Lanterna Rally

Author: Walter William Rouse Ball

Publisher: Theclassics.Us

Published: 2013-09

Total Pages: 64

ISBN-13: 9781230366029

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 edition. Excerpt: ... the error arose has been satisfactorily explained by Rigaud and Edleston. Another blunder, which may be noticed in passing, is that made by Newton in a memorandum quoted below (see below, p. 58), where the discovery of some of the results given in his lectures of 1684 is assigned to June and July, 1684; they cannot have been made before August, but must have been made before the end of November. The tract Propositiones De Motu is memorable as marking the point at which Newton had arrived about the end of 1684; it contains the chief propositions given in his lectures of that year, as also two or three theorems on motion in a resisting medium. The tract contains eleven propositions, preceded by three definitions, a statement of four hypotheses or assumptions, and two lemmas. The proofs are geometrical. The propositions are as follows--the corresponding proposition in the Principia being indicated by a reference in square brackets: (i) the equable description of areas by the radius vector of a body moving under a central force book i. prop. 1; (ii) comparison of the forces under which bodies describe circles uniformly, with five corollaries book i. prop. 4; (iii) the law of centripetal force to a given point under which any curve can be described book i. prop. 6; (iv) application to a circle described under a force directed to a point in the circumference book i. prop. 7 of the first edition; (v) application to an ellipse described about the centre book i. prop. 10; (vi) application to an ellipse described about the focus, with a scholium on the application to the planets book i. prop. 11 j (vii) if ellipses be described under a central force which varies inversely as the square of the distance, then the squares of the periodic times are...