am afterwards to make, it will appear, that, without general terms, all our reafonings muft neceffarily have been limited to particulars; and, confequently, it is owing to the ufe of thefe, that the philofopher is enabled to fpeculate concerning claffes of objects, with the fame facility with which the favage or the peafant fpeculates concerning the individuals of which they are compofed. The technical terms, in the different sciences, render the appropriated language of philofophy a ftill more convenient inftrument of thought, than thofe languages which have originated from popular ufe; and in proportion as thefe technical terms improve in point of precision and comprehensiveness, they will contribute to render our intellectual progrefs more certain and more rapid. "While engaged" (fays Mr. Lavoifier) "in "the compofition of my elements of Chemistry, I "perceived, better than I had ever done before, the "truth of an obfervation of Condillac, that we think only through the medium of words; and that lanແ guages are true analytical methods. Algebra, "which, of all our modes of expreffion, is the most "fimple, the most exact, and the best adapted to its purpose, is, at the fame time, a language and an "analytical method. The art of reasoning is nothing more than a language well arranged." The influence which thefe very enlightened and philofophical views have already had on the doctrines of chemistry, cannot fail to be known to most of my readers.

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The foregoing remarks, in fo far as they relate to the poffibility of affifting our reafoning and inventive powers, by new inftrumental aids, may perhaps appear to be founded too much upon theory; but this objection cannot be made to the reafonings I have offered on the importance of the ftudy of method.-To the juftnefs of these, the whole history of fcience bears teftimony; but more especially, the

hiftories of Phyfics and of pure Geometry; which afford fo remarkable an illuftration of the general doctrine, as can scarcely fail to be fatisfactory, even to those who are the moft difpofed to doubt the efficacy of art in directing the exertions of genius.

With refpect to the former, it is fufficient to mention the wonderful effects which the writings of Lord Bacon have produced, in accelerating its progrefs. The philofophers, who flourished before his time, were, undoubtedly, not inferior to their fucceffors, either in genius or industry: but their plan of investigation was erroneous; and their labours have produced only a chaos of fictions and abfurdities. The illuftrations which his works contain, of the method of induction, general as the terms are, in which they are expreffed, have gradually turned the attention of the moderns to the rules of philofophifing; and have led the way to thofe important and fublime discoveries in phyfics, which reflect fo much honour on the prefent age.

The rules of philofophifing, however, even in phyfics, have never yet been laid down with a fufficient degree of precision, minutenefs, or method; nor have they ever been ftated and illuftrated in fo clear and popular a manner, as to render them intelligible to the generality of readers. The truth, perhaps, is; that the greater part of physical inquirers have derived what knowledge of them they poffefs, rather from an attention to the excellent models of investigation, which the writings of Newton exhibit, than from any of the fpeculations of lord Bacon, or his commentators: and, indeed, fuch is the incapacity of most people for abftract reafoning, that I am inclined to think, even if the rules of inquiry were delivered in a perfectly complete and unexceptionable form, it might ftill be expedient to teach them to the majority of ftudents, rather by examples, than in the form of general principles. But it does not

therefore follow, that an attempt to illuftrate and to methodize these rules, would be useless; for it must be remembered, that, although an original and inventive genius, like that of Newton, be sufficient to establish a standard for the imitation of his age, yet, that the genius of Newton himself was encouraged and led by the light of Bacon's philofophy.

τική

The ufe which the ancient Greek geometers made of their analyfis, affords an additional illustration of the utility of method in guiding fcientific invention. To facilitate the ftudy of this fpecies of investigation, they wrote no lefs than thirty-three preparatory book; and they confidered an addrefs, in the practice of it, (or, as Marinus calls it a duvas avaλutin) as of much more value, than an extenfive acquaintance with the principles of the fcience.* Indeed, it is well known, to every one who is at all converfant with geometrical investigations, that although it may be poffible for a perfon, without the affiftance of the method of analysis, to stumble accidentally on a folution, or on a demonstration; yet it is impoffible for him to poffefs a juft confidence in his own powers, or to carry on a regular plan of invention and discovery. It is well known, too, that an acquaintance with this method brings geometers much more nearly upon a level with each other, than they would be otherwife: not that it is poffible, by any rules, to fupercede, entirely, ingenuity and addrefs; but, becaufe, in confequence of the uniformity of the plan on which the method proceeds, experience communicates a certain dexterity in the ufe of it; which muft in time give to a very ordinary degree of fagacity, a fuperiority, on the whole, to the greatest natural ingenuity, unaffisted by rule.†

* Μειζον εςι το δυναμιν αναλυτικήν κτήσασθαι, του πολλας αποδείξεις των επί μέρους εχειν.

"Mathematica multi sciunt, mathesin pauci. Aliud est enim nosse propositiones aliquot, et nonnullas ex iis obvias elicere, casu

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To thefe obfervations, I believe, I may add, that, after all that was done by the Greek philofophers to facilitate mathematical invention, many rules ftill remain to be fuggefted, which might be of important ufe, even in pure geometry. A variety of fuch occur to every experienced mathematician, in the courfe of his inquiries, although, perhaps, he may not be at the trouble to ftate them to himself in words; and it would plainly have faved him much expence of time and thought, befide enabling him to conduct his refearches on a more regular plan, if he had been taught them fyftematically at the commencement of his ftudies. The more varied, abftrufe, and general investigations of the moderns, ftand in need, in a much greater degree, of the guidance of philofophical principles; not only for enabling us to conduct, with skill, our particular researches, but for directing us to the different methods of reasoning, to which we ought to have recourse on different occafions. A collection of fuch rules would form, what might be called with propriety, the logic of mathematics; and would probably conrtibute greatly to the advancement of all thofe branches of knowledge, to which mathematical learning is fubfervient.

The obfervations which have been now made, on the importance of method in conducting phyfical and mathematical researches, particularly those which re

potius quam certa aliqua discurrendi norma, aliud scientiæ ipsius naturam ac indolem perspectam habere, in ejus se adyta penetrare, et as universalibus instructum esse præceptis, quibus theoremata ac problemata innumera excogitandi, eademque demonstrandi facilitas comparetur. Ut enim pictorum vulgus prototypon sæpe sæpius exprimendo, quendam pingendi usum, rullam vero pictoriæ artis quam optica suggerit, scientiam adquirit, ita multi, lectis Euclidis et aliorum geometrarum libris, eorum imitatione fingere propositiones aliquas ac demonstrare solent, ipsam tamen secretissimam difficiliorum theorematum ac problematum solvendimethodum prorsus ignorant."-Joannis de la Faille Theoremata de Centro Gravitatis, in præfat.-Antwerpiæ, 1632.

late to the last of these subjects, will not apply literally to our inquiries in metaphyfics, morals, or politics; because, in these sciences, our reasonings always confift of a comparatively small number of intermediate fteps; and the obftacles which retard our progress, do not, as in mathematics, arise from the difficulty of finding media of comparison among our ideas. Not, that these obstacles are less real, or more easily furmounted on the contrary, it seems to require a ftill rarer combination of talents to furmount them; for how fmall is the number of individuals, who are qualified to think juftly on metaphyfical, moral, or political subjects; in comparison of thofe, who may be trained by practice to follow the longeft proceffes of mathematical reafoning. From what these obstacles arife, I fhall not inquire particularly at prefent. Some of the more important of them may be referred to the imperfections of language; to the difficulty of annexing precife and steady ideas to our words; to the difficulty, in fome cafes, of conceiving the subjects of our reafoning; and, in others, of discovering, and keeping in view, all the various circumftances upon which our judgment ought to proceed; and above all, to the prejudices which early impreflions and affociations create, to warp our opinions.-To illuftrate these fources of error, in the different sciences which are liable to be affected by them, and to point out the most effectual means for guarding against them, would form another very interesting article, in a philofophical fyftem of logic.

The method of communicating to others, the principles of the different fciences, has been as much neglected by the writers on logic, as the rule of inveftigation and difcovery; and yet, there is certainly no undertaking whatever, in which their affistance is more indifpenfibly requifite. The first principles of all the sciences are intimately connected with the

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