MARGATE, ESSA Y

On the Usefulness of Mathematical Learning, in a Letter from a Gentleman in the City to his Friend in Oxford.

I

A M glad to hear from you, that the study of the Mathematicks is Promoted and Encouraged among the Youth of your University. The great influence, which thefe Sciences have on Philofophy and all useful Learning, as well as the Concerns of the Publick, may fufficiently recommend them to your choice and confideration: and the particular advantages, which you of that Place enjoy, give us just reason to expect from you a fuitable improvement in them. I have here fent you fome short reflections upon the Usefulness of Mathematical Learning, which may ferve as an argument to incite you to a lofer and more vigorous pursuit of it.

In all Ages and Countries, where Learning hath prevailed, the Mathematical Sciences have been looked upon as the most confiderable Branch of it. The very name Málnais implies no lefs; by which they were called either for their excellency, or because of all the Sciences they were firft taught, or because they were judg'd to comprehend πάντα τὰ Μαθής Mara. And amongst thofe, that are commonly reckoned

A 3

reckoned to be the feven Liberal Arts, four are Mas thematical, to wit, Arithmetick, Mufick, Geometry, and Aftronomy.

But notwithstanding their Excellency and Repu tation, they have not been taught nor ftudy'd so univerfally, as fome of the reft; which I take to have proceeded from the following caufes: The averfion of the greatest part of Mankind to ferious attention and clofe arguing; Their not comprehending Sufficiently the neceffity or great usefulness of these in other parts of Learning; An Opinion that this ftudy requires a particular Genius and turn of Head, which few are fo happy as to be Born with; And the want of Publick Encouragement, and able Mafters. For thefe, and perhaps fome other reafons, this study hath been generally neglected, and regarded only by fome few perfons whofe happy Genius and Curiofity have prompted them to it, or who have been forced upon it by its immediate fubferviency to fome particular Art or Office.

Therefore I think I cannot do better fervice to Learning, Youth, and the Nation in general, than by fhewing, That the Mathematicks of all parts of humane Knowledge, for the improvement of the Mind, for their fubferviency to other Arts, and their usefulnefs to the Common-wealth, deferve most to be encou raged. I know a difcourfe of this nature will be offenfive to fome, who, while they are ignorant of Mathematicks, yet think themselves Masters of all valuable Learning: but their difpleasure must not deter me from delivering an ufeful truth.

The advantages which accrue to the Mind by Mathematical tudies confift chiefly in thefe things; ft. In accuftoming it to attention. 2dly. In giving it a habit of close and demonftrative reasoning. 3dly. In freeing it from prejudice, credulity, and fuperftition.

First,

irft, the Mathematicks make the Mind attentive to the objects, which it confiders. This they do by entertaining it with a great variety of truths, which are delightful and evident, but not obvious. Truth is the fame thing to the understanding, as Mufick to the ear, and Beauty to the eye. The pursuit of it does really as much gratify a natural faculty implanted in us by our wife Creator, as the pleafing of our Senfes only in the former cafe, as the Object and Faculty are more Spiritual, the delight is the more pure, free from the regret, turpitude, laffitude, and intemperance, that commonly attend fenfual pleasures. The moft part of other Sciences confifting only of probable reafonings, the Mind has not where to fix; and wanting fufficient principles to pursue its searches upon, gives them over as impoffible. Again, as in Mathematical inveftigations truth may be found, fo it is not always obvious: This fpurs the Mind, and makes it diligent and attentive. In Geometria (fays Quinctilian, 1. i. c. 10.) partem fatentur effe utilem teneris ætatibus: agitari namque animos, atque acui ingenia, & celeritatem percipiendi venire inde concedunt. And Plato (in Repub. lib. viii.) obferves, that the Youth, who are furnished with Mathematical knowledge, are prompt and quick at all other Sciences, ἔις πάντα τα Μαθήματα ὀξεῖς φαίνονται. Therefore he calls it, κατὰ παιδείαν ὁδόν. And indeed Youth is generally fo much more delighted with Mathematical ftudies, than with the unpleasant tasks, that are fome times impofed upon them, that I have known fome reclaimed by them from idleness and neglect of learning, and acquire in time a habit of thinking, diligence, and attention; qualities, which we ought to ftudy by all means to beget in their defultory and roving Minds.

The fecond advantage, which the Mind reaps from Mathematical knowledge, is a habit of clear, demonftrative, and methodical Reafoning. We are contriv'd by Nature to learn by Imitation more than by Precept: And I believe in that refpect Reafoning is much like other inferior Arts (as Dancing, Singing, &c.) acquired by practice. By accuftoming our felves to Reafon closely about quantity, we acquire a habit of doing fo in other things. It is furprizing, to fee, what fuperficial inconfequential Reafonings, fatisfy the most part of Mankind. A· piece of wit, a jeft, a fimile, or a quotation of an Author, paffes for a mighty Argument: with fuch things as these are the moft part of Authors ftuffed: and from these weighty premises they infer their conclufions. This weaknefs and effeminacy of Mankind in being perfwaded where they are delighted, have made them the fport of Orators, Poets, and Men of wit. Thofe lumina Orationis are indeed very good diverfion for the Fancy, but are not the proper bufinefs of the Understanding; and where a Man pretends to write on abstract fubjects in a Scientifical method, he ought not to debauch in them. Logical precepts are more useful, nay, they are abfolutely neceffary for a rule of formal arguing in publick difputations, and confounding an obftinate and perverfe adverfary, and expofing him to the audience, or readers. But in the fearch of truth, an imitation of the method of the Geometers will carry a Man further than all the Dialectical rules. Their Analyfis is the proper model we ought to form our felves upon, and imitate in the regular difpofition and progrefs of our enquiries; and even he, who is ignorant of the nature of Mathematical Analyfis, ufes a method fomewhat Analogous to it. The Compofition of the Geometers, or their method of demonftrating truths already found out, viz.

by