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may be more unbounded, and its accidental excursions may excite more astonishment, 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 predecessors, in such a manner as to insure the gradual and regular improvement of science. So just is the remark of Lord Bacon: “ Certo fciant homines, artes inveniendi solidas et
veras adolescere et incrementa sumere cum ipsis 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 assisted, by the use of tools and instruments. Is it not possible to de vise, in like manner, certain aids to our intellectual faculties?
That such a query is not altogether chimerical, ap. pears from the wonderful effects of algebra (which is precisely such an instrument of thought, as I have been now alluding to) in facilitating the inquiries of modern mathematicians. Whether it might not be possible to realise a project which Leibnitz has somewhere mentioned, of introducing a similar contrivance into other branches of knowledge, I shall not take upon me to determine ; but that this idea has at least some plausibility, must, I think, be evident to those who have reflected on the nature of the general terms which abound more or less in every cultivated language; and which may be considered as one species of instrumental aid, which art has discovered to our intellectual powers. From the observations which I
am afterwards to make, it will appear, that, without general terms, all our reasonings must necessarily have been limited to particulars; and, consequently, it is owing to the use of these, that the philosopher is enabled to speculate concerning classes of objects, with the same facility with which the favage or the peasant speculates concerning the individuals of which they are composed. The technical terms, in the different sciences, render the appropriated language of philosophy a still more convenient instrument of thought, than those languages which have originated from popular use; and in proportion as these technical terms improve in point of precision and comprehensiveness, they will contribute to render our intellectual progress more certain and more rapid. “ While engaged” (fays Mr. Lavoisier) “ in the composition of my Ele. “ ments of Chemistry, I perceived, better than I had
ever done before, the truth of an observation 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 expreflion, is the most simple, the most exact, * and the best adapted to its purpose, is, at the " same time, a language and an analytical method. “ The art of reafoning is nothing more than a •
language well arranged." The infiuence which chefe very enlightened and philofophical views have al. ready bad on the doctrines of chemistry, cannot fail to be known to most of my readers.
The foregoing remarks, in so far as they relate to the pocity of aütag our reasoning and inventive peres, by av inftrunkn:al aids, :ay perhaps are
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 study of method.-To the justness of these, the whole history of science bears testimony; but more especially, the histories of Physics and of pure Geometry; which afford so remarkable an illustration of the general doctrine, as can scarcely fail to be satisfactory, even to those who are the most difposed to doubt the efficacy of art in dire&ting the exertions of genius.
With respect to the former, it is sufficient to mention the wonderful effects which the writings of Lord Bacon have produced, in accelerating its progress. The philosophers, who flourished before his time, were, undoubtedly, not inferior to their successors, either in genius or industry: but their plan of investigation was erroneous; and their labours have produced only a chaos of fictions and absurdities. The illustrations which his works contain, of the method of induction, general as the terms are, in which they are expressed, have gradually turned the attention of the moderns to the rules of philosophising; and have led the way to those important and sublime discoveries in physics, which reflect so much honour on the pre
The rules of philosophising, however, even in phy. fics, have never yet been laid down with a sufficient degree of precision, minuteness, or method; nor have they ever been stated and illustrated in so 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 possess, rather from an attention to the excellent models of investigation, which the writings of Newton exhibit, than from any of the speculations of Lord Bacon, or his commentators : and, indeed, such is the incapacity of most 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 still 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 illustrate 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 philosophy.
The use which the ancient Greek geometers made of their analysis, affords an additional illustration of the utility of method in guiding scientific invention. To facilitate the study of this species of investigation, they wrote no less than thirty-three preparatory books; and they considered an address, in the practice of it, (or, as MARINUS calls it, a duveepers a vaautixn) as of much more value, than an extensive acquaintance with the principles of the science *. Indeed, it is well known, to every one who is at all conversant with geometrical investigations, that although it may be possible for a person, without the assistance of the me. thod of analysis, to stumble accidentally on a solution,
* Μιζον εςι το δυναμιν αναλυτικην κτησασθαι, του πολλές αποδειξεις των επι μέρους εχειν. .
or on a demonstration ; yet it is impossible for him to possess a just 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 otherwise: not that it is possible, by any rules, to supersede, entirely, ingenuity and address; but, because, in consequence of the uniformity of the plan on which the method proceeds, experience communicates a certain dexterity in the use of it; which must in time give to a very ordinary degree of fagacity, a superiority, on the whole, to the greatest natural ingenuity, unaslisted by rule ..
To these observations, I believe, I may add, that after all that was done by the Greek philosophers to facilitate mathematical invention, many rules still 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 sciunt, mathesin pauci. Aliud est enim nofle propofitiones aliquot, et nonnullas ex iis obvias elicere, casu potius quam certa aliqua discurrendi norma, aliud scientiæ ipfius naturam ac indolem perspectam habere, in ejus se adyta penetrare, et ab universalibus instructum esse præceptis, quibus theoremata ac problemata innumera excogitandi, eademque demonstrandi facilitas comparetur. Ut enim pictorum vulgus prototypon fæpe fæpius exprimeudo, quendam pingendi ufum, nullam vero pictoriæ artis quam optica suggerit scientiam adquirit, ita multi, lectis Euclidis et aliorum geometrarum libris, eorum imitatione fingere propofitiones aliquas ac demonftrare solent, ipsam tamen secretisimam difficiliorum theorematum ac problematum folvendi methodum prorsus ignorant.”—Joannis de la Faille Theoremata de Centro Gravitatiss in præfat.-Antwerpiæ, 1632. E 4