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nydus/Miscellanea Curiosa, Vol. 1Public
Page 375 of 441
Table of Contents

Miscellanea Curiosa.

but perpetually approaching to A, in the Nature of Asymptotes.

  1. The Spaces Fl, Fm, Fn, &c. are therefore as Logarithms (in Arithmetical Progression increasing) answering to the Lines AF, AL, AM, &c. or to FL, LM, MN, &c. in Geometrical Progression decreasing.
  1. Because FL, LM, MN, &c. are as 1m, 1mm, 1m3, &c. (infinitely) terminated at A; therefore (by ¶ 10) their Aggregate FA or dh, is to DH, (so much Length as would have been dispatched, in the same time, by such impressed Force undiminished) as 1 to m - 1 = n.
  1. If therefore we take, as 1 to n, so AF to DH; this will represent the Length to be dispatched, in the same time, by such undiminished Force.
  1. And if such DH be supposed to be divided into equal Parts innumerable (and therefore infinitely small;) these answer to those
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