As results of Roberval's labours outside the department of pure mathematics may be noted a work on the system of the universe, in which he supports the Copernican system and attributes a mutual attraction to all particles of matter; and also the invention of a special kind of balance which goes by his name.

For pure mathematics he had a special gift - almost a passion.

In pure mathematics the hypotheses which a set of entities are to satisfy are given, and a group of interesting deductions are sought.

This survey of the existing developments of pure mathematics confirms the conclusions arrived at from the previous survey of the theoretical principles of the subject.

In the next and last period the progress of pure mathematics has been dominated by the critical spirit introduced by the German mathematicians under the guidance of Weierstrass, though foreshadowed by earlier analysts, such as Abel.