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fo many good Mathematicians, as would be neceffary to fail the hundredth part of the Ships of the Nation. But the Mathematicians have laid down fo plain and diftinct. Precepts, calculated neceffary Tables, and contrived convenient Inftruments, fo that a Sea-man, that knows not the Truths which his Precepts and Tables depend, may practife fafely by them. They refolve Triangles every day, that know not the reafon of any one of their Operations. Seamen in their Calculations make use of artificial Numbers or Logarithms, that know nothing of their contrivance: and indeed all thofe great Inventions of the most famous Mathematicians had been almost uselefs for those common and great Affairs, had not the practice of them been made eafy to those who cannot understand them. From hence it is plain, that it is to thofe Speculative Retired Men we owe the Rules, the Inftruments, the Precepts for using them, and the Tables which facilitate the difpatch of fo many great Affairs, and fupply Mankind with fo many conveniencies of Life. They were the Men that taught the World to apply Arithmetick, Aftronomy, and Sailing, without which the Needle would be ftill useless. Juft the fame way in the other parts of Mathematicks, the Precepts that are practifed by multitudes, without being understood, were contrived by fome few great Mathematicians.

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Since then it has been fhewn, how much Mathematicks improve the Mind, how fubfervient they are to other Arts, and how immediately ufeful to the Commonwealth, there needs no other arguments or motives to a Government to encourage them. This is the natural conclufion from thefe premifes. Plato in his Republick (lib. VII.) takes care, That whoever is to be Educated for Magiftracy, or any confiderable Poft in the Commonwealth, may be inftructed first

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in Arithmetick, then in Geometry, and thirdly in Aftronomy. And however neceffary thofe Arts were in Plato's time, they are much more fo now: The Arts o of War and Trade requiring much more the Affiftance of thofe Sciences now than they did then, as being brought to a greater height and perfection. And accordingly we fee, thefe Sciences are the particular care of Princes that defign to raise the Force and Power of their Countries. It is well known, that this is none of the leaft Arts, whereby the French King has brought his fubjects to make that Figure at Sea, which they at this time do; I mean, the care He takes for Educating those appointed for Sea-fervice in Mathematical Learning. For in the Ordonnance Marine, tit. viii. He orders, that there be Profeffors to teach Navigation publickly in all the Seaport Towns, who muft know defigning, and teach it to their Scholars, in order to lay down the appearances of Coafts, &c. They are to keep their Schools open, and read four times a week to the Sea-men, where they must have Charts, Globes, Spheres, Compaffes, Quadrants, Astrolabes, and all Books and Inftruments neceffary to teach their Art. The Directors of Hofpitals are obliged to fend thither yearly two or three of their boys to be taught, and to furnish them with Books and Inftruments. Thofe Profeffors < are obliged to examine the Journals depofited in the Office of Admiralty, in the place of their ⚫ establishment; to correct the errors in prefence: of the Seamen, and to restore them within a month, &c." King Charles the fecond, who well understood the importance of Eftablishments of this nature, founded one fuch School in Chrift's Hofpital, London; which, I believe, is inferior to none of the French: but it is to be wifhed there were many more fuch. His prefent Majefty, during

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the time of the late War, eftablished a Mathematical Lecture to breed up Engineers and Officers, as knowing very well the importance thereof. And this continued fome time after the Peace. And it is worthy the confideration of the Wisdom of the Nation, whether the restoring and continuing this, even in Peace, be not expedient for the breeding of Engincers, who are fo useful and valuable, and fo dif ficult to be had in time of War, and fo little dangerous in times of Peace.

Befides the crowd of Merchants, Seamen, Surveyors, Engineers, Ship carpenters, Artifans, &c. that are to be inftructed in the practice of fuch parts of Mathematicks as are neceffary to their own bu finess respectively, a complete number of able Ma thematicians ought to be entertained, in order to apply themfelves to the practice; not only to instruct the former fort, but likewife to remove thofe obftacles, which fuch as do not think beyond their common Rules, cannot overcome. And no doubt it is no fmall impediment to the Advancement of Arts, that Speculative Men and good Mathematician's are unacquainted with their particular defects, and the feveral circumftances in them, that render things practicable or impracticable. But if there were pubdick encouragement, we fhould have fkilful Mathematicians employed in thofe Arts, who would certainly find out and remedy the imperfections of them. The prefent Lords Commiffioners of the Admiralty knowing, that there are ftill two great Defiderata in Navigation, to wit, The Theory of the Variation of the magnetical Needle, and a method of studying out the Longitude of any place, that may be practicable at Sea by Seamen, and being fenfible of what importance it would be to find out either of them, have imployed a very fit perfon, the ingenious Mr. Hally, who has joined an entire acquaintance in the

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practice, to a full and thorough knowledge of the more abftrufe parts of Mathematicks. And now that he is returned, it is not doubted, but he will fatisfy thofe that fent him, and in due time the World too with his difcoveries in both thofe particulars, and in many other, that he has had occafion to make. And where a long feries of Observations and Experiments is necellary, he has no doubt laid fuch a foundation, as that After-Cbfervers may gradually perfect them. If it were not for more than the correcting the fituation of the Coafts, where he touched, and by them others, whofe relation to the former is known, the Nation is more than triply paid: and thofe, who fent him, have by his Miffion fecured to themfelves more true Honour and lafting Fame, than by Actions that at firft view appear more magnificent.

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The next thing; that is neceffary for the Improvement of Mathematical Learning, is, That Mathematicks be more generally ftudied at our Universities than hitherto they have been. From thofe Seminaries the State juftly expects and demands thofe, who are acquainted both with the Speculation and Practice. In those are all the encouragements to them imaginable, Leisure and Affiftance. There are ftill at hand Books and Inftruments, as alfo other Scholars that have made equal progrefs, and may be Comrades in ftudy, and the direction of the Profeffors. There are alfo in perfection all the incitements to this ftudy, and efpecially an acquaintance with the works of the Ancients, where this Learning is fo much recommended: There other Faculties are ftudied, to which it is fubfervient. There alfo are the Nobility and Gentry bred, who in due time must be called to their hare in the Government of the Fleets, Army, Treafury, and other Publick Employments, where

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Mathematical Learning is abfolutely neceffary, and without which they, tho' of never fo great natural parts, must be at the mercy and difcretion of their Servants and Deputies; who will firft cheat them, and then laugh at them. And not only Publick Employments, but their Private Concerns demand Mathematical Knowledge. If their Fortunes lie in Woods, Coal, Salt, Manufactures, &c. the neceffity of this knowledge is open and known; and even in Land-Eftates, no undertaking for improvement can be fecurely relied upon without it. It not only makes a Man of Quality and Eftate his whole Life more illuftrious, and more useful for all Affairs, (as Hippocrates fays, Ισοδίης δὲ μελέτω σοὶ ὦ παῖ, Γεωμετρικῆς καὶ Αριθμήσιος. ἐγὰς μόνον, σέο καὶ τὸν βίον εὐκλέα καὶ ἐπὶ πολλὰ χρήσιμον ἐς ἀνθρωπίνην μοίρην ἐπιτελέσες, ἀλλὰ καὶ τὴν ψυχὴν ὀξυτέρην τε καὶ τηλαυγετέρην, &c.) but in particular, it is the best Companion for a Country Life. Were this once become a fashionable ftudy (and the Mode exercifes its Empire over Learning as well as other things) it is hard to tell, how far it might influence the Morals of our Nobility and Gentry, in rendering them Serious, Diligent, Curious, taking them off from the more fruitlefs and airy exercises of the Fancy, which they are apt to run into.

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The only Objection, I can think of, that is brought against these studies, is that Mathematicks require a particular turn of Head, and a happy Ge-. nius that few people are Masters of, without which all the pains bestowed upon the study of them are in vain: They imagine that a Man must be a Mathematician. I anfwer, that this Exception is common to Mathematicks and other Arts. That there are perfons that have a particular capacity and fitness to one more than another, every body owns: And from experience I dare fay, it is not in any higher degree true concerning Mathematicks than the other. A

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