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I. THERE are some men that can neither give nor take an answer, but writing merely for the sake of writing multiply words to no purpose. There are also certain careless writers, that in defiance of common sense publish such things as, though they are not ashamed to utter, yet, other men may well be ashamed to answer. Whether there be any thing in Mr. Walton's method of vindicating fluxions, that might justify my taking no farther notice of him on the abovementioned considerations, I leave you and every other reader to judge. But those, Sir, are not the reasons I shall assign for not replying to Mr. Walton's full answer. The true reason is, that he seems at bottom a facetious man, who under the colour of an opponent writes on my side of the question, and really believes no more than I do of Sir Isaac Newton's doctrine about fluctions, which he exposes, contradicts, and confutes, with great skill and humour, under the mask of a grave vindication.
II. At first I considered him in another light, as one who had good reason for keeping the beaten track, who had been used to dictate, who had terms of art at will, but was indeed at small trouble about putting them together, and perfectly easy about his reader's understanding them. It must be owned, in an age of so much ludicrous. humour, it is not every one can at first sight discern a writer's real design. But, be a man's assertions ever so strong in favour of a doctrine, yet if his reasonings are directly levelled against it, whatever question there may be about the matter in dispute, there
can be none about the intention of the writer. Should a person, so knowing and discreet as Mr. Walton, thwart and contradict Sir Isaac Newton under pretence of defending his fluxions, and should he at every turn. say such uncouth things of these same fluxions, and place them in such odd lights as must set all men in their wits against them, could I hope for a better second in this cause? Or could there remain any doubt of his being a disguised free-thinker in mathematics, who defended fluxions just as a certain free-thinker in religion did the rights of the Christian church.
III. Mr. Walton indeed after his free manner calls my Analyst a libel.* But this ingenious gentleman well knows a bad vindication is the bitterest libel. Had you a mind, Sir, to betray and ridicule any cause under the notion of vindicating it, would you not think it the right way to be very strong and dogmatical in the affirmative, and very weak and puzzled in the argumentative parts of your performance? To utter contradictions and paradoxes without remorse, and to be at no pains about reconciling or explaining them? And with great' good humour, to be at perpetual variance with yourself and the author you pretend to vindicate? How successfully Mr. Walton hath practised these arts, and how much to the honour of the great client he would seem to take under his protection, I shall particularly examine throughout every article of his full answer.
IV. First, then, saith Mr. Walton, "I am to be asked, whether I can conceive velocity without motion, or motion without extension, or extension without magnitude?" To which he answereth in positive terms, that he can conceive velocity and motion in a point (p. 7). And to make out this, he undertakes to demonstrate," that if a thing be moved by an agent operating continually by the same force, the velocity will not be the same in any two different points of the described * Vindication, p. 1.