What additional confirmation it is poffible in fuch circumftances to receive, was afforded me by your affent, when I formerly mentioned to you my ideas concerning demonstrative evidence. Your uncommon proficiency in mathematical science, and your no lefs uncommon difcernment, I was well affured, perfectly qualified you to decide on fuch a question. To thofe who catch an idea the inftant it is prefented, and who have facts in abundance at command, by which they can determine the validity of a principle, I fhall frequently appear tedious. That ungrateful feeling, I will own to you, oftener than once while I was writing, came across my mind. But you are at no loss to conceive the manner in which I would defend my prolixity. What I have written, if it should obtain regard, will be viewed by most readers with an eye of fufpicion; and by by many, if they follow their first movement, it will be rejected as paradoxical. Will not fuch confiderations as these juftify a variety of illustrations, and even repetitions? They have alfo induced me to run the rifque of appearing ridiculously minute, in tracing the origin of terms. Fortunately for the diffusion of just sentiments, Mr. Harris has loft that authority which even among the learned he maintained too long. Our young men, however, I believe, ftill frequently refort to HERMES for that inftruction, which he has not to fupply. For obferve, I beseech you, what they will learn from this once redoubted doctor of univerfals, concerning mathematical reasoning.- "It is fome"what remarkable," fays he, farcaftically glancing at the attention paid to the phyfical fciences, "amid the prevalence of fuch notions, that there fhould ftill re❝ main "main two sciences in fashion, and these 66 "METRY." 8 In a curious note, but which is too long to be inserted entire, he has the " DOM, 66 66 DOM, with respect to all PURE and SPE"CULATIVE SCIENCE, it has not the leaft "to do. For who ever heard of Logic, or "Geometry, or Arithmetic being proved experimentally * ?" That the affirmations of Mr. Harris may lofe nothing of their. effect, they are here introduced in all their native pomp of CAPITALS and archness of italics. 66 The more I confider the subject, the more I am inclined, in spite of Mr. Harris, to believe not only in the poffibility, but the utility of rendering the elements of geometry palpable. If they be taught at an early age-a plan in which I think I fee many advantages-models would make the study infinitely more engaging: From the mere flate and pencil most beginners experience a repulfive fenfation. But if a child had fomething to handle and to place in * Hermes, p. 351-3. various various postures, he might learn many pro perties of geometrical figures without any constraint upon his inclinations. He would have no difficulty in transferring the properties of palpable to merely visible figures, nor in generalizing the inferences. You will not object, that one cannot proceed far by this road: you will perceive, that much more would be gained in reality than appearance. We fhould have laid a good foundation for the invaluable habit of accurate obfervation in general; and towards future progrefs in mathematics, we should have warded off the first disagreeable impreffion of the afpect of the fcience, which is fo very apt to strike a damp to the heart of the beginner. I need not explain to you the advantage of trying to engage Fancy on our side, by all the allurements we can offer to her. It is fhe that smooths every path and strews it |
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