To pass by that sharp Contest, he was engaged in by some Professors of Divinity at Utrecht, who endeavoured to discredit his Philosophy, as leading to Libertinisme and Atheisme, notwithstanding he made it so much his business, to assert the Existence of a Deity, and the Immortality of the Soul: We shall take notice of what is more to our purpose, vid. the Differences, he had touching his Dioptricks and Geometry.
As for his Dioptricks, though a great part of the Learned World have much esteem'd that Treatise, as leaving little to be said after him upon that Subject; yet there have not been wanting Mathematicians, who have declared their disagreement from his Principles in that Doctrine. The first of them was the Jesuit Bourdin, Mathematick Professor in the Colledg of Clermont at Paris; but this difference was soon at an end. A second was Mr. Hobbs, upon whose account he wrote several Letters to Mersennus, containing many remarks conducing to the Knowledge of the Nature of Reflection and Refraction. But the Person, that did most learnedly and resolutely attack the said Dioptricks, was Monsieur Fermat,
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 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-Carte's Geometry; whereupon many Letters were exchanged, to be found 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
M. Des-Cartes to that late Noble and Learned English Knight, Sir Charles Cavendish. The other is, whether Motion can be made without supposing a Vacuum: where 'tis represented, That, if one comprehend well the Nature, ascribed to the Materia subtilis, and how Motions, called Circular, are made, which need not be just Ovals or true Circles, but are only called Circular, in regard that their Motion ends, where it had begun, whatever irregularity there be in the Middle; and also, that all the Inequalities, that may be in the Magnitude or Figure of the parts, may be compensated by other inequalities, met with in their Swiftness, and by the facility, with which the parts of the Subtle Matter, or of the first Cartesian Element, which are found every where, happen to be divided, or to accommodate their Figure to the Space, they are to fill up: If these things be well understood and considered, that then no difficulty can remain touching the Motion of the parts of Matter in pleno.
Besides all these particulars, treated of in this Tome, there occur many pretty Questions concerning Numbers, the Cycloid, the manner of Working Glasses for Telescopes, the way of Weighing Air, and many other Curiosities, Mathematical and Physical.
II. ASTRONOMIA REFORMATA, Auctore JOHANNE BAPT. RICCIOLI, Soc. Jesu.
For the Notice of this Book, and the Account of the Chief Heads contained therein, we are obliged to the Journal des Scavans; which informs us,
First, That the Design of this Work is, that, because several Astronomers, having had their several Hypotheses, there is found so great a diversity of opinions, that it is difficult thence to conclude any thing certain; this Author judged it also necessary, to compare together all the best Observations, and upon examination of what they have most certain in them, to reform upon that measure the Principles of Astronomy.