# ROBERVAL (Giles-Personne)

, an eminent French mathematician, was born in 1602, at Roberval, a parish in the diocese of Beauvais. He was first professor of mathematics at the College of Maitre-Gervais, and afterwards at the College-royal. A similarity of taste connected him with Gassendi and Morin; the latter of whom he succeeded in the mathematical chair at the Royal College, without quitting however that of Ramus.

Roberval made experiments on the Torricellian vacuum: he invented two new kinds of balance, one of which was proper for weighing air; and made many other curious experiments. He was one of the first members of the ancient Academy of Sciences of 1666; but died in 1675, at 73 years of age. His principal works are,

I. A treatise on Mechanics.

II. A work entitled Aristarchus Samos.

He had several memoirs inserted in the volumes of the Academy of Sciences of 1666, viz,

1. Experiments concerning the Pressure of the Air.

2. Observations on the Composition of Motion, and on the Tangents of Curve Lines.

3. The Recognition of Equations.

4. The Geometrical Resolution of Plane and Cubic Equations.

5. Treatise on Indivisibles.

6. On the Trochoid, or Cycloid.

7. A Letter to Father Mersenne.

8. Two Letters from Torricelli.

9. A new kind of Balance.

ROBERVALLIAN *Lines,* a name given to certain
lines, used for the transformation of figures: thus
called from their inventor Roberval.

These lines bound spaces that are infinitely extended in length, which are nevertheless equal to other spaces that are terminated on all fides.

The abbot Gallois, in the Memoirs of the Royal Academy, anno 1693, observes, that the method of transforming figures, explained at the latter end of Roberval's treatise of Indivisibles, was the same with that afterwards published by James Gregory, in his Geometria Universalis, and also by Barrow in his Lectiones Geometricæ; and that, by a letter of Torricelli, it appears, that Roberval was the inventor of this manner of transforming figures, by means of certain lines, which Torricelli therefore called Robervallian Lines.

He adds, that it is highly probable, that J. Gregory first learned the method in the journey he made to Padua in 1668, the method itself having been known in Italy from the year 1646, though the book was not published till the year 1692.

This account David Gregory has endeavoured to refute, in vindication of his uncle James. His answer is inserted in the Philos. Trans. of 1694, and the abbot rejoined in the French Memoirs of the Academy of 1703.