PIERRE DE, equally celebrated as a restorer of ancient mathematics, and an original author of modern improvements, was born at Toulouse about 1595. His public life was occupied by the active duties attached to the situation of a counsellor of the parliament of Toulouse, in which he was distinguished both for legal knowledge and for strict integrity of conduct. Besides the sciences, which were the principal objects of his private studies, he was an accomplished scholar, an excellent linguist, and even a respectable poet.

His Opera Mathematica were published at Toulouse, in two volumes folio, 1670 and 1679; they are now become very scarce. The first contains the Arithmetic of Diophantus, illustrated by a commentary, and enlarged by a multitude of additional propositions. In the second we find a Method or the Quadrature of Parabolas of all kinds, and a Treatise on Maxima and Minima, on Tangents, and on Centres of Gravity; containing the same solutions of a variety of problems as were afterwards incorporated into the more extensive method of fluxions, by Newton and Leibnitz; and securing to their author, in common with Cavalieri, Roberval, Descartes, Wallis, Barrow, and Sluse, an ample share of the glory of having immediately prepared the way for the gigantic steps of those illustrious philosophers. The same volume contains also several other treatises on Geometric Loci, or Spherical Tangencies, and on the Rectification of Curves, besides a restoration of Apollonius's Plane Loci; together with the author's correspondence, addressed to Descartes, Pascal, Roberval, Huygens, and others.

It was too much Fermat's custom to leave his most important propositions wholly undeemonstrated; sometimes, perhaps, because he may have obtained them rather by induction than by a connected train of reasoning; and, in other cases, for the purpose of proposing them as a trial of strength to his contemporaries. The deficiency, however, has in many instances been supplied by the elaborate investigations of Euler and Lagrange, who have thought it no degradation to their refined talents to go back a century in search of these elegant intricacies, which appeared to require further illustration. It happened not uncommonly, that the want of a more explicit statement of the grounds of his discoveries deprived Fermat, in the opinion of his rivals, of the credit justly due to him for accuracy and originality. It was thus that Descartes attempted to correct his method of maxima and minima, and could never be persuaded that Fermat's first propositions on the subject were unexceptionable. Fermat was however enabled to pursue his favourite studies with less interruption than Descartes; and the products of his labour were proportionate, as Lacroix remarks, to the opportunities he enjoyed, as well as to the talents he possessed.

There is a very ingenious proposition of Fermat, which deserves to be particularly noticed, on account of the discussion that it not long ago excited among mathematical