(Peter Sylvain), a French philosopher, and great propagator of Cartesianism, was born in Agenois 1632. He cultivated the languages and philosophy under the Jesuits at Cahors, and afterwards divinity in the university of that town, being designed for the church. He made so uncommon a progress, that at the end of four years he was offered a doctor's degree without the usual charges; but he did not think it became him to accept of it till he had studied also in the Sorbonne at Paris. He went thither, but was soon disgusted with theology; and as the philosophy of Descartes began at that time to make a noise through the lectures of Rohault, he conceived a taste for it, and gave himself up entirely to it. He frequented these lectures; and becoming an adept, went to Toulouse in 1655, and read lectures in it himself. Having fine parts, a clear and fluent manner, and a happy way of making himself understood, he drew all sorts of people; the magistrates, the learned, the ecclesiastics, and the very women, who now all affected to abjure the ancient philosophy. In 1680 he returned to Paris, where the concourse about him was such, that the flickers for Peripateticism began to be alarmed. They applied to the archbishop of Paris, who thought it expedient, in the name of the king, to put a stop to the lectures; which accordingly were discontinued for several months. The whole life of Regis was spent in propagating the new philosophy. In 1690 he published a formal system of it, containing logic, metaphysics, physics, and morals, in 3 vols. 4to, and written in French. It was reprinted the year after at Amsterdam, with the addition of a discourse upon ancient and modern philosophy. He wrote afterwards several pieces in defence of his system; in which he had disputes with M. Huet, Du Hamel, Malebranche, and others. His works, though abounding with ingenuity and learning, have been disregarded, in consequence of the great discoveries and advancement in philosophic knowledge that have been since made. He died in 1707.

He had been chosen member of the academy of sciences in 1699.

REGULAR solid, called also Platonic Body, is a body or solid comprehended by like, equal, and regular plane figures, and whose solid angles are all equal.

The plane figures by which the solid is contained are the faces of the solid; and the sides of the plane figures are the edges, or linear sides of the solid.

There are only five regular solids, viz:

- The tetrahedron, or regular triangular pyramid, having four triangular faces; - The hexahedron, or cube, having six square faces; - The octahedron, having eight triangular faces; - The dodecahedron, having twelve pentagonal faces; - The icosahedron, having twenty triangular faces.

Besides these five, there can be no other regular bodies in nature. See Platonic Body, Suppl.