The work of M. Newton is a mechanics, the most perfect that one could imagine, as it is not possible to make demonstrations more precise or more exact than those that he gives in the first two books on lightness, on springiness, on the resistance of fluid bodies, and on the attractive and repulsive forces that are the principal basis of Physics. But one has to confess that one cannot regard these demonstrations otherwise than as only mechanical; indeed, the author recognizes himself at the end of page four and the beginning of page five that he has not considered their Principles as a Physicist, but as a mere Geometer.
He confesses the same thing at the beginning of the third book, where he endeavors nevertheless to explain the System of the World. But it is [done] only by hypotheses that are, most of them, arbitrary, and that, consequently, can serve as foundation only to a treatise of pure mechanics. He bases the explanation of the inequality of the tides on the principle that all the planets gravitate reciprocally toward each other ... But this supposition is arbitrary as it has not been proved; the demonstration that depends on it can therefore only be mechanics. In order to make an opus as perfect as possible, M. Newton has only to give us a Physics as exact as his Mechanics. He will achieve this when he substitutes true motions for those he has supposed.---Anonymous, Journal des Scavans (2 August 1688), pp. 153 sq., translated by Alexandre Koyré, Newtonian Studies, p.115. [see also here]
The 1688 review was the first public continental response to Isaac Newton. It is often taken to be the expression of a (neo-)Cartesian rejection of the Principia along the lines of Huygens or Leibniz. This is undoubtedly influenced by Koyré suggestion (he's not the first) that the reviewer was probably the Cartesian Regius. On the now standard reading the reviewer is rejecting action at a distance and asking for an explanation in terms of colliding bodies. I now think this standard reading does not do justice to the details of the review. I was prompted to re-think the review by a fascinating paper, "Beyond the “Continental Translation” of Newtonian Mechanics: The Beginnings of Rational Mechanics Reconsidered" (forthcoming in a OUP Handbook on Isaac Newton edited by Smeenk & Schliesser) by J.B. Shank (who has independent grounds to think the reviewer is Varignon).+
There are two oddities in the review that are incompatible with the reviewer being a standard neo-Cartesian-mechanical philosopher: the author of the review (i) rejects hypotheses; and s/he (ii) insists that knowledge of "true motions" of the planets is possible. But, as Huygens affirmed in his introduction in the Treatise on Light and Discourage on Gravity (which includes his published response to Newton's Principia) the mechanical philosophy was a hypothetical philosophy, relying on reduction to intelligible models, and it insisted that motions of the planets were too complex to be fully known with certainty. (Descartes himself had thought the motions of planets could only be known with rough approximation.) They were, in fact, in no position to complain about a science grounded on hypotheses or suppositions--that was, in fact, Newton's complaint about them. (They could, of course, claim that different hypotheses than those adopted by Newton's were preferable, but not that they were hypotheses.) In fact, for the first time since the Copernican hypothesis had errupted, Newton's Principia gave genuine hope that the true motions of the planets and their causes could be found and were within possible reach.
But the anonymous reviewer is attacking Newton from a more rationalist side: action at a distance is criticized for being (a) arbitrary and (b) un-grounded in indubitable foundations (that track the causal structure of the world).* In the Preface to the Principia, Newton himself had allowed that his foundations were, in an important sense, provisional: "the principles set down here will shed some light on either this mode of philosophizing or some truer one." Unfortunately, the reviewer does not explain what the starting points or standards of an exact and certain physics look like.
There is a sense, in fact, in which the reviewer can be read as a disappointed Newtonian. For, in the early 1670s, in his early lectures and correspondence on color, Newton had grown infamous for his assertion that his mathematical science of optics could be certain. The claim was watered down in print such that Newton granted Hooke that "the absolute certainty of a science cannot exceed the certainty of its principles." In fact, one can discern in the anonymous reviewer somebody who, after all the high flowing rhetoric of the 1670s (say), had expected from Newton more certain principles than the ones he had supplied in the Principia.
If I am right about this then one can say that rather than representing the informed response of a leading figure in an old paradigm, the 1688 review expresses the perspective of a new possible paradigm, what we may be dub -- with a glance ahead toward Émilie du Châtelet -- Newtonian-rationalism.
+Any faults in what follows should not be attributed to JB.
*By 'arbitrary' the reviewer could mean un-grounded in any evidence. But this would be misleading and also unfair to Newton's complex, abductive argument for the interaction of distant (systems of) bodies. Since the reviewer is otherwise very competent, I treat him/her as saying that there is no rational foundation for this supposition in first principles.