Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/75

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The Analyst.
65

Fluxions of a given Quantity, it might be more conſiſtent and leſs liable to exception to ſay, the Fluxion of the firſt naſcent Increment, i. e. the ſecond Fluxion; the Fluxion of the ſecond naſcent Increment, i. e. the third Fluxion; the Fluxion of the third naſcent Increment, i. e. the fourth Fluxion, which Fluxions are conceived reſpectively proportional, each to the naſcent Principle of the Increment ſucceeding that whereof it is the Fluxion.


XLI. For the more diſtinct Conception of all which it may be conſidered, that if the finite Increment LM[1] be divided into the Iſochronal Parts Lm, mn, no, oM; and the Increment MN into the Parts Mp, pq, qr, rN Iſochronal to the former; as the whole Increments LM, MN are proportional to the Sums of their deſcribing Velocities, even ſo the homologous Particles Lm, Mp are alſo proportional to the reſpective accelerated Velocities with which they are deſcribed. And as the Velocity with which Mp is generated, exceeds that with which Lm was generated, even ſo the Particle Mp ex-

F
ceeds
  1. See the foregoing Scheme in Sect. 36.