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a gloss which the compilers of the Commercium Epistolicum had not disdained to avail themselves of; that the very words

adhibet semperque adhibuit' were intended to imply the difference between the case of Newton and that of Fabri, to whose practice alone the word substituit applied.

Now, first, Dr Guhrauer seems to have established the fact, that Leibnitz himself was the author of the obnoxious Review-a fact not much to his credit; secondly, he affirms that Leibnitz'constantly denied any, knowledge of the authorship. If this fact were true, we should hardly know what to think of Leibnitz's regard for truth. But, in reality, there nowhere appears, in as far as we have been able to discover, any proof that Leibnitz either denied knowledge of the authorship, or disclaimed the paragraph. He constantly defends the statement it contains, merely denying that it conveyed or could be intended to convey a charge of plagiarism. * To the benefit of this interpretation we would charitably admit him, since he wishes his words to be so taken; but it is impossible not to suspect that the equivocal sentence was framed with little care as to whether it might not be misunderstood. Indeed, so natural is the interpretation of Newton, and the English mathematicians, that Dr Gubrauer himself adopts it; declares that Leibnitz vainly strove to explain the sentence away; and that it is a proof - von Leibnitzens wahrer eigenster Meinung und Gesinnung gegen Newton.'

• Defend me from my friends,’ Leibnitz might well say on this occasion; for if we adopt this interpretation as Leibnitz's true meaning, what are we to think of his shuffling exculpations ?

Dr Guhrauer is not a little indignant with Sir David Brewster, for the supposed injustice which, in his Life of Newton, he has done to Leibnitz, and to which he frequently refers with much bitterness. Never was a complaint more unreasonable. Our distinguished countryman does not question Leibnitz's claim to be regarded as a true inventor of the Calculus; he merely asserts the undoubted priority of Newton's discovery. He expressly affirms, that there is no reason to believe Leibnitz a plagiarist ; but that if there were any necessity for believing either to be so, it must be Leibnitz, and not Newton, who is open to the charge. Dr Guhrauer angrily replies, not simply by saying, (which is true,) that there is no sufficient evidence of Leibnitz's having stolen Newton's invention, but by denying the essential identity of the two methods, and by affirming that they are so different as to be considered unlike things;'-than which nothing can, in our judgment, be more uncandid.

* Dutens' Edition of his Works, Vol. iii, p. 464, &c.

There is only one statement which, as respects Leibnitz, Dr Guhrauer could fairly find any fault with, in Sir David Brewster's work; and that is, that Keill had a "right to express his opinion' that the Letters of Newton, of 1676, gave indications from which Leibnitz. derived, or might derive,' the principles of his Calculus. For reasons already assigned, we do not think that any man had a right to say this ; nor that any one could say it, without being of a different opinion from Newton himself, who undoubtedly must have thought that he had not disclosed what he had designed to conceal. With po other statements of Sir David Brewster as regards Leibnitz, are we disposed to find fault. If he has shown any undue partiality in this matter at all, it is not by excessive severity towards Leibnitz, but by undeserved leniency towards Newton ; for while he has expressed strong indignation at Leibnitz's atrocious charges of plagiarism against Newton, he has very gently touched the virulent reprisals into which Newton was betrayed; who even declared, at last, that Leibnitz's method was but a plagiarism from Barrow—a charge upon which only the very blindness of polemical animosity could have ventured; for it would equally show whence his own Fluxions might have been derived. It exposed him at once to Leibnitz's quiet sarcasm, that if any

could have been profited by Barrow's instructions, it must have o been Newton himself.' • Si quelqu'un a profité de M. Barrow,

ce sera plutôt M. Newton, qui a étudié sous lui, que moi ; qui, autant que je puis m'en souvenir, n'ai vu les livres de M. Barrow qu'à mon second voyage d'Angleterre.'

As both of these illustrious men could justly claim the honour of the disputed invention, so both, in the conduct of the controversy, and in the virulence of expression to which they were carried, in their reciprocal charges and accusations, exhibit themselves in much the same sorry light as the Philosopher in Le Bourgeois Gentilhomme, who begins to lecture the rival masters of dancing and fencing out of Seneca, and ends by forgetting that he is a philosopher altogether. The controversy is indeed an instructive spectacle of human infirmity-showing how passion can cloud the serenest intellects, and inflame the most philosophic temperaments; that its thunder-storms may be found in the highest latitudes—disturbing the frigid poles as well as the burning tropics ; that there is no domain of speculation, however remote, or purely abstract, into which it cannot intrude; and that the Mathematician, as well as the Theologian, can exhibit all the rancour of the most vulgar controvertists. There is probably nothing parallel in history, except the controversy between the Nominalists and Realists, who actually began to fight for and against their shadowy universals. Yet even they first added a religious to the

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purely speculative element, which they at last introduced to such an extent, that they charged each the other with having committed the sin against the Holy Ghost! Newton and Leibnitz had neither the excuse nor the guilt of this superadded provocation.*

However paradoxical apparently may be the phraseology of Leibnitz, in his first expositions of the Differential Calculus, respecting his infinitesimal quantities, (as, that there are quantities infinitely less than quantities infinitely little, and that of two quantities infinitely great, one may be infinitely greater than the other,) it is plain, that he soon worked his own conceptions completely clear, and gave his abbreviated expressions their true interpretation. The explanations of Leibnitz are in fact often so perspicuous, that they ought to have satisfied every objector ; and to bave prevented the elegant and ingenious nonsense which Bishop Berkeley ventured upon, in regard to them, more than thirty years after, in his Analyst. Thus, among many other places, in an explanatory letter to M. Varignon, in 1701, Leibnitz says :

• Je ne me souviens pas assez des expressions dont je puis m'être servi ; mais mon dessein a été de marquer qu'on n'a pas besoin de faire dépendre l'analyse mathématique des controverses métaphysiques, ni d'assurer qu'il y a dans la nature des lignes infiniment petite á la rigeur, en comparaison des nôtres, ni par conséquent qu'il y a des lignes infiniment plus grandes que les nôtres. C'est pourquoi afin d'éviter ces subtilités j'ai crû que pour rendre le raisonnement sensible à tout le monde, il suffisait d'expliquer ici l'infini par l'incomparable, c'est-à-dire, de concevoir

* One other unjust statement of Dr Guhrauer's, we cannot pass un. noticed. The unhappy controversy on the Calculus commenced, it is well known, by some slight skirmishes in the year 1699, when Fatio insinuated, that the applause which Leibnitz was receiving for his Differential Calculus, (first given to the world by him in 1684,) would be more justly bestowed on Newton—its first inventor. Dr Guhrauer is pleased to intimate that Newton was privy to Fatio's attack, and prompted it. This is most unjust, as it is in express contradiction to Newton's assertion, that he knew nothing of Fatio's intention, and was no party to it. In several other places Dr G. insinuates, that it is easy to see that Newton was behind the curtain in the early attacks on Leibnitz, (vol. i. p. 303,) though he did not choose to appear in the controversy himself. Whether it was wise or not in Newton to stand so long aloof-whether it was in sullen pride or real magnanimity—from confidence in his claims, or dislike of controversy-certain it is, that during all the earlier stages of the dispute he remained silent; and being so, no man has a right to charge on him, without explicit evidence, the language of his adherents, whose just pride in the reputation of their countryman is quite sufficient to account both for the rashness of their zeal, and the intemperance of their expressions.

des quantités incomparablement plus grandes ou plus petites que les nôtres; ce qui fournit autant qu'on veut de dégrés d'incomparables, puisque ce qui est incomparablement plus petit, entre inutilement en ligne de compte à l'égard de celui qui est incomparablement plus grand que lui. C'est ainsi qu'une parcelle de matière magnétique, qui passe à traverse du verre, n'est pas comparable avec un grain de sable, ni ce grain avec le globe de la terre, ni ce globe avec le firmamento’s

Dr Guhrauer is very severe on the narrowness of mind'implied in Newton's concealing his Fluxions under ciphers, in his correspondence with Leibnitz; and contrasts it with the frank and manly conduct of the latter, when, in his reply to Newton's second Letter, he communicated the principles of his Calculus to his rival. It ought at all events to reconcile Dr Guhrauer to Newton's procedure, that it formed in fact the safeguard of Leibnitz's claims; for had Newton disclosed his secret, it would have been impossible to establish them.

We must now conclude, though we could have wished to add a few observations on several other matters ;-on Leibnitz's religious opinions,* and theological controversies—especially with Clarke, Bossuet, and Pelisson,-on his political and diplomatic life, in which, with his accustomed versatility, he seems to have been as much at his ease as in literature and

* Of Leibnitz's reputed adoption of the doctrines of Romanism, we have said nothing. It is certain that if he adopted he never avowed them, nor did he ever join the Romish communion. If the unfinished manuscript, called the Systema Theologicum, (not so entitled by him,) really expresses his views, it is, as Dr Guhrauer observes, ' in opposition to all his other writings, and to his whole life also.' Dr Guhrauer's remarks on its origin and purport may be found in Vol, ii. pp. 32-34. . He also treats the whole question of Leibnitz's opinions on this subject very ably in Vol. i. pp. 340-358. It is at the same time certain, that Leibnitz’s tolerant temper, the eclecticism of his philosophy, which always disposed him to find points of reconciliation in opposing systems, whether those of Aristotle and Des Cartes, or of Rome and Luther, his reverence for antiquity, cherished by his profound historical researches—all predisposed him to regard the differences between Romanists and Protestants as far less important than they are. In the attempt to negotiate a reconciliation between them, he expended no small portion of his time and energies, and, in his controversy with Bossuet, he sometimes makes far too liberal concessions for that object. It is not a little curious, and highly characteristic, that he always flattered himself that he was in possession of a metaphysical solution of the Doctrine of Transubstantiation. In this instance at least he verified a naïve assertion he was accustomed to make respecting himself,— That to him, unlike the generality of people, all difficult things were easy, and all

easy things difficult.

science,*-on the influence he exerted on Literature as the
centre of all the literary commerce of the age-an influence
which Mr Stewart has so justly appreciated, and finely illus-
trated in his well-known Dissertation. But on all these topics
our space compels us to be silent, while on others we gladly
content ourselves with referring to the admirable criticisms of
the last-mentioned writer, and his other illustrious coadjutors,
Sir James Mackintosh and Professor Playfair, in their associated
Dissertations on the History of Metaphysical, Ethical, Ma-
thematical, and Physical Science.t In each of these, Leibnitz
is made, so to speak, to re-enter; for while few other names
appear in more than one of them, he is of sufficient importance
to be subjected to a fresh examination in all. So various, in-
deed, are the phases of his character and genius, so numberless
his accomplistiments, that we may apply to him the well-known
lines of Dryden, divested of the satire which was designed in
their original application-

• A man so various that he seem'd to be
Not one, but all mankind's epitome.'

1

Art. II.-1. Exploration Scientifique de l'Algérie pendant les

années 1840, 1841, 1842. Publiée par ordre du Gouvernement, et avec le concours d'une Commission Académique. (Sciences Historiques et Géographiques.) 8vo. Tom. I., II., III.

Paris : 1844. 2. Le Sahara Algérien; Etudes Géographiques, Statistiques, et

Historiques, sur la région au Sud des Etablissements Français en Algérie : ouvrage rédigé sur les Documents recueillis par les soins de M. LE LIEUT.-Col. DAUMAS, et publié avec l'autori

sation de M. le Ministre de la Guerre. 8vo. Paris : 1845.
3. Les Khouan, Ordres Religieux chez les Musulmans de l'Algérie.

Par M. LE CAPITAINE DE Neveu, Membre de la Commission
Scientifique. 8vo. Paris : 1846.

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T HE occupation by France of a large territory upon the northern

coast of Africa, and the vast amount of treasure and num

Of this, a proof rendered more especially remarkable by long subsequent events, is furnished in a Memorial addressed by him to Louis XIV., proposing that memorable plan for keeping some of the chief nations of Europe in check, afterwards attempted to be consummated by Buonaparte ; namely, the conquest and colonization of Egypt. Of this posthumous Piece, an English translation was published in London, in 1803, but which seems now entirely forgotten.

† Prefixed to the Seventh Edition of the Encyclopædia Britannica.

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