| He summed series, and discovered addition theorems for trigonometric and hyperbolic functions using the differential equations they satisfy. |
| Moreover, the inability to assert theorems containing free variables makes it impossible to prove any de re modal validities. |
| Even with his results on free fall he was much more interested in proving geometrical theorems than in their relation to the real world. |
| There are certainly mathematical logicians who are formalists, even in the light of the incompleteness theorems. |
| This work continues the tradition of mathematical experiment to help discover patterns, suggest conjectures, and develop new theorems. |
| He worked on conic sections and produced important theorems in projective geometry. |
