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.