Dr. Pemberton observes, that though his memory was much decayed, in the last years of his life, yet he perfectly under stood his own writings, contrary to what I had formerly heard says the doctor, in discourse from many persons: This opi nion of theirs might arise, perhaps, from his not being always ready at speaking on these subjects, when it might be expect ed he should. But on this head it may be observed, that great geniuses are often liable to be absent, not only in relation to common life, but with regard to some of the parts of science that they are best in formed of; inventors seem to treasure up in their minds what they have found out, after another manner than those do the same things who have not this inventive faculty. The former, when they have occasion to produce their knowledge, are in some measure obliged immediately to investigate part of what they want ; and for this they are not equally fit at all times; from whence it has often happen ed, that such as retain things chiefly by means of a very strong memory, have appeared off-hand more expert than the discoverers themselves.
It was evidently owing to the same in ventive faculty that Newton, as this writer found, had read fewer of the modern ma thematicians lhan one could have expect ed ; his own prodigious invention readily supplying him with what he might have occasion for in the pursuit of any subject he undertook. However, he often cen sured the handling ofgeometrical subjects of algebraic calculations; and his book of Algebra, he called by the name of Uni versal Arithmetic, in opposition to the injudicious title of Geopetry, which Des Cartes had given to the treatise, in which he shows how the geometrician may assist his invention bysuch ki ndof comp utatioos. He frequently praised Slusius, Barrow, and Huygens, for not being influenced by the false taste which then began to prevail. He used to commend the laudable attempt of Hugo d'Omerique to restore the anci ent analysis; and very much esteemed Apolonius's book De Sectione Rationis, for giving us a clearer notion of that ana lysis than we had before. Dr. Barrow may be esteemed as having shewn a com pass of invention, equal, if not superior, to any of the moderns, our author only excepted ; but Newton particularly re commended Huygens's style and manner: he thought him the most elegant of any mathematical writer of modern times, and the truest imitator of the ancients.
Of their taste and mode of demonstra tion, our author always professed himself a great admirer; and even censured him self for not following them yet more close ly than he did; and spoke with regret of his mistake at the beginning of his mathe matical studies; in applying himself to the works of Des Cartes, and other algebraic writers, before he had considered the Elements of Euclid with that attention which so excellent a writer deserves.
But if this was a fault, it is certain it was a fault to which we owe both his great inventions in speculative mathema tics, and the doctrine of fluxions and in finite series. And perhaps this might be
one reason why his particular reverence for the ancients is omitted by Fontenelle, who, however, certainly makes some amends by that jest eulogium which he makes of our author's modesty, which amiable quality he represents as standing foremost in the character of this great man's mind and manners. It was in re ality greater than can be easily imagined, or will be readily believed; yet it always continued so, without any alteration, though the whole world, says Fontenelle, conspired against it ; let us add, though he was thereby robbed of his invention of Fluxion. Nicholas Mercator, publishing his Logarithmotechnia in 1668, where he gave the quadrature of the hyperbola by an infinite series, which was the first ap pearance in the learned world of a series of this sort, drawn from the particular na thre of the curve, and that in a manner very new and abstracted. Dr. Barrow, at that time at Cambridge, where Mr. New ton, then about twenty-six years of age, resided, recollected that he had met with the same thing, in the writings of that young gentleman, and there not confined to the hyperbola only, but extending, by general forms, to all sorts of curves, even such as are mechanical ; to their quadra tures, their rectifications, and centres of gravity ; to the solids formed by their ro tations, and to the superficies of those solids, so that, when their determinations were possible, the series stopped at a cer tain point, or at least their sums were given by stated rules ; and if the absolute determinations were impossible, they could yet be infinitely approximated ; which is the happiest and most refined method, says Fontenelle, of supplying the defects of human knowledge, that man's imagination could possibly invent. To be master of so fruitful and general i theory was a mine of gold to a geometrician ; but it was a greater glory to have been the discoverer of so surprising and inge nious a system. So that Newton, finding by Mercator's book that be was in the way to it, and that others might follow in his track, should naturally have been for ward to open his treasures, and secure the property which consisted in making the discovery ; but he contented himself with his treasure which he had found, without regarding the glory. What an idea does it give us of his unparalleled modesty, when we find him declaring, that he thought Mercator had entirely dis covered his qeoret, or that others would, before he should become of a proper age foe writing! His manuscript upon Infi nite Series was communicated to none but Mr. John Collins, and Lord Brounker, then president of the Royal Society, who had also done somethine in this way him self ; and even that had not been compli ed with, but for Dr. Barrow, who would not suffer him to indulge his modesty so much as he desired.