This is fynthetic method, and is called the method of inftruction. We may know fuperficially what plants are; but it is by the information which the study of botany gives that we become inftructed in the component parts of any one, and diftinguish its calix, ftamina, corolla, piftillum, fpecies and We genus. may likewise have a general notion of an animal, but it is by the study of anatomy we gain a particular knowledge of its cartileges, bones, veins, nerves, and all other parts. This is analytic method, and is called the method of invention.

This fhort treatife may be fufficient to prove that Logic, beginning with the fources and firft principles of thought, afcends regularly from one act of the understanding to another, and connects our ideas in fuch a manner, that every ftage of their progrefs is clear and fatisfactory;—that reafoning is the ability of deducing unknown truths from thofe already known; and that method is neceffary for marshalling our ideas, and giving clearness and regularity to them.

After having acquired a proper knowledge of the moft useful diftinctions marked out by Logic, and thus made ourselves acquainted with the rules prefcribed for the exercife and improvement of the understanding, we ought to direct our attention to thofe authors, who have given the beft examples of accurate reafoning; that we may make a pleafing and easy application of the preceding principles.

We

We fhall find them fully illuftrated in the works of Bacon, Grotius, Locke, Clarke, and Paley. Thefe authors will not fail to recompenfe our refearches, by giving us a clear and comprehenfive infight into the moft interefting topics. They will point out not only the proper employment of our reason, but its limits and boundaries. They will inftruct us in its ufe and application to the fublime doctrines of Revelation-" they will convince us that reafon is not injured or difturbed, but affifted and improved by new difcoveries of truth, coming from the eternal Fountain of all knowledge.'

2 Locke, book iv. c. 18.

VOL. IN

G

PHILO

OBJECTIONS agamft the ftudy of 'the Mathematics have been conveyed in the form of ludicrous narrative by Swift, and armed with the force of ingenious argument by Warburton, and other writers. It feems, however, that the cenfures of these authors are levelled not fo much against the ftudy itfelf as against the extreme length to which it is fometimes carried, and the unremitting application, with which it is fometimes purfued: fo that they might with equal propriety apply their obfervations to the immoderate pursuit of any other kind of knowledge. That thefe ftudies deferve a confpicuous place among the general topics of a liberal education, there can be no doubt, when their value is fairly weighed, and their utility is properly eftimated: and that they ought to be limited within certain bounds is equally reafonable, in order that the other branches of knowledge may not be neglected in the general cultivation of the mind.

It is propofed in the prefent and following chapter to confider,

I. The utility of mathematical ftudies.

II. The principal branches of fcience.

III. Some account will be given of those eminent men, whofe difcoveries and researches form memorable eras in the hiftory of science.

I. The Utility of Mathematical Studies.

They make us fix

These studies are calculated to produce effects highly beneficial to the mind. our attention steadily upon the objects placed before us, and are therefore very properly recommended as the best remedy to cure an unfteady and volatile difpofition. They teach us a method of close reasoning, and coincide both in principles and rules with logic: they form indeed the best and cleareft exemplification of it. They give a manly vigour to our understanding, and free us from doubt and uncertainty on the one hand, and credulity and rafh prefumption on the other. They teach exactness and perfpicuity in definition, connexion and conclufivenefs in argument, and carefulness in obfervation; and from no exercises can the fcholar go better prepared and difciplined to the pursuit of the higher branches of knowledge. The benefits to be derived from them are thus ftated by Mr. Locke: "I have mentioned Mathematics as a way to fettle in the mind a habit of reafoning clofely, and in train; not that I think it neceffary that all men fhould be deep mathematicians: but G2

that

that having got the way of reafoning, which that ftudy neceffarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they fhall have occafion "."

The greatest perfpicuity is found to prevail in every part of thefe refearches. By reasonings reprefented to the eye by lines and figures, the cleareft truths are conveyed to the understanding. In one refpect thefe ftudies claim the pre-eminence over all others; they reach the highest degree of evidence, that is, demonstration?

11. The principal Branches of Science.”

The name of Mathematics was originally intended, either to denote by way of eminence the high rank, which the feiences hold in the order of intellectual difcipline, on account of their peculiar clearnefs and utility; or it was defigned to convey an idea of their extent, as containing every kind of ufeful knowledge. According to their proper definition, they conftitute the fcience of quantity, either as fubject to measure or number. Their various branches are adapted to the common ufes of life, and to the deepest and most abftra&t fpeculations. They are pure and mixed. The for

Conduct of the Underftanding, vol. i. p. 339, "In geometria partem fatentur efle utilem teneris ætatibus: agitari namque animos, atque acui ingenia, et celeritatem percipiendi venire inde concedunt." Quint. lib. i. c. 10.

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