Reading: Papus: the epilogue of Greek geometry

From the 3rd century BC, Rome established itself as a military power. It annexed Greece in 146 B.C. and Egypt in 31 B.C. Before that, in 47 B.C., a fire started in the Egyptian fleet, by order of Caesar, reached the library of Alexandria and consumed around 500 thousand texts. Alexandria would still be the cultural capital of the world for a long time, but Greek mathematics began to decline: the model of deductive geometry, without algebraic symbolism, showed signs of exhaustion, and the Romans only valued practical knowledge. In 529, the Greek schools of philosophy were closed, including Plato’s Academy.

Plato, later artistic representation.Roman copy of a portrait of Silanion · Wikimedia Commons · Public domain

The last great encouragement came from Papus of Alexandria (c. 300 AD). Its Mathematical Collection, in eight books, contains precious historical information, new demonstrations and original contributions. One of them is what is now called Guldin’s theorem: the volume of the solid generated by the rotation of a flat region around a straight line is equal to the area of the region times the length of the trajectory of its center of gravity. Another is Papus’ theorem of projective geometry: if $A$, $B$, $C$ are on a straight line and $A^{\prime}$, $B^{\prime}$, $C^{\prime}$ on another, the meetings of $AB^{\prime}$ with $A^{\prime}B$, $AC^{\prime}$ with $A^{\prime}C$ and $BC^{\prime}$ with $B^{\prime}C$ are collinear. Papus also owes the concept of focus and guideline of a conic. He strove to revive Greek geometry, but the forces of history were against him.

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Reading: Papus: the epilogue of Greek geometry

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