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minima, for drawing tangents, and for similar operations, which was equally applicable both to rational and irrational quantities: that illustrious man replied that he also had fallen on a method of the same kind (se quoque in ejusmodi methodum incidisse), and communicated to me his method, which scarcely differed from mine, except in the notation and the idea of the generation of quantities."

There is a curious ambiguity in the words, "he replied that he had fallen on a method of the same kind," which, to those who had not seen the letters that were interchanged, might convey the idea, that Leibnitz had discovered the key to Newton's anagram; but this meaning is not to be found in Leibnitz's letter; he only announces a supposition, honourable to his character, viz. that the concealed method of Newton has, perhaps, some connexion with that which he communicates to him. With this explanation, the above passage in the Principia is in truth a formal recognition of Leibnitz's claims. It was so considered by every one when it appeared, and during twenty years Leibnitz was allowed, without any dispute, to develope all the parts of the differential calculus, and to deduce from it an immense number of brilliant applications, which seemed to extend the power of mathematical analysis far beyond any preconceived limits. In this interval, Wallis, by publishing the above-mentioned letters between Leibnitz and Newton, only rendered, if possible, the claims of the former more complete and more incontestable in the eyes of every impartial person. It was not till 1699 that Nicholas Fatio de Duillier,* in a Memoir, in which he employed the infinitesimal calculus, claimed, in favour of Newton, the first invention of it; "and," added he, "with regard to what Mr. Leibnitz, the second inventor of this calculus may have borrowed from Newton, I refer to the judgment of those persons who have seen the letters and manuscripts relating to this business." Did Fatio really believe what he was writing, or did he wish to flatter the national pride of the country in which he lived? or was he not in some manner irritated at Leibnitz having rendered so little justice to the Principia, and at his appearing to arrogate to himself a sort of empire over all discoveries made by

A Genevese settled in England.

the aid of the new calculus? These questions we do not pretend to decide; but the two latter suppositions are the most probable. Leibnitz replied, by stating the facts, and quoting his letters, and the testimony rendered to him by Newton himself. Fatio was silent; and thus the matter stood till 1704, when Newton published the Optics. In giving an account of the treatise on the quadratur of curves, which was joined to this work, the editor of the Leipzig Acts naturally mentioned the evident analogy that existed between Newton's method of fluxions and the differential calculus which had been published twenty years previously by Leibnitz, in the same Acts, and which had since become the means of making an infinity of analytical discoveries. In comparing the two methods, the editor (whom Newton supposes to have been Leibnitz himself) did not precisely say, that the method of fluxions was a mere transformation of the differential calculus; but he used terms which might bear such an interpretation. This was the signal for attack, on the part of the English writers: one of the most violent of them, Keil, professor of astronomy at Oxford, said, in a paper printed in the Philosophical Transactions, not only that Newton was the first inventor of the method of fluxions, but also that Leibnitz had stolen it from him, by merely changing the name and the notation used by Newton. This produced an indignant reply from Leibnitz, who had the imprudence to submit the question to the judgment of the Royal Society, that is to say, of a tribunal which was presided over by his rival. The society, with scrupulous fidelity, collected all the original letters that could be found bearing on the matter in question, and thus, with regard to the facts, its conduct was unimpeachable; but the most important and delicate part of the business, viz. the discussion of those papers, and the consequences to be deduced by them, it referred to arbitrators chosen by itself, who were not known, and about whose appointment Leibnitz was not consulted. These arbitrators decided that Newton had indubitably been the first discoverer of the method of fluxions, a truth which is certainly incontestable in the sense that discovery and invention are synonimous terms; but they also added two assertions, which can only be considered as the expression of their personal opinion-first, that the differential and

Auxional methods are one and the same thing; and, secondly, that Leibnitz must have seen a letter of Newton's, (dated 10th December, 1672,) in which the method of fluxions is described in a manner sufficiently clear for any intelligent person to understand. Now of these two assertions, the second is not proved in any one of its parts, and the letter of Newton alluded to, appears, according to his custom, to have been more intended for establishing his right, than proper for indicating the manner of attaining his method. With regard to the first assertion, that the methods are absolutely identical, it may easily be refuted by the simple consideration, that if the method of fluxions alone existed at the present moment, the invention of the differential calculus with its notation, and its principle of decomposition into infinitely small elements, would still be an admirable discovery, and one which would immediately bring to light a number of applications, which we now possess, but which probably would not have been obtainable without its assistance. Admitting then, as certain, the priority of Newton's ideas on this subject, we think that the reserve he maintained regarding it left the field open to all other inventors; and that from the general tendency of the mathematical researches of that period, both Leibnitz and Newton might have separately arrived by different means at the knowledge of a method, the want of which was then so sensibly felt in all analytical researches. The quarrel between Newton and Leibnitz has not been without advantage to mathematical science; since it produced the precious collection of letters on infinitesimal analysis, collected by the Royal Society, and published in 1712, under the name of the Commercium Epistolicum. But as regards these two great men themselves, the bitterness with which it inspired the one against the other, became the torment and the misfortune of the remainder of their lives. Newton went so far as to affirm, that Leibnitz had deprived him of the differential calculus, and then that this calculus was identical with Barrow's method of tangents: an assertion of which he could not but have perceived the injustice, since, if he pretended, on the one hand, that the differential calculus and the method of flux. ions were the same, he must have also admitted the method of fluxions to be identical with Barrow's method of tan

gents, an assertion which he was far from admitting. Newton suffered himself to be carried away so far as to pretend that the paragraph inserted in the Principia, by which he had so openly acknowledged the independent rights of Leibnitz, was by no means intended to render him that testimony, but, on the contrary, to establish the priority of the method of fluxions over that of the differential calculus. Newton's animosity was not even calmed by the death of Leibnitz, in 1716: for he immediately afterwards printed two manuscript letters of Leibnitz, written in the preceding year, accompanied with a bitter refutation. Six years later, (in 1722) he caused a new edition of the Commercium Epistolicum to be printed, at the head of which he placed a very partial extract from this Collection. This was apparently made by himself, and had already appeared two years before the death of Leibnitz, in the Philosophical Transactions for 1715. Finally, Newton had the weakness to leave out, or allow to be left out, in the third edition of the Principia, published under his own inspection, 1725, the famous Scholium, in which he had admitted the rights of his rival. To render such conduct, not to say excusable, but even comprehensible, on the part of a man who must so well have known that the only tribunal that can decide on such causes is impartial posterity, it is necessary to say that Leibnitz, on his side, had neither been less passionate nor less unjust. Hurt by the unexpected publication of the Commercium Epistolicum, and irritated by a decision, given without his knowledge, by judges whom he had not appointed, and who had not waited for his defence, he summoned contrary testimonies in his support. Leibnitz had the misfortune to produce proofs equally exaggerated with those brought forward by Newton. He printed, and spread throughout Europe, an anonymous letter (since discovered to have been written by J. Bernoulli), extremely injurious to Newton, whom it represented as having fabricated his method of fluxions from the differential calculus. Leibnitz committed a still greater fault. He was in the habit of corresponding with the Princess of Wales, daughterin law to George the First. This princess, endowed with a highly cultivated mind, had received Newton with extreme kindness, and was fond of conversing with him, She declared that she esteemed

herself happy in living at a time that enabled her to become acquainted with so great a genius. Leibnitz made use of his correspondence with the princess, to lower Newton in her eyes, and to represent his philosophy to her not only as physically false, but also as dangerous in a religious point of view; and, what is still more inconceivable, he founded these accusations on passages in the Principia, and in the Optics, which Newton had evidently composed and inserted with intentions sincerely religious, and as genuine professions of his firm belief in a divine Providence. For instance, in explaining the true method to be pursued in natural philosophy, Newton says, in his Twenty-eighth Query," the main business of this science is to argue from phenomena, without feigning hypotheses, and to deduce causes from effects, till we come to the very First Cause; which certainly is not mechanical: and not only to unfold the mechanism of the world, but chiefly to resolve these and such like questions. What is there in places almost empty of matter, and whence is it, that the sun and planets gravitate towards one another, without dense matter between them? Whence is it that nature doth nothing in vain, and whence arises all that order and beauty, which we see in the world? To what end are comets, and whence is it that planets move all one and the same way, in orbs concentric, while comets move all manner of ways in orbs very eccentric; and what hinders the fixed stars from falling upon one another? How came the bodies of animals to be contrived with so much art? and for what ends were their several parts? was the eye contrived without skill in optics, and the ear without knowledge of sounds? How do the motions of the body follow from the will, and whence is the instinct in animals? Is not the sensoryof animals that place to which the sensitive substance is present; and into which the sensible species of things are carried through the nerves and brain, that there they may be perceived, by their immediate presence to that substance? And these things being rightly dispatched, does it not appear from phenomena, that there is a Being incorporeal, living, intelligent, omnipresent, who in infinite space, as it were, in his sensory, sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself; and

which things, the images only, carried through the organs of sense into our little sensoriums, are there seen and beheld, by that which in us perceives and thinks; and though every true step made in this philosophy bring us not immediately to the knowledge of the First Cause, yet it brings us nearer to it, and on that account is to be highly valued?"

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It is thus that Newton speaks of a Supreme Being; and even those who might dispute the arguments which he gives for such an existence, must still recognize, in this passage, the sentiments of a mind deeply imbued with religious feelings, and convinced of their true foundation. It was upon this ground, however, that Leibnitz attacked him in his correspondence with the princess: "it appears," says he, in one of his letters, that natural religion is diminishing extremely in England;" and he cites as a proof the works of Locke, and the above passage from Newton; elsewhere he "that says, these principles are precisely those of the materialists." When we see a mind of the order of that of Leibnitz expressing itself with such blind contempt for the grand and incontrovertible discovery of universal gravitation, and employing such arguments in objecting to it, we are disposed to compassionate the occasional weakness of the finest intellects, and to deplore the petty passions which tarnish the splendour of genius. The rank of the person to whom this accusation was addressed increased its importance in those days. The king was informed of the matter, and expressed his expectation that Newton would reply. It would appear that it was this authority that determined Newton personally to enter the lists; but he only undertook the defence of the mathematical part of the question; the philosophical part he left to Dr. Clarke, who, though inferior as a mathematician, was a better metaphysician than himself. From this resulted a great number of letters, written by Clarke and Leibnitz to each other, which were all inspected by the princess. In the course of this correspondence, as often happens, the original question was lost amidst collateral disquisitions. On reading these letters, it must excite surprise that a woman of rank could amuse herself with discussions of this sort,

These letters were published in France by Des maizeaux.

mixed up as they were with the coarse and erudite jests made use of by Leibnitz. To this taste, however, of the princess for serious matters we owe our acquaintance with a work of Newton, very different from those that we have hitherto mentioned. Conversing one day on some historical subject, Newton explained to her a system of chronology, which he had formerly composed, simply for amusement. The princess was so much pleased with it, that she requested a copy, for her own use, on which latter condition Newton complied with her request: he, however, gave also a copy to the Abbé Conti, who had made himself remarkable by interfering in the disputes between Leibnitz and Newton. No sooner was the Abbé in Paris, than he communicated this manuscript to the world. It was immediately translated and printed, not only without the consent or knowledge of Newton, but even accompanied with a refutation by Fréret. Newton had thus the mortification to hear at the same time of the publication and reply, without having had any suspicion of the transaction; and was hence obliged, though contrary to his original intention, at least to give a more correct edition; but he was only able to prepare one: it did not appear till after his death in 1728.

This leads us to speak of another work of Newton, which, though appearing to differ much in its title from the one we have just mentioned, is, like it, an historical memoir; the title is, “Observations upon the Prophecies of Holy Writ, particularly the Prophecies of Daniel and the Apocalypse of St. John." Notwithstanding the singularity such a subject appears to offer, when treated of by a mind like that of Newton, we venture to affirm, that more persons have spoken of this dissertation than have given themselves the trouble to read it; it therefore becomes our duty here to point out more particularly the object which Newton had in view, and his manner of proceeding. The groundwork of his reasoning is concisely expressed by the following words in the work itself: *

"The folly of interpreters hath been to foretell times and things by this prophecy, as if God designed to make them prophets. By this rashness they have not only exposed themselves, but brought

• Age of Apocalypse.

the prophecy also into contempt. The design of God was much otherwise. He gave this and the prophecies of the Old Testament, not to gratify men's curiosities, by enabling them to foreknow things; but that after they were fulfilled, they might be interpreted by the event; and his own Providence, not the interpreters', be then manifested thereby to the world. Now," says Newton, "for understanding the prophecies, we are in the first place to acquaint ourselves with the figurative language of the prophets; this language is taken from the analogy between the world natural and an empire or kingdom considered as a world politic." He then successively enters into all the details of this connexion; first of all considering the heavens and the earth as representing thrones and people; then taking the astronomical phenomena, the rain, the hail, the meteors, the animals, the vegetables, their different parts, their different actions, and those of man himself; and finally, every thing in the material world, as having a peculiar mystic signification which he fixes and defines : "for instance," says he, "when a beast or man is put for a kingdom, his parts and qualities are put for the analogous parts and qualities of the kingdom: as the head of a beast for the great men who precede and govern; the tail for the inferior people who follow and are governed; the heads, if more than one, for the number of capital parts, or dynasties or dominions in the kingdom, whether collateral or successive, with respect to the civil government; the horns on any head for the number of kingdoms in that head, with respect to military power; seeing for understanding and policy; and in matters of religion for T, bishops; speaking for making laws; the mouth for a lawgiver, &c. &c."+ Down to this point we find, in fact, nothing new, except the precise and, in some degree, systematic explanation of the method of interpretation: for at bottom this method is that which has been employed by all commentators; and it is really impossible to employ any other, in applying a prophecy which is not explicit in its terms. The distinguishing character of Newton's work is, that having thus made his glossary beforehand, it often suffices him for explaining a prophecy, to place the figu

Prophecies, part 1. chap. 2. + Prophecies, part 1. chap. 2. p. 8. D

rative terms word for word opposite to the explanations: by these means he makes a quicker and more extended progress. We will not follow him in the vast career he proposed to go over. Furnished with what he considered a key to prophetical language, he successively questions Daniel and St. John, and endeavours to produce, from their prophecies, the historical events that have taken place since their time. His work is immense; it embraces not only the principal epochs, and the most important events, in the ancient and in a part of the middle ages, but also a multitude of particular facts, of chronological observations, and of researches on civil or ecclesiastical antiquities, showing deep and extensive knowledge, taken from the most authentic sources. To give an idea of the detailed applications by which Newton has allowed himself to be carried away in this singular composition, and at the same time not to leave unnoticed the spirit of prejudice of which unhappily it bears the stamp, we will extract a passage in the seventh and eighth chapters of the first part. Newton has explained the ten horns of the fourth beast of Daniel by the ten kingdoms which the barbarians founded on the ruins of the Roman empire in the west, and has rapidly traced the history of each of these kingdoms, in order to show how it agrees with the prophecies. It remains to explain the eleventh horn of the same beast: the words of scripture are: "Now Daniel considered the horns, and behold there came up among them another horn, before whom there were three of the first horns plucked up by the roots; and behold in this horn were eyes like the eyes of a man, and a mouth speaking great things, and his look was more stout than his fellows, and the same horn made war with the saints, and prevailed against them: and one who stood by, and made Daniel know the interpretation of these things, told him, that the ten horns were ten kings that should arise, and another should arise after them and be diverse from the first, and he should subdue three kings, and speak great words against the Most High, and wear out the saints, and think to change times and laws and that they should be given into his hands until a time and times and half a time." "Now," says Newton, "kings are put for kingdoms as above; and therefore the little horn is a little kingdom. It was a horn of the

fourth beast, and rooted up three of his first horns; and therefore we are to look for it among the nations of the Latin empire, after the rise of the ten horns. But it was a kingdom of a different kind from the other ten kingdoms, having a life or soul peculiar to itself, with eyes and a mouth. By its eyes it was a seer; and by its mouth speaking great things, and changing times and laws, it was a prophet as well as a king. And such a seer, a prophet, and a king, is the church of Rome." Newton then supports this analogy by an historical account of the rise and progress of the papal power, the details of which he, in succession, compares with the prophecy. Newton carries this investigation no further than the last half of the eighth century, because," says he, "the Pope, by acquir ing temporal power, is clearly designated by the prophet:" but carried beyond the limits previously assigned by himself to interpreters, he goes on to predict the epoch of the fall, or at least decline of this temporal power, for translating the expression of Daniel, "a time and times and half a time," by 1260 solar years, and indicating the year 800 as about the point to count from, he fixes the fatal term to be about the year 2060. We must remark, that this conclusion is not, in his work, as in those of some other protestant writers, dictated by any sectarian or party feeling; he states it with all the calm of entire conviction, and with all the simplicity of an evident demonstration. It appears to be not Newton, but St. John and Daniel, who attack the power of modern Rome, who characterize it by injurious terms, and finally predict its ruin.

It will, doubtless, be asked, how a mind of the character and force of Newton's, so habituated to the severity of mathematical considerations, so accustomed to the observation of real phenomena, so methodical, and so cautious, even at his boldest moments in physical speculation, and consequently so well aware of the conditions by which alone truth is to be discovered, could put together such a number of conjectures, without noticing the extreme improbability that is involved in all of them, from the infinite number of arbitrary postulates on which he endeavours to establish his system. The answer to this question must be taken entirely from the ideas and the habits of the age

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