carpus may (or may not) have been criticising Geminus

Geminus

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...

. Proclus also quotes the view of Carpus that "an angle

Angle

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

 is a quantity, namely a distance between the lines of surfaces containing it." According to Pappus

Pappus of Alexandria

Pappus of Alexandria was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection , and for Pappus's Theorem in projective geometry...

, Carpus made use of mathematics for practical applications. According to Iamblichus

Iamblichus of Chalcis

Iamblichus, also known as Iamblichus Chalcidensis, was an Assyrian Neoplatonist philosopher who determined the direction taken by later Neoplatonic philosophy...

, Carpus also constructed a curve for the purpose of squaring the circle

Squaring the circle

Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge...

, which he calls a curve generated by a double motion.