MATHEMATICIAN, GEOGRAPHER, ENGINEER

Life
Pappus of Alexandria was a mathematician and the author of commentaries on Euclid and Ptolemy and of a work on universal geography, much of which is now lost. He lived in Alexandria during the reign of Diocletian, and his writings inspired much later work.


Work
These were:

"Mathematical Collection": A vast work in 8 books, this was the last great treatise on mathematics of the Alexandrian age. All but the first and part of the second book have survived. An invaluable record of the mathematical accomplishments of the ancient Greek world, it contains a systematic account of the principal theorems in arithmetic, geometry, astronomy and mechanics, with commentaries, improvements and alterations, as well as original material.

Book 3 contains problems in plane and solid geometry, including the famous "Delian problem" of finding two mean proportionals between two given lines; it studies the 10 kinds of means, giving examples of each, and develops the theory of regular solids.

Book 4 contains, besides studies of various curves, an account of the three classical problems (the squaring of the circle, the duplication of the cube, and the trisection of an angle). It also contains a generalisation of the theorem of Pythagoras on right-angled triangles.

Book 5 contains problems in geometry concerning the areas of different plane figures and the volumes of different solids, and observations on the cells of a honeycomb (hexagonal figure occupying the least possible space).

Book 6 contains an account of problems in astronomy treated by Theodosius of Bithynia, Autolycus of Pitane, Aristarchus and others.

Book 7 explains the terms analysis and synthesis, and the distinction between theorem and problem. It presents an outline of the work of the greatest of the ancient mathematicians, and discusses the 13 semi-regular polyhedra. It also treats the subject of conic sections, completing the work of Apollonius of Perga. Finally, it contains a theorem on the creation of lines of harmonic progression, and a method for finding the volume generated by a surface rotated about a line and the area generated by a curve rotated about its centre (Guldin's theorem). This book inspired the analytical geometry of Rene Descartes (17th century).

Book 8 deals principally with mechanics, in both practical and theoretical terms. It also contains "Pappus'-Pascal's theorem" on conic sections, which includes the lineal pairs of a plane figure, an early example of the principle of duality.

Commentary on Euclid's "Elements": Part of this work has survived in Arabic translation.

Commentary on Euclid's "Data"

Commentary on the "Analemma" of Diodorus of Alexandria

Commentary on Aristarchus' "On magnitudes"

Commentary on Ptolemy's "Syntaxis"

None of these commentaries survive.