| Pappus of Alexandria is the last of the great Greek geometers and one of his theorems is cited as the basis of modern projective geometry. |
| It contained a number of projective geometry theorems, including Pascal's mystic hexagon. |
| He summed series, and discovered addition theorems for trigonometric and hyperbolic functions using the differential equations they satisfy. |
| He worked on conic sections and produced important theorems in projective geometry. |
| He wrote textbooks on arithmetic, algebra and geometry with the aim of including only theorems which could be applied to the crafts. |
| Moreover, the inability to assert theorems containing free variables makes it impossible to prove any de re modal validities. |
