Selection of Early Statistical Papers (v.3) (Mathematical Principles of Natural Philosophy) - Hardcover

Newton, Sir Isaac

Hardcover

ISBN 10: 0520009924 ISBN 13: 9780520009929

Publisher: University of California Press, 1967

Synopsis

This historic book may have numerous typos, missing text or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1803. Not illustrated. Excerpt: ... tangent acb in c is parallel to the tangent dxe in x, and therefore ab the ordinate is bisected in c the point of contact. [Leva. 26, cor.] This is the same with prob. 32, of the Universal Arithmetic. [Lem. 27, cor. in the construction] for then IH : HF: (iX : XY : :) ih : hf. And IH : HG : :(iL: LM : :) ih hg. Or, if it be made as iL: : LM : : IH : HG, it will be ih hf: : IH : HF; therefore, on the contrary, if it be ih : hf:.: (iE : EV : : iX ; XY : :) IH : HF, it will be iL: LM : : IH : HG, which conies to the former construction. For the solution of prop. 22, 23, 24, 25, 26, 27, see' prop. 70, 71, 72, 73, 74, 75, b. III. my Conic Sections. [Prop. 29, sea.] Make also KA to AS (Fig. 21), and LT to AT, as HG to GF, and draw MS, NA. Then the figures SA KM and ATLN are similar to FGHI; and since three of the angles S, A, K, or A, T, L, are in the proper lines CB, ED, DB, if the fourth angle M or N was in the fourth line EC, the problem would be rightly.constructed. Therefore it is plain its place can be no where but where the line MN intellects EC, as at i, which is the place of the angle I. Now we are to prove that PQ cuts BA in f, where F is to be placed. The triangle FGI is similar to PEi (by construction), and suppose them similar to fgi; then the triangles Pfi and Egi are also similar; for the angles at i are equal, and the sides about these angles proporiional; therefore the angle Egi =: Pfi; and since goi == Qof, oQf or PQE will be=fig. So that to have fig similar to FIG, PQF must intersect Eg in Q, to make the < PQE = F1G ; and the rest follows of course. SECTION VI. [Prop. 30, cor. 1.] "For the times are as the area», that is, as«GH X AS to § X AS X 2AS. [Ib. cor. 2.] For wherever the point P salls, viz. insinitely near A, still }GH X A...

About this title

Product Description

This historic book may have numerous typos, missing text, images, or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1729. Not illustrated. Excerpt: ... The mathematical principles of natural philosophy Sir Isaac Newton

Edition details

• Publisher: University of California Press
• Publication date: 1967
• ISBN 10: 0520009924
• ISBN 13: 9780520009929
• Binding: Hardcover
• Language: English
• Editor: Neyman Jerzy