Items related to Principia
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. 1863 Excerpt: ...E. From these observed facts, we see that when the force, under the action of which E moves, is applied to the Moon in the contrary direction, the remaining force tends in the directions of the arrows. By the supposition that the Earth and Moon are acted on by forces tending to the Sun, whose distance compared with EM is very great, and that the differences of the forces on these bodies are not very great, the circumstances of the description of areas in the motion of the Moon are accounted for. Prop. IV. Theorem IV. The centripetal forces of equal bodies, which describe different circles with uniform velocity, tend to the centers of the circles, and are to each other as the squares of arcs described in the same time, divided by the radii of the circles. The bodies move uniformly, therefore the arcs described are proportional to the times of describing them; and the sectors of circles are proportional to the arcs on which they stand, therefore the areas described by radii drawn to the centers are proportional to the times of describing them; hence, by Prop. II, the forces tend to the centers of the circles. Again, let AB, ab be small arcs described in equal times, AD, ad tangents at A, a, ACSG, acsg diameters through A, a. Join AB, ab, and draw BC, be perpendicular to AG, ag. By similar triangles, AC: AB:: AB: AG,:. AC. AG = (chord AB?;. A„... (chord ABf (chord abf Air ag But, ultimately, when the arcs AB,'ab are indefinitely diminished, since AC, ac are sagittse of the double of arcs AB, ab, and are therefore, by Prop. i. Cor. 4, ultimately as the forces at A and a, therefore ultimately, „,.,. (chord AB) (chord ab) force at A:force at a:: j-77---: ' AG ag (wrcAB) (arcaft)2. T:: Ag:' byLemraam Take AE, ae two arcs described in any equal finite t...
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About the Author:
I. Bernard Cohen (1914-2003) was Victor S. Thomas Professor (Emeritus) of the History of Science at Harvard University. Among his recent books are "Benjamin Franklin's Science" (1996), "Interactions" (1994), and "Science and the Founding Fathers" (1992). Anne Whitman was coeditor (with I. Bernard Cohen and Alexander Koyre) of the Latin edition, with variant readings, of the "Principia" (1972). Julia Budenz, author of "From the Gardens of Flora Baum" (1984), is a multilingual classicist and poet.
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- PublisherRareBooksClub.com
- Publication date2012
- ISBN 10 1236081528
- ISBN 13 9781236081520
- BindingPaperback
- Number of pages70
- Rating
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