A Commentary on Newton's Principia; With a Supplementary Volume. Designed for the Use of Students at the Universities

A Commentary on Newton's Principia; With a Supplementary Volume. Designed for the Use of Students at the Universities

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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. 1833 edition. Excerpt: ...C V is equal and parallel to A B. But A B = B c by construction and they are in the same line. Therefore C V is equal and parallel to B c Hence B V is parallel to C c. But S B is also parallel to C c by construction, and B V, B S have one point in common, viz. B. They therefore coincide. That is B V, when produced passes through S. 127. Cor. 3. The body when at B is acted on by two forces; one in the direction B c, the momentum which is measured by the product of its mass and velocity, and the other the attracting single impulse in the direction B S. These acting for an instant produce by composition the momentum in the direction B C measurable by the actual velocity X mass. Now these component and compound momentums being each proportional to the product of the mass and the initial velocity of the body m the directions B c, B V, and B C respectively, will be also proportional to their initial velocities simply, and therefore by (125) to B V, B c, B C Hence B V measures the force which attracts the body towards S when the body is at B--and so on for every other position of the body. 128. Cor. 1. Prop. II. In the annexed figure B c = A B, C c is parallel to S B, and C c is parallel to S' B. Now A S C B = S c B = S A B, and if the body by an impulse of S have deflected from its rectilinear course so as to be in C, by the proposition the direction in which the centripetal force acts is that' of C c or S B. But if, the body having arrived at C, the A S B C be S A B (the times of description are equal by hypothesis) and.. S B C, the vertex C falls without the A S B C, and the direction of the force along c C or B S', has clearly declined from the course B S in consequentia. The other case is readily understood from this other diagram. 129. To prove...show more

Product details

  • Paperback | 90 pages
  • 189 x 246 x 5mm | 177g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236653653
  • 9781236653659