that resolution. It is true, the public was thereby a gainer; that book, which is indeed no more than a corollary of some propositions in the first, being originally drawn up in the popular way, with a design to publish it in that form; whereas he was now convinced that it would be best, not to let it go abroad without a strict demon stration. In contemplating his genius, it presently becomes a doubt which of these endowments had the greatest share, sagacity, penetration, strength, or diligence; and after all, the mark that seems most to distinguish it is, that he himself made the justest estimation of it, declaring, that if he had done the world any service, it was due to nothing but industry and patient thought; that he kept the subject of consideration constantly before him, and waited till the first dawning opened gradually, by little and little, into a full and clear light. It is said, that when he had any mathematical problems or solutions in his mind, he would never quit the subject on any account. And his servant has said, when he has been getting up in a morning he has sometimes begun to dress, and with one leg in his breeches sat down again on the bed, where he has remained for hours before he has got his clothes on: and that dinner has been often three hours ready for him before he could be brought to table. Upon this head several little anecdotes are related; among which is the following. Dr. Stukely coming in accidentally one day, when Newton's dinner was left for him upon the table, covered up, as usual, to keep it warm till he could find it convenient to come to table; the doctor, lifting the cover found under it a chicken, which he presently ate, putting the bones in the dish, and replacing the cover. Some time after Newton came into the room, and after the usual compliments sat down to his dinner; but on taking up the cover and seeing only the bones of the fowl left, he observed with some little surprise, "I thought I had not dined, but I now find that I have." After all, notwithstanding his anxions care to avoid every occasion of breaking his intense application to study, he was at a great distance from being steeped in philosophy. On the contrary, he could lay aside his thoughts, though engaged in the Imost intricate researches, when his other affairs required his attention: and, as soon as he had leisure, resume the subject at the point where he had left off. This he seems to have done not so much by any extraor dinary strength of memory, as by the force of his inventive facnity, to which every thing opened itself again with ease, if nothing intervened to ruffle him. The readiness of his invention made him not think of putting his memory much to the trial; but this was the offspring of a vigorous intenseness of thought, out of which he was but a common man. He spent therefore the prime of his age in those abstruse researches, when his situation in a college gave him leisure, and while study was his proper business. But as soon as he was removed to the Mint, he applied himself chiefly to the duties of that office; and so far quitted mathematics and philosophy, as not to engage in any pursuits of either kind afterwards. Dr. Pemberton observes, that though his memory was much decayed, in the last years of his life, yet he perfectly understood his own writings, contrary to what I had formerly heard, says the Doctor, in discourse from many persons. This opinion of theirs might arise perhaps from his not being always ready at speaking on these subjects, when it might be expected 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 informed 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 happened, that such as retain things chiefly by means of a very strong memory, have appeared offhand more expert than the discoverers themselves. It was evidently owing to the same inventive faculty that Newton, as this writer found, had read fewer of the modern' mathematicians than one could have expected; his own prodigious invention 'readily supplying him with what he might have occasion for in the pursnit of any subject he undertook. However he often censured the handling of geometrical subjects of algebraic calculations; and his book of Algebra, he called by the name of Universal Arithmetic, in opposition to the injudicious title of Geometry, which Des Cartes had twenty-six years of age, resided, recollectgiven to the treatise in which he shews howed that he had met with the same thing in the geometrician may assist his invention by such kind of computations. 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 ancient analysis; and very much esteemed Apolo nius's book De Sectione Rationis, for giving us a clearer notion of that analysis than we had before. Dr. Barrow may be esteemed as having shewn a compass of invention, equal, if not superior, to any of the moderns, our author only excepted; but Newton particularly recommended 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 démonstration our author always professed himself a great admirer; and even censured himself for not following them yet more closely than he did; and spoke with regret of his mistake at the beginning of his mathematical 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 mathematics, and the doctrine of fluxions and infinite series. And perhaps this might be one reason why his particular reverence for the ancients is omitted by Fontenelle, who however cer. tainly makes some amends by that just elogium which he makes of our author's nodesty, which amiable quality he represents as standing foremost in the character of this great man's mind and manners. It was in reality 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 Fluxions. Nicholas Mercator publishing his Logarithmotechnia in 1668, where he gave the quadrature of the hyperbola by an infinite series, which was the first appear ance in the learned world of a series of this sort drawn from the particular nature of the carve, and that in a manner very new and abstracted. Dr. Barrow, at that time at Cambridge, where Mr. Newton, then about 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 quadratures, their rectifications, and centres of gravity; to the solids formed by their rotations, and to the superficies of those solids, so that, when their determinations were possible, the series stopped at a certain 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 a theory was a mine of gold to a geometrician; but it was a greater glory to have been the discoverer of so surprising and ingenious a system. So that Newton, finding by Mercator's book, that he was in the way to it, and that others might follow in his track, should naturally have been forward 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 discovered his secret, or that others would, before he should become of a proper age for writing! His manuscript upon Infinite Series was communicated to none but Mr. John Collins, and Lord Brounker, then President of the Royal Society, who had also done something in this way himself; and even that had not been complied with, but for Dr. Barrow, who would not suffer him to indulge his modesty so much as he desired. It is further observed, concerning this part of his character, that he never talked either of himself or others, nor ever behaved in such a manner as to give the most malicious censurers the least occasion even to suspect him of vanity. He was candid and affable, and always put himself upon a level with his company. He never thought either his merit or his reputation sufficient to excuse him from any of the common offices of social life. No singularities, either natural or affected, distinguished him from other men. Though he was firmly attached to the Church of England, he was averse from the He persecution of the nonconformists. judged of men by their manners, and the true schismatics, in his opinion, were the vicious and the wicked. Not that he confined his principles to natural religion, for it is said he was thoroughly persuaded of the truth of revelation; and amidst the great variety of books which he had constantly before him, that which he studied with the greatest application was the Bible, at least in the latter years of his life; and he understood the nature and force of moral certainty, as well as he did that of a strict demonstration. Sir Isaac did not neglect the opportunities of doing good, when the revenues of his patrimony and a profitable employment, improved by a prudent economy, put it in his power. We have two remarkable instances of his bounty and generosity; one to Mr. Maclaurin, extra professor of mathematics at Edinburgh, to encourage whose appoint. ment he offered 201. a year, to that office; and the other to his niece Barton, upon whom he settled an annuity of 100l. per annum. When decency upon any occasion required expense and shew, he was magni. ficent without grudging it, and with a very good grace; at all other times, that pomp which seems great to low minds only, was utterly retrenched, and the expense reserved for better uses. Newton never married; and it has been said, that "perhaps he never had leisure to think of it; that, being immersed in profound studies during the prime of his age, and afterwards engaged in an employment of great importance, and even quite taken up with the company which his merit drew to him, he was not sensible of any vacancy in life, nor the want of a companion at home." These however do not appear to be any sufficient reasons for his never marrying, if he had had an inclination so to do. It is much more likely that he had a constitutional indifference to the state, and even to the sex in general. He left at his death, it seems, 32,000l., but he made no will; which, Fontenelle tells us, was because he thought a legacy was no gift. As to his works, besides what were published in his lifetime, there were found after his death, among his papers, several discourses upon the subjects of antiquity, history, divinity, chemistry, and mathematics; several of which were published at different times, as appears from the following catalogue of all his works; where they are ranked in the order of time in which those upon the same subject were published. 1. Several Papers relating to his Teleprinted in the Philosophical Transactions, scope, and his Theory of Light and Colours, Numbers 80, 81, 82, 83, 84, 85, 88, 96, 97, 110, 121, 123, 128; or Vols. 6, 7, 8, 9, 10, 11. tions, Refractions, and Inflections, and the several Letters to Mr. Oldenburg, Secre- article. 4. Lectiones Opticæ, 1729, 4to. thematica, 1687, 4to. A second edition in 5. Naturalis Philosophia Principia Ma1713, with a Preface by Roger Cotes. The third edition in 1726, under the direction of Dr. Pemberton. An English Translation by Motte, 1729, 2 vols. 8vo. printed nations, particularly an edition, with a large in several editions of his works, in different Commentary by the two learned Jesuits, Le Seur and Jacquier, in 4 vols. 4to. in 1739, 1740, and 1742. 6. A System of the World, translated from the Latin original, 1727, 8vo. This, as has been already observed, was at first intended to make the third book of his Principia. An English Translation, by Motte, 1729, 8vo. 7. Several Letters to Mr. Flamsteed, Dr. Halley, and Mr. Oldenburg. 8. A Paper concerning the Longitude, drawn up by order of the House of Cominons. 9. Abregé de Chronologie, &c. 1726, under the direction of the Abbé Conti, together with some Observations upon it. 10. Remarks upon the Observations made upon a Chronological Index of Sir I. Newton, &c. Philosophical Transactions, vol. 33. See also the same, vols. 34 and 35, by Dr. Halley. 11. The Chronology of Ancient Kingdoms amended, &c. 1728, 4to. 12. Arithmetica Universalis, &c. under the inspection of Mr. Whiston, Cantab. 1707, 8vo. Printed without the author's consent, and even against his will, an of fence which, it seems, was never forgiven. There are also English editions of the same, particularly one by Wilder, with a Commentary, in 1769, 2 vols. 8vo.; and a Latin edition, with a Commentary, by Castilion, 2 vols. 4to. Amst. &c. 13. Analysis per Quantitatum Seriæs, Fluxiones, et Differentias, eum Enumeratione Linearum Tertii Ordinis, 1711, 4to. under the inspection of W. Jones, Esq. F. R. S. The last tract had been published before, together with another on the Quadrature of Curves, by the method of Fluxions, under the title of Tractatus duo de Speciebus et Magnitudine Figurarum Curvilinearum, subjoined to the first edition of his Optics, in 1704, and other Letters in the Appendix to Dr. Gregory's Catoptrics, &c. 1735, 8vo. Under this head may be ranked Newtoni Genesis Cur. varum per Umbras, Leyden, 1740. 14. Several Letters relating to his dispute with Leibnitz, upon his right to the Invention of Fluxions; printed in the Commercium Epistolicum D. Johannis Collins et Aliorum, de Analysi Promota, jussu Societatis Regiæ editum, 1712, 8vo. 15. Postscript and Letter of M. Leib nitz to the Abbé Conti, with remarks, and a Letter of his own to that Abbé, 1717, 8vo. To which was added Raphson's History of Fluxions, as a Supplement. 16. The Method of Fluxions and Analysis, by Infinite Series, translated into English from the original Latin; to which is added, a Perpetual Commentary by the Translator, Mr. John Colson, 1736, 4to. 17. Several Miscellaneous Pieces and Letters, as follows: 1. A Letter to Mr. Boyle upon the Subject of the Philosopher's Stone; inserted in the General Dictionary under the article Boyle. 2. A Letter to Mr. Aston, containing Directions for his Travels; ibid. under our Author's article. 3. An English Translation of a Latin Dissertation upon the Sacred Cubit of the Jews; inserted among the Miscellaneous Works of Mr. John Greaves, vol. 2, published by Dr. Thomas Birch, in 1737, 2 vols. 8vo. This Dissertation was found subjoined to a work of Sir Isaac's, not finished, intitled Lexicon Propheticum. 4. Four Letters from Sir Isaac Newton to Dr. Bentley, containing some Arguments in Proof of a Deity, 1756, 8vo. 5. Two Letters to Mr. Clarke, &c. 18. Observations on the Prophecies of Daniel, and the Apocalypse of St. Johm, 1733, 4to. 19. Is. Newtoni Elementa Perspectiva Universalis, 1746, 8vo. 20. Tables for Purchasing College Leases, 1742, 12mo. 21. Corollaries, by Whiston. 22. A Collection of several Pieces of our Author's, under the following title: Newtoni Is. Opuscula Mathematica Philos. et Philol. Collegit I. Castilioneus, Laus. 1744, 4to. 8 tomes. 23. Two Treatises of the Quadrature of Curves, and Analysis by Equations of an Infinite Number of Terms explained, translated by John Stewart, with a large Commentary, 1745, 4to. 24. Description of an Instrument for Observing the Moon's Distance from the Fixed Stars at Sea. Philosophical Trans actions, vol. 42. 25. Newton also published Barrow's Optical Lectures, in 1699, 4to.; and Bern. Varenii Geographia, &c. 1681, 8vo. 26. The Whole Works of Newton, pub. lished by Dr. Horsley, 1779, 4to. in five volumes. NEWTONIAN philosophy, the doctrine of the Universe, and particularly of the Heavenly bodies; their laws, affections, &c. as delivered by Sir Isaac Newton. The term Newtonian philosophy is applied very differently by different authors. Some under this philosophy include all the Corpuscular philosophy, considered as it now stands corrected and reformed by the discoveries and improvements made in the several parts thereof by Sir Isaac Newton. In this sense it is that 's Gravesande calls his Elements of Physics, an Introduction to the Newtonian philosophy; and in this sense, the Newtonian is the same with the new philosophy, in opposition to the Cartesian, the Peripatetic, and the ancient Corpuscular philosophy. Others, by Newtonian philosophy, mean the method or order which Sir Isaac observes in philosophizing, viz. the reasoning and drawing of conclnsions directly from phenomena, exclusive of all previous hypotheses; the beginning from simple principles, deducing the first powers and laws of nature from a few select phenomena, and then applying those laws, &c. to account for other things; and in this sense the Newtonian is the same with Experimental philosophy. Others again, by Newtonian philosophy, mean that wherein physical bodies are considered mathematically, and where geometry and mechanies are applied to the solution of phenomena; in which sense the Newtonian is the same t with the mechanical and mathematical philosophy. Others again, by Newtonian philosophy, understand that part of physical knowledge which Sir Isaac Newton has handled, improved, and demonstrated in his Principia. And, lastly, some by Newtonian philosophy, mean the new principles which Sir Isaac has brought into philosophy, the new system founded thereon, and the new solutions of phenomena thence deduced; or that which characterizes and distinguishes his philosophy from all others: and this is the sense, in which we shall chiefly consider it. As to the history of this philosophy, we have but little to say: it was first made public in 1686, by the author, then a fellow of Trinity College, Cambridge; and in the year 1713, republished with considerable improvements. Several other authors have since attempted to make it plainer, by set ting aside many of the more sublime mathe matical researches, and substituting either more obvious reasonings or experiments in lien thereof; particularly Mr. Whiston, in his Prelect. Phys. Mathem. 's Gravesaude, in bis Elem. and Inst. and the learned Comment of Le Seur and Jacquier upon Sir Isaac's Principia. The philosophy itself is laid down chiefly in the third book of the Principia; the two preceding books being taken up in preparing the way, and demonstrating such principles of mathematics as have the most relation to philosophy: such are the laws and conditions of powers; and these, to render them less dry and geometrical, the author illustrates by scholia in philosophy, relating chiefly to the density and resistance of bodies, the motion of light and sounds, a vacuum, &c. In the third book he proceeds to the philosophy itself; and from the same principles deduces the structure of the universe, and the powers of gravity, whereby bodies tend towards the Sun and planets; and, from these powers, the motions of the planets and comets, the theory of the Moon and the tides. This book, which he calls De Mundi Systemate, he tells us, was first written in the popular way; but considering, that such as are unac quainted with the said principles, would not conceive the force of the consequences, nor be induced to lay aside their ancient prejudices; for this reason, and to prevent the thing from being in continual dispute, he digested the sum of that book into pro. positions, in the mathematical manner, so as it might only come to be read by such as had first considered the principles; not that it is necessary a man should master them all, many of them, even the first rate mathematicians, would find a difficulty in getting over. It is enough to have read the definitions, laws of motion, and the three first sections of the first book; after which, the author himself directs us to pass on to the book De Systemate Mundi. The great principle on which the whole philosophy is founded, is the power of gravity: this principle is not new; Kepler, long ago, hinted at it in his Introduct. ad Mot. Martis. He even discovered some of the properties thereof, and their effects in the motions of the primary planets; but the glory of bringing it to a physical demonstration, was reserved to the English philosopher. See GRAVITATION. proof of this principle from phenomena, together with the application of the same principle to the various other appearances of nature, or the deducing those appearances from that principle, constitute the Newtonian system; which, drawn in miniature, will stand thus: His I. The phenomena are, 1. That the satellites of Jupiter do, by radii drawn to the centre of the planet, describe areas proportional to the times; and that their periodical times are in a sesquiplicate ratio of their distances from its centre; in which the observations of all astronomers agree. 2. The same phenomenon holds of the satellites of Saturn, with regard to Saturn; and of the Moon, with regard to the Earth. 3. The periodical times of the primary planets about the Sun, are in a sesquiplicate ratio of their mean distances from the Sun. But, 4. The primary planets do not describe areas any way proportional to their periodical times about the Earth; as being sometimes seen stationary, and sometimes retrograde, with regard thereto. 11. The powers whereby the satellites of Jupiter are constantly drawn out of their rectilinear course, and retained in their orbits, respect the centre of Jupiter, and are reciprocally as the squares of their distances from the same centre. The same holds of the satellites of Saturn, with regard to Saturn; of the Moon, with regard to the Earth; and of the primary planets, with regard to the Sun. See CENTRAL FORCES. III. The Moon gravitates towards the Earth, and by the power of that gravity is retained in her orbit: and the same holds of the other satellites with respect to their น |