Apollonius of Perga


Mathematician, Astronomer (c.262 BC – c.190 BC)

He is known as “The Great Geometer”. He was a contemporary of Apollonius of Rhodes, Eratosthenes and Archimedes, who was 25 years older than him. He studied in Alexandria and later became a scholar there. His works, primarily on the conic sections, influenced hundreds of mathematicians throughout history, from Pappus, Hipparchus and Proclus to Vieta, Descartes, Dessargues and Fermat. He is the third greatest mathematician of antiquity next to Archimedes and Eudoxus and the third greatest Greek mathematician of all time.

While in his youth Apollonius wrote his treatise Conics. It is considered his magnum opus and consisted of 8 books. Books 1 to 4 survive in Greek, books 5 to 7 in Arabic while book 8 is lost. They were written in Alexandria and were further furnished in Pergamum before being published. They provide the first systematic study on the conic sections. The mathematical terms “eclipse”, “hyperbola” and “parabola” are first established. He was the first to show that the conic sections are actually curves from sectioned cones and planes, regardless of their angles and managed to solve second degree equations using conic sections.

Apollonius is the founder of Analytical Geometry. Professor Max Simpson writes in his book History of Mathematics in Antiquity: “As untrue as it is, that Galileo, Fermat, Leibnitz, Newton discovered Calculus, while they exist in the works of Archimedes, […] that much untrue is that the modern scientists discovered Analytical Geometry, which are found in the works of Archimedes and Apollonius”.

The only other book that has survived from Apollonius’ collection is a book on the solution of the doubling of the cube. The works that did not survive are namely the following: De Rationis Sectione, consisting of two books in Arabic translation, De Spatii Sectione (Cutting of an Area), De Tactionibus, De Inclinationibus, a book which contained 125 theorems and which Halley attempted to re-synthesize and De Locis Planis. All these books have been grouped under the name “Geometrical Analysis”. In addition, Apollonius wrote On the Cylindrical Helix, On the Comparison of the dodecahedron and the eicosahedron, Peri Atakton Alogon. Furthermore, he wrote the Ὠκυοτόκιον (Quick Bringing-to-Birth) was a book containing Apollonius’ method of finding the true value of π with greater precision than that of Archimedes, the NotAtAll Treatise (Ἡ Καθόλου Πραγματεία), which contained the foundation of the geometric science, On the Burning Glass, which was about parabolic mirrors used to light fire and finally a treatise on astronomy whose name did not survive concerning phenomena of the sun and the moon as well as the anomalous motion of celestial bodies. Ptolemy references him as having proven two significant astronomical theorems. Finally, Apollonius invented two machines: the first clock, a sundial-like clock and the hydraulus, a musical instrument.

The contributions of Apollonius as a mathematician, astronomer and inventor are unique. Conics is one of the greatest treatises of higher mathematics from the ancient world to have survived, together with Euclid’s Elements and Archimedes’ Palimpsest. It is also the most perfect work on conic sections ever written, with none of his successors ever having surpassed its perfection. While the Ὠκυοτόκιον (Quick Bringing-to-Birth) is considered by modern scientists to be the prodrome of the theory of arithmomechanics (calculators). He is also considered to be one of the founders of mathematical astronomy, together with Eudoxus. He was portrayed on the 50 drachma banknote of Greece and today, a lunar crater bears his name.


  1. Apollonius of Perga. School of Mathematics and Statistics University of St. Andrews, Scotland. History.mcs.st-and.ac.uk. Web. September 18, 2016
  2. Georgakopoulos, Konstantinos. Ancient Greek Scientists. Athens: Georgiades, 1995. Print.
  3. Koutoulas, Diamantis. The Ancient Greek Religion and the Mathematics. Thessaloniki: Psaras, 2001. Print.
  4. Δημόφιλος, Ίων. ΟΙ ΒΑΣΕΙΣ ΤΗΣ ΑΝΑΛΥΤΙΚΗΣ ΓΕΩΜΕΤΡΙΑΣ ΑΠΟ ΤΟΝ ΑΠΟΛΛΩΝΙΟ ΤΟΝ ΠΕΡΓΑΙΟ. 23.09.2009. freeinquiry.gr. Web. September 18, 2016.
Apollonius of Perga

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