Mathematical Tracts, Publ. by J. Wilson (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated.1761 Excerpt: ... another sense; and I am also very sensible, how sir quently he accommodated himself to the way of writing of the mathematicians of his time, parcly for assisting their imagination, and partly, perhaps, for sear he might seem to affect innovation. But I make no scruple of interpreting these expressions suitably to my representation of this doctrine; for otherwise I acknowledge myself totally incapable o reconciling this method of prime and ultimate ratios with the character, the author himself has given of it. 103. He presers it to indivisibles, because, he fays, they have no place in geometry, or in nature; and he often insists, that his method is conformable to the geometry of the ancients. But how can we pursue the variable and fleeting forms of the inscribing and circumscribing figures in infinitum, so that, when they should become equal to, the curve, they may not totally withdraw themselves from the imagination, and all idea about them be lost? It is certain such refined metaphysical notions are not in the least analogous to that simplicity and clearness in the ideas, to which the ancient geometers ever confined themselves. However, the conception of vanishing quantities ever actually arriving at their ultimate proportion, has above been shewn to be unquestionably inconsistent with nature. Nay farther, I will not pretend on any other principles, than those I have set forth in my discourse, to desend Sir Isaac Newton from the consequences of the mistakes, he has been charged with: for the asserting, that the varying ratios of vanishing quantities, and the changing forms of vanishing figures would ever attain those ultimate ratios, and last forms, seems to me directly to impinge upon those principles, he has expressly declared to be absurd. ADDITIO...