Page:Philosophical Transactions - Volume 001.djvu/409

 writing first about it to Mersennus, who soon communicated his Objections to M. Des-Cartes, who failed not to return his Answer to them. But Fermat replied, and Des-Cartes likewise; and after many reciprocations, in which each party pretended to have the advantage, the matter rested; until M. Fermat taking occasion to write afresh of it to M. De la Chambre, several years after Des-Cartes's death, upon occasion of a Book, written by M. De la Chambre, Of Light; discoursed with this new Author after the same rate, as he had done before with Des-Cartes himself, and seemed to invite some-body of his friends, to re-assume the former contest. Whereupon M. Clerselier and M. Rohault took up the Gantlet, to assert the Doctrine of the deceased Philosopher, exchanging several Letters with M. Fermat, all inserted in this Tome, and serving fully to instruct the Reader of this Difference, and withal to elucidate many difficult points of the Subject of Refractions; especially of this particular, Whether the Motion of Light is more easily, and with more expedition, perform'd through dense Mediums, than rare.

Besides this, though one would think, Disputes had no place in Geometry, since all proofs there, are as many Demonstrations; yet M. Des-Cartes hath had several scufles touching that Science. As M. Fermat had assaulted his Dioptricks, so He reciprocally examined his Treatise De Maximis & Minimis, pretending to have met with Paralogismes in it. But the Cause of M. Fermat was learnedly pleaded for, by some of his Friends, who took their turn to examine the Treatise of Des-Cartes's Geometry; whereupon many Letters were exchanged, to be found in this Book, and deserving to be considered; which doubtless the Curious would easily be induced to do, if Copies of this Book were to be obtain'd here in England, besides that one, which the Publisher received from his Parisian Correspondent, and which affords him the opportunity of giving this, though but Cursory, Account of it.

As to Physicks, there occur chiefly two Questions, learnedly treated of in this Volume, though not without some heat between M. Des-Cartes and M. Roberval. The one is, touching the Vibrations of Bodies suspended in the Air, and their Center of Agitation: about which, there is also a Letter inserted of Rh