may be more unbounded, and its accidental excurfions may excite more aftonishment, than in a cultivated and enlightened age; but it is only in such an age, that inventive genius can be trained by rules founded on the experience of our predeceffors, in fuch a manner as to insure the gradual and regular improvement of fcience. So juft is the remark of Lord Bacon: "Certo fciant homines, artes inveniendi folidas et

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veras adolefcere et incrementa fumere cum ipfis in"ventis."

The analogy between the mechanical arts, and the operations of scientific invention, might perhaps be carried further. In the former, we know how much the natural powers of man have been affifted, by the ufe of tools and inftruments. Is it not poffible to devise, in like manner, certain aids to our intellectual dev faculties?

That fuch a query is not altogether chimerical, appears from the wonderful effects of algebra (which is precisely such an inftrument of thought, as I have been now alluding to) in facilitating the inquiries of modern mathematicians. Whether it might not be poffible to realise a project which Leibnitz has fome. where mentioned, of introducing a fimilar contrivance into other branches of knowledge, I shall not take upon me to determine; but that this idea has at least fome plaufibility, muft, I think, be evident to those who have reflected on the nature of the general terms which abound more or lefs in every cultivated language; and which may be confidered as one fpecies of inftrumental aid, which art has discovered to our intellectual powers. From the obfervations which I

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 use of these, that the philofopher is enabled to fpeculate concerning claffes of objects, with the fame facility with which the favage or the peasant fpeculates concerning the individuals of which they are compofed. The technical terms, in the different sciences, render the appropriated language of philofophy a still more convenient inftrument of thought, than those languages which have originated from popular ufe; and in proportion as thefe technical terms improve in point of precifion and comprehensiveness, they will contribute to render our intellectual progress more certain and more rapid. "While engaged" (says Mr. Lavoifier)" in the compofition of my Ele"ments 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 languages are true analytical "methods. Algebra, which, of all our modes "of expreffion, is the moft fimple, the moft exact,

and the best adapted to its purpofe, is, at the fame time, a language and an analytical method. "The art of reafoning 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.

The foregoing remarks, in fo far as they relate to the pofiiblity of affling our reafoning and inventive powers, by new inftrumental aids, may perhaps ap

pear

pear to be founded too much upon theory; but this objection cannot be made to the reasonings I have offered on the importance of the ftudy of method.-To the justness of these, the whole history of science bears testimony; but more especially, the hiftories of Phyfics and of pure Geometry; which afford fo remarkable an illustration of the general doctrine, as can scarcely fail to be fatisfactory, even to those who are the most difposed to doubt the efficacy of art in directing the exertions of genius.

With respect to the former, it is fufficient to mention the wonderful effects which the writings of Lord Bacon have produced, in accelerating its progress. 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 those important and fublime discoveries in physics, which reflect so much honour on the prefent age.

The rules of philofophifing, however, even in phy. fics, have never yet been laid down with a fufficient degree of precifion, minuteness, or method; nor have they ever been stated 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 phyfical inquirers have derived what

E 3

know

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 moft people for abstract reasoning, 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 students, 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 fufficient 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.

The use which the ancient Greek geometers made of their analyfis, affords an additional illuftration of the utility of method in guiding fcientific invention. To facilitate the study of this species of investigation, they wrote no less than thirty-three preparatory books; and they confidered an addrefs, in the practice of it, (or, as MARINUS calls it, a duvaμis avaλutixn) as of much more value, than an extenfive acquaintance with the principles of the science *. Indeed, it is well known, to every one who is at all converfant with geometrical investigations, that although it may be poffible for a person, without the affiftance of the me. thod of analysis, to stumble accidentally on a solution,

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

or

or on a demonstration; yet it is impoffible for him to poffefs a just confidence in his own powers, or to carry on a regular plan of invention and difcovery. 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 otherwise: not that it is poffible, by any rules, to fuperfede, entirely, ingenuity and addrefs; but, because, in confequence of the uniformity of the plan on which the method proceeds, experience communicates a certain dexterity in the use of it; which muft in time give to a very ordinary degree of fagacity, a fuperiority, on the whole, to the greatest natural ingenuity, unaffifted by

rule *.

To these observations, 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 suggested, which might be of important use, even in pure geometry. A variety of such occur to every experienced mathematician, in the course of

* "Mathematica multi fciunt, mathefin pauci. Aliud eft enim noffe propofitiones aliquot, et nonnullas ex iis obvias elicere, casu potius quam certa aliqua difcurrendi norma, aliud fcientiæ ipfius naturam ac indolem perfpectam habere, in ejus fe adyta penetrare, et ab univerfalibus inftructum effe præceptis, quibus theoremata ac problemata innumera excogitandi, eademque demonftrandi facilitas comparetur. Ut enim pictorum vulgus prototypon fæpe fæpius exprimeudo, quendam pingendi ufum, nullam vero pictoriæ artis quam optica fuggerit fcientiam adquirit, ita multi, lectis Euclidis et aliorum geometrarum libris, eorum imitatione fingere propofitiones aliquas ac demonftrare folent, ipfam tamen fecretiffimam difficiliorum theorematum ac problematum folvendi methodum prorfus ignorant."-Joannis de la Faille Theoremata de Centro Gravitatis, in præfat.-Antwerpiæ, 1632.