First, 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 Senses; only in the former cafe, as the Object and Faculty are more Spiritual, the delight is the more pure, free from the regret, turpitude, lasfitude, and intemperance, that commonly attend fenfual pleasures. The most part of other Sciences confifting only of probable reafonings, the Mind has not where to fix ; and wanting fufficient principles to purfue its fearches 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 atatibus: 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, s návтα τα Μαθήματα ἐξεῖς 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 fometimes impofed upon them, that I have known fome reclaimed by them from idlenefs and neglect of learning, and acquire in time a habit of thinking, diligence, and attention; qualities which we ought to study by all means to beget in their defultory and roving Minds.

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The fecond advantage, which the Mind reaps from Mathematical knowledge, is a habit of clear, demonftrative, and methodical Reasoning. We are contrived 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 ourselves to Reafon clofely 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. piece of wit, a jeft, a fimile, or a quotation of an Author, paffes for a mighty Argument: with fuch things as thefe are the most part of Authors stuffed : and from thefe weighty premifes they infer their conclufions. This weaknefs and effeminacy of Mankind in being perfuaded 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 abftract fubjects in a Scientifical method, he ought not to debauch in them Logical precepts are more ufeful, 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 ourselves 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.

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by Definitions of words agreed upon, by Self-evident truths, and Propofitions that have been already demonftrated, is practicable in other fubjects, tho' not to the fame perfection, the natural want of evidence in the things themselves not allowing it; but it is imitable to a confiderable degree. I dare appeal to fome writings of our own Age and Nation, the Authors of which have been Mathematically inclined. shall add no more on this head, but that one who is accustomed to the methodical Syftems of truths, which the Geometers have reared up in the several branches of thofe Sciences which they have cultivated, will hardly bear with the confufion and diforder of other Sciences, but endeavour as far as he can to reform them.

Thirdly, Mathematical Knowledge adds a manly Vigour to the Mind, frees it from Prejudice, Credulity, and Superftition. This it does two Ways, 1. By accuftoming us to examine, and not to take Things upon Truft. 2dly. By giving us a clear and extensive Knowledge of the Syftem of the World; which, as it creates in us the most profound Reverence of the Almighty and wife Creator, fo it frees us from the mean and narrow Thoughts which Ignorance and Superstition are apt to beget. How great an Enemy Mathematicks are to Superftition, appears from this, that in thofe Countries where Romish Priests exercise their barbarous Tyranny over the Minds of Men, Aftronomers, who are fully perfuaded of the Motion of the Earth, dare not speak out but though the Inquifition may extort a Recantation, the Pope and a general Council too will not find themfelves able to perfuade to the contrary Opinion. Perhaps this may have given Occafion to a calumnious Suggestion, as if Mathematicks were an Enemy to Religion, which is a Scandal thrown both on the one and the other; for Truth can never

be an enemy to true Religion, which appears always to the beft advantage when it is moft examined.

On the contrary, the Mathematicks are friends to Religion; inafmuch as they charm the paffions, reftrain the impetuofity of imagination, and purge the Mind from Error and Prejudice. Vice is Error, Confufion, and falfe Reafoning; and all Truth is more or lefs oppofite to it. Befides Mathematical studies may ferve for a pleafant entertainment for thofe hours, which young Men are apt to throw away upon their Vices; the delightfulness of them being fuch, as to make folitude not only eafy, but defirable.

What I have faid may ferve to recommend Mathematicks for acquiring a vigorous Conftitution of Mind; for which Purpose they are as ufeful as Exercife is for procuring Health and Strength to the Body. I proceed now to fhew their vaft Extent and Ufefulnefs in other Parts of Knowledge. And here it might fuffice to tell you, that Mathematicks is the Science of Quantity, or the Art of Reafoning about things that are capable of more and lefs, and that the most part of the objects of our knowledge are fuch; as matter, fpace, number, time, motion, gravity, &c. have but imperfect ideas of things without Quantity, and as imperfect a cne of quantity itfelf without the help of Mathematicks. All the vifible works of God Almighty are made in Number, Weight, and Meafure; therefore to confider them we ought to understand Arithmetick, Geometry, and Staticks; and the greater advances we make in thofe Arts, the more capable we are of confidering fuch things as are the ofdinary objects of our Con

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ceptions. But this will farther appear from particulars.

And firft, if we confider, to what perfection we now know the Courfes, Periods, Order, Distances, and Proportions of the feveral great Bodies of the Universe, at least fuch as fall within our view, we fhall have caufe to admire the Sagacity and Induftry of the Mathematicians, and the power of Numbers and Geometry well applied. Let us caft our Eyes backward, and confider Aftronomy in its Infancy; or rather let us fuppofe it fill to begin: for inftance, a Colony of Rude Country people, tranfplanted into " an Iand remote from the Commerce of all Mankind, without fo much as the knowledge of the Kalendar, and the Periods of the Seafons, without Infruments to make Obfervations, or any the leaft notion of Obfervations or Inftruments. When is it we could expect any of their Pofterity fhould arrive at the Art of predicting an Eclipfe? Not only fo, but the Art of reckoning all Eclipfes that are paft or to come, for any number of Years. When is it we could fuppofe that one of thofe Inlanders, tranfported to any other place of the Earth, fhould be able by the infpection of the Heavens to find how much he were South or North, Eaft or West of his own Ifland, and to conduct his Ship back thither? For my part, tho' I know this may be, and is daily done, by what is known in Aftronomy; yet, when I confider the vaft Industry, Sagacity, multitude of Obfervations, and other extrinfick things neceffary for fuch a fublime piece of knowledge, I fhould be apt to pronounce it impoffible, and never to be hoped for. Now we are let fo much into the knowledge of the Machine of the Univerfe, and motion of its parts, by the Rules of this Science, perhaps the invention may feem eafy. But when we reflect, what Penetration and Contrivance were necessary to

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