The Mathematician

The Mathematician

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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. 1751 edition. Excerpt: ... D: Then will any two Lines that are to each other as the Velocities with which those Points are carried in any two cotemporary Positions as R, S. bjjthe Fluxions of the generated Lines, AR, Irthe generating Points flow uniformly, any two Augments, Increments or Spaces as Rr, Ss, described in the same Time, will exactly express the Velocities of those Points, or the Fluxions of the Lines AR, CS. For by the Nature, of uniform Motion and the ist Lemma above, when T--t then V: v.i.: S: f. Therefore the Ratio of Rr to Sj is the Ratio of the Fluxions required to be assigned. In like Manner the Fluxion of two plane SurFaces or, Superficies may be conceived by supposing two Lines, as aby cd to move continually parallel to themselves over the parallel and immoveable Lines AF, BG, and CR, DS. If the Spaces or Augments or Increments, the Parallelograms ab, cdy be both described uniformly in equal Times by the Motion of the said generating Lines, they will acT turately express the Fluxions of the generated Parallelograms Ab, Cd. And because bb, dd, the Fluxions of the Lines Bb, Dd, are as the Velocities with which the geherating Lines are carried; therefore the Fluxion of any Space generated by the Motion of a Line always parallel to itself, will ever be exactly as the Length of the generating Line multiplied iby its Velocity. Thisilso holds true in the Generation of Curves, where the Lengths of the generating Lines continually vary: E. g. Suppose the curve-lined Space Amv and the Parallleogram As to be generated by the continued uniform Motion of the Line rs in the fame Time; then will the Fluxions of these two Spaces be to each other, as the Parallelograms: sa9 (being the simultaneous Increments or Augments) C 2 or or as the generating Lines mv: vs more

Product details

  • Paperback | 70 pages
  • 189 x 246 x 4mm | 141g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236541855
  • 9781236541857