tion readily supplying him with what he might have occasion for in the pursuit of any subject he undertook. However he often censured the handling of geometrical subjects by 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 bad given to the treatise in which he shews how 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 be gan to prevail. He used to commend the laudable attempt of Hugo d'Omerique to restore the ancient analysis; and very much esteemed Apollonius'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 demonstration 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 de

serves.

But if this were 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 certainly makes some amends by that just eulogium which he makes of our author's modesty, which amiable quality be 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 Logarithmotechuia in 1668, where he gave the quadrature of the hyperbola by an infinite series, which was the first appearance in the learned world of a series of this sort drawn from the particular nature of the curve, and that in a manner very new and abstracted. Dr. Barrow, at that time at Cambridge, where Mr. Newton, 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 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 imagina

tion 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 modes ty, 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 Infiante 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 af fected, distinguished him from other men. Though he was firmly attached to the church of England, he was averse from the persecution of the nonconformists. He judged of men by their conduct, and the true schismatics, in his opinion, were the vicious and the wicked. Not that he confined his principles to natural religion, for he was doubtless 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 appointment he offered 20%. a year to that office; and the other to his niece Barton, upon whom he settled an annuity of 1004. per annum. When decency upon any occasion required expence and shew, he was magnificent 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 expence reserved for better uses.

Sir Isaac added to his other great qualities not only a belief in revelation, but a decided aversion to the too common habit of speaking lightly of the scriptures. One anecdote of this great man may be useful,and therefore merits a place here. Dr. Halley was an unbeliever, and was once speaking rather freely on the subject of revelation, in company with sir Isaac, who pointedly said to him"Dr. Halley, I am always glad to hear you when you speak about astronomy, or other parts of ma

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 importauce, 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 ineli ation so to do. It is much more likely that he had a constitutional in lifference to the state.

He left at his death, it seems, 32,000/., but he made no will: which, Fontenelle tells us, was hecause 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 Telescope, and his Theory of Light and Colours, printed in the Philosophical Transactions, numbers 80, 81, 82, 83, 84, 85, 88, 96, 97, 110, 121, 123, 128; or vols. 6, 7, 8, 9, 10, 11.

2. Optics, or a Treatise of the Reflections, Refractions, and Inflections, and the Colours of Light, 1704, 4to. A Latin Translation, by Dr. Clarke, 1706, 4to.; and a French Translation, by P. Caste, Amst. 1729, 2 vols. 12mo. Besides several English editions in 8vo.

5. Optical Lectures, 1728, 8vo.; also in several Letters to Mr. Oldenburg, Secretary to the Royal Society, inserted in the General Dictionary, under our author's article.

4. Lectiones Opticæ, 1729, 4to.

5. Naturalis Philosophiæ Principia Mathematica, 1687, 4to. A second edition in 1713, with 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 in several editions of his works, in different nations, particularly an edition, with a large 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 Commons.

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 55, by Dr. Halley.

11. The Chronology of Ancient Kingdoms amended, &c. 1728, 4to.

12. Arithmetica Universalis, &c. under the in

spection of Mr. Whiston, Cantab. 1707, 8vo. Printed without the author's consent, and even against his will; an offence which, it seems, was scarcely 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 Castillion, 2 vols. 4to. Amst. &c.

13. Analysis per Quantitatum Series, Fluxiones, et Differentias, cum 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 Curvarum per Umbras, Leyden, 1740.

14. Several Letters relating to his dispute with Leibnitz, upon the right to his 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. Leibnitz 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 Euglish 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. John, 1733, 4to. 19. Is. Newtoui Elementa perspectivæ Univer salis, 1746, 8vo.

20. Tables for Purchasing College Leases, 1748, 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. Casti lioneus, 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 lustrument for observing the Moon's Distance from the fixed Stars at Sea. Philosophical Transactions, 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, published by Dr. Horsley, 1779, 4to. in Live volumes.

lude all the corpuscular philosophy, considered as it now stands, corrected and reformed by the discoveries and improvement made in several parts thereof by sir Isaac Newton. In which sense it is that Gravesar de calls his elements of physics, Introductio ad Philosophiam Newtonianam. And in this sense the Newtonian is the same with the new

philosophy; and stands contradistinguished from the Cartesian, the Peripatetic, and the ancient corpuscular.

Others, by Newtonian philosophy, mean the method or order which sir Isaac Newton observes in

philosophising; viz. the reasoning and drawing of conclusions 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 philosophy is the same with the experimental philosophy, and stands opposed to the ancient corpuscular.

Others, by Newtonian philosophy, mean that wherein physical bodies are considered mathematically, and where geometry and mechanics are applied to the solution of the appearances of nature. In which sense the Newtonian is the same 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.

Others, lastly, by Newtonian philosophy, mean the new principles which sir Isaac Newton 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.-It is in this sense principally we shall here consider it.

The whole of the Newtonian philosophy, as defivered by the author, is contained in his Principia, or Mathematical Principles of Natural Philosophy. He founds his system on the following definitions. 1. The quantity of matter is the measure of the same, arising from its density and bulk conjanctly. Thus air of a double density, in a double space, is quadruple in quantity; in a triple space, sextuple in quantity, &c.

2. The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly. This is evident, because the motion of the whole is the motion of all its parts; and therefore in a body double in quantity, with equal velocity, the motion is double, &c.

3. The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest, or moving uniformly forward in a right line.

4. An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uniformly forward in a right line.-This force consists in the action only; and remains no longer in the body when the action is over. For a body maintains every new state it acquires by its vis inertia only.

It is here implied, and indeed fully expressed, that motion is not continued by the same power that produced it. Now there are two grounds on which the truth of this doctrine may be supposed to rest.

"First, On a direct proof that the impressed force does not remain in the body, either by showing the nature of the force to be transitory and incapable of more than its first action; or that it acts

only on the surface, and that the body escapes from it; or that the force is somewhere else, and not remaining in the body. But none of these direct proofs are offered.

"Secondly, It may rest on an indirect proof, that there is in the nature of a body a sufficien for the continuance of every new state acqui and that therefore any adventitious force to continue motion, though necessary for its production, is su perfluous and inadmissible. As this is the very ground on which the supposition stands, it ought to have been indubitably certain that the innate force of the body is sufficient to perpetuate the motion it has once acquired, before the other agent, by which the motion was communicated, had been dismissed from the office. But the innate force of body has been shown not to be that which continues its motion; and therefore the proof, that the impressed force does not remain in the body, fails. Nor indeed is it in this case desirable to support the proof, because we should then be left without any reason for the continuance of motion." When we mention an impressed force, we mean such a force as is communicated either at the surface of the body or by being diffused through the mass.

5. A centripetal force is that by which bodies are drawn, impelled, or any way tend towards a point, as to a centre.-The quantity of any centripetal force may be considered as of three kinds, absolute, accelerative, and motive.

6. The absolute quantity of a centrifugal force is a measure of the same, proportional to the efficacy of the cause that propagates it from the centre, through the spaces round about.

7. The accelerative quantity of a centripetal force is a measure of the same, proportional to the velocity which it generates in a given time.

8. The motive quantity of a centripetal force is the measure of the same, proportional to the motion which it generates in a given time.-This is always known by the quantity of a force equal and contrary to it, that is just sufficient to hinder the descent of the body.

SCHOLIA.

1. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably, without regard to any thing external, and, by another name, is called duration. Relative, apparent, and common time, is some sensible and external measure of duration, whether accurate or not, which is commonly used instead of true time; such as an hour, a day, a month, a year, &c.

II. Absolute space, in its own nature, without regard to any thing external, remains always similar and immoveable. Relative space is some moveable dimension or measure of the absolute spaces; and which is vulgarly taken for immoveable space. Such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position to bodies, and which is vulgarly taken for immoveable space; as the distance of a subterraneous, an acrial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air which, relatively and in respect of the earth, remains always the same, will at one time be one part of the absolute space into which the earth passes; at another time it will be another part of the same; and so absolutely understood, it will be perpetually mutable.

III. Place is a part of space which a body takes

mp; and is, according to the space, either absolute or relative. Our author says it is a part of space; not the situation, nor the external surface of the body. For the places of equal solids are always equal; but their superficies, by reason of their dissimilar figures, are often unequal. Positions properly have no quantity, nor are they so much the places themselves as the properties of places. The motion of the whole is the same thing with the sum of the motions of the parts; that is, the translation of the whole out of its place is the same thing with the sum of the translations of the parts out of their places: and therefore the place of the whole is the same thing with the sum of the places of the parts; and for that reason it is eternal, and in the whole body.

IV. Absolute motion is the translation of a body from one absolute place into another; and relative motion the translation from one relative place into another. Thus, in a ship under sail, the relative place of a body is that part of the ship which the body possesses, or that part of its cavity which the body fills, and which therefore moves together with the ship: and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real absolute rest is the continuance of the body in the same part of that immoveable space in which the ship itself, its cavity, and all that it contains, is moved. Wherefore, if the earth is really at rest, the body which relatively rests in the ship will really and absolutely move with the same velocity which the ship has on the earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth in immoveable space; partly from the relative motion of the ship on the earth and if the body moves also relatively in the ship, its true motion will arise partly from the true motion of the earth in immoveable space, and partly from the relative motions as well of the ship on the earth as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth. As if that part of the earth where the ship is was truly moved towards the east, with a velocity of 10010 parts; while the ship itself with a fresh gale is carried towards the west, with a velocity expressed by 10 of these parts; but a sailor walks in the ship towards the east with one part of the said velocity: then the sailor will be moved truly and absolutely in immoveable space towards the east with a velocity of 1001 parts; and relatively on the earth towards the west, with a velocity of 9 of those parts.

Absolute time, in astronomy, is distinguished from relative, by the equation or correction of the vulgar time. For the natural days are truly unequal, though they are commonly considered as equal, and used for a measure of time: astronomers correct this equality for their more accurate deducing of the celestial motions. It may be that there is no such thing as an equable motion whereby time may be accurately measured. All motions may be accelerated or retarded; but the true or equable progress of absolute time is liable to no change. The duration or perseverance of the exist ence of things remains the same, whether the motions are swift or slow, or none at all; and therefore ought to be distinguished from what are only sensible measures thereof, and out of which we collect it by means of the astronomical equation. The necessity of which equation for determining the times of a phenomenon is evinced, as well from the experiments of the pendulam-clock as by eclipses of the satellites of Jupiter.

As the order of the parts of time is Immutable, so also is the order of the parts of space. Suppose those parts to be moved out of their places, and they will be moved (if we may be allowed the expression) out of themselves. For times and spaces are, as it were, the places of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary_places of things should be moveable is absurd. These are therefore the absolute places; and translations out of those places are the only absolute motions.

But because the parts of space cannot be seen, of distinguished from one another by the senses, therefore in their stead we use sensible measures of them. For, from the positions and distances of things from any body, considered as immoveable, we define all places; and then, with respect to such places, we estimate all mutions, considering bodies as transferred from some of those places into others. And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs: but in philosophical disquisitions we ought to abstract from our senses, and consider things themselves distinct from what are only sensible measures of them. For it may be, that there is no body really at rest, to which the places and motions of others may be referred.

But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects. It is a property of rest, that bodies really at rest do rest in respect of each other. And therefore, as it is possible, that, in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest, though it be impossible to know from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body; it follows, that absolute rest cannot be determined from the position of bodies in our regions.

It is a property of motion, that the parts which retain given positions to their wholes do partake of the motion of their wholes. For all parts of revolv ing bodies endeavour to recede from the axis of motion; and the impetus of bodies moving for wards arises from the joint impetus of all the parts, Therefore if surrounding bodies are moved, those that are relatively at rest within them will partake of their motion. Upon which account the true and absolute motion of a body cannot be determined by the translation of it from those only which seem to rest; for the external bodies ought not only to appear at rest, but to be really at rest. For otherwise all included bodies, beside their translation from near the surrounding ones, partake likewise of their true motions; and though that translation was not made, they would not really be at rest, but only seem to be so. For the surrounding bodies stand in the like relation to the surrounded, as the exterior part of a whole does to the interior, or as the shell does to the kernel; but if the shell moves, the kernel will also move, as being part of the whole, without any removal from near the shell.

A property near akin to the preceding is, that if a place is moved, whatever is placed therein moves along with it; and therefore a body which is moved from a place in motion, partakes also of the motion of its place. Upon which account all motions from places in motion, are no other than parts of entire and absolute motions; and every entire motion in composed of the motion of the body out of its first place, and the motion of this place out of its place;