It is to Sir Isaac Newton's Application of Geometry to Philosophy, that we owe the routing of this Army of Goths and Vandals in the philosophical World; which he has enriched with more and greater Discoveries, than all the Philosophers that went before him: And has laid such Foundations for future Acquisitions, that even after his Death, his Works still promote natural Knowledge. Before Sir Isaac, we had but wild Guesses at the Cause of the Motion of the Comets and Planets round the Sun', but now he has clearly deduced them from the universal Laws of Attraction (the Existence of which he has proved beyond Contradiction) and has shewn, that the seeming Irregularities of the Moon, which Astronomers were unable to express in Numbers, are but the just Consequences of the Actions of the Sun and Earth upon it, according to their different Positions. His Principles clear up all Difficulties of the various Phænomena of the Tides; and the true Figure of the Earth is now plainly shewn to be a flatted Spheroid higher at the Equator than the Poles, notwithstanding many Assertions and Conjectures to the contrary.

Were it possible to trace the succession of ideas in the mind of Sir Isaac Newton, during the time that he made his greatest discoveries, I make no doubt but our amazement at the extent of his genius would a little subside. But if, when a man publishes discoveries, he, either through design, or through habit, omit the intermediate steps by which he himself arrived at them; it is no wonder that his speculations confound others... [W]here we see him most in the character of an experimental philosopher, as in his optical inquiries... we may easily conceive that many persons, of equal patience and industry... might have done what he did. And were it possible to see in what manner he was first led to those speculations, the very steps by which he pursued them, the time that he spent in making experiments, and all the unsuccessful and insignificant ones that he made in the course of them; as our pleasure of one kind would be increased, our admiration would probably decrease. Indeed he himself used candidly to acknowledge, that if he had done more than other men, it was owing rather to a habit of patient thinking, than to any thing else. ...[T]he interests of science have suffered by the excessive admiration and wonder, with which several first rate philosophers are considered; and... an opinion of the greater equality of mankind, in point of genius, and powers of understanding, would be of real service in the present age.

My quotations from Newton suggest the motive which induced him to take a stand against the use of hypotheses, namely, the danger of becoming involved in disagreeable controversies. ...Newton could no more dispense with hypotheses in his own cogitations than an eagle can dispense with flight. Nor did Newton succeed in avoiding controversy.

I can measure the motions of bodies,” Sir Isaac Newton once observed, “but I cannot measure human folly.” Nor could he do so as regards his own. He was to lose

In explaining the Notion of & , I have followed Sir Isaac Newton in the first Book, imagining that there can be no difficulty in conceiving Velocity wherever there is Motion; nor do I think that I have departed from his Sense in the second Book; and in both I have endeavoured to avoid several expressions, which, though convenient, might be liable to exceptions, and, perhaps, occasion disputes. I have always represented Fluxions of all... Orders by finite Quantities, the Supposition of an infinitely little Magnitude being too bold a Postulatum for such a Science as Geometry.

I esteem his [Newton's] understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of this work, where the author studies things of little use or when he builds on the improbable principle of attraction.

The prejudice for Sir Isaac has been so great, that it has destroyed the intent of his undertaking, and his books have been a means of hindering that knowledge they were intended to promote. It is a notion every child imbibes almost with his mother's milk, that Sir Isaac Newton has carried philosophy to the highest pitch it is capable of being carried, and established a system of physics upon the solid basis of mathematical demonstration.

The method applied by Newton to the grounding of the Infinitesimal Calculus, and which since the beginning of this century has been recognised by the best mathematicians as the only one that furnishes sure results, is the method of limits. The method consists in this, viz., instead of considering a continuous transition from one value of a quantity to another, from one position to another, or, speaking generally, from one determination of a concept to another, one considers in the first place a transition through a finite number of intervals and then allows the number of these intervals to increase so that the distances of two successive points of division all decrease infinitely.

When the certainty of any part of geometry is brought into question, the most effectual way to set the truth in a full light, and to prevent disputes, is to deduce it from s or first principles of unexceptionable evidence, by demonstrations of the strictest kind, after the manner of the antient geometricians. This is our design in the following treatise; wherein we do not propose to alter Sir Isaac Newton's notion of a , but to explain and demonstrate his method, by deducing it at length from a few self-evident truths, in that strict manner: and, in treating of it, to abstract from all principles and postulates that may require the imagining any other quantities but such as may be easily conceived to have a real existence.

During my controlled near-death experiences, I’ve met Sir Isaac Newton, who died back in 1727 as often as I’ve met Saint Peter. They both hang out at the Heaven end of the blue tunnel of the Afterlife. Saint Peter is there because it’s his job. Sir Isaac is there because of his insatiable curiosity about what the blue tunnel is, how the blue tunnel works.
It isn’t enough for Newton that during his eighty-five years on Earth he invented calculus, codified and quantified the laws of gravity, motion and optics, and designed the first reflecting telescope. He can’t forgive himself for having left it to Darwin to come up with the theory of evolution, to Pasteur to come up with the germ theory, and to Albert Einstein to come up with relativity. “I must have been deaf, dumb, and blind not to have come up with those myself,” he said to me. “What could have been more obvious?”

I can measure the motions of bodies,” Sir Isaac Newton once observed, “but I cannot measure human folly.

After these came to be relished, an infinite scale of infinites and s (ascending and descending always by infinite steps) was imagined and proposed to be received into geometry, as of the greatest use for penetrating into its abstruse parts. Some have argued for quantities more than infinite; and others for a kind of quantities that are said to be neither finite nor infinite, but of an intermediate and indeterminate nature.

While Newton seemed to draw off the veil from some of the mysteries of nature, he showed at the same time the imperfections of the mechanical philosophy, so agreeable to the natural vanity and curiosity of men; and thereby restored her ultimate secrets to that obscurity, in which they ever did and ever will remain.

But, because the Method of Infinitesimals is much in use, and is valued for its conciseness, I thought it was requisite to account explicitly for the truth, and perfect accuracy of the conclusions that are derived from it; the rather, that it does not seem to be a very proper reason that is assigned by Authors, when they determine what is called the Difference (but more accurately the ) of a Quantity, and tell us, That they reject certain Parts of the Element, because they become infinitely less than the other parts; not only because a proof of this nature may leave some doubt as to the accuracy of the conclusion, but because it may be demonstrated that those parts ought to be neglected by them at any rate, or that it would be an error to retain them.