The analyst; or, A discourse addressed to an infidel mathematician 2024 pdf epub mobi 电子书

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book:, XI. The Points or meer Limits of riaf- cent Lines are undoubtedly equal, as having no more magnitude one than another, a Limit as fuch being no Quantity. If by a Momentum you mean more than the very initial Limit, it muft be either a finite Quantity or an Infinitefimal. But all finite Quantities are exprefly excluded from the Notion of a Momentum. Therefore the Momentum muft be an Infini- tefimal. And indeed, though much Artifice hath been employ'd to efcape or avoid the admiffion of Quantities infinitely fmall, yet it feems ineffectual. For ought I fee, you can admit no Quantity as a Medium between a finite Quantity and nothing, without admitting Infinitefimals. An Increment generated in a finite Particle ot Time, is itfelf a finite Particle; and cannot therefore be a Momentum. You muft therefore take an Infinitefimal Part of Time wherein to generate your Momentum. It is faid, the Magnitude of Moments is not confidered: And yet thefe fame Moments are fuppofed to be divided into Parts. This is not eafy to conceive, no more than it is why we mould take Quantities 'Quantities lefs than A and B in order to obtain the Increment of A B, of which proceeding it muft be owned the final Caufe or Motive is very obvious; but it is not fo obvious or eafy to explain a juft and legitimate Reafon for it, or fhew it to be Geometrical. XII. From the foregoing Principle fo demonftrated, the general Rule for finding the Fluxion of any Power of a flowing Quantity is derived. But, as there feems to have been fome inward Scruple or Confcioufnefs of defect in the foregoing Demon ftration, and as this finding' the Fluxion of a given Power is a Point of primary Importance, it hath therefore been judged proper to demonftrate the fame in a different manner independent of the foregoing Demonftratio...