. The first three sections of Newton's Principia; with an appendix, and the ninth and eleventh sections. Edited by John H. Evans . OR P V 1Since .^,|^=_.— , and by similar triangles, QTV, SPY, . limit QV SP- QT SY- SPSA QR 1 QT- ~ -iSA 2h^ 1 CP4SA SECTION III. OS THK MOTION Of HOD IKS IN CONIC SECTIONS, ABOUT ACENTPIR OF KOKCK IN ONE OF THE Pitoi. XI. A hod}/ hi /in ellipse, to Jind thelaw of force tending to our of the fori. liCt the focus S be the centerof force, PQ an arc, QR a sub-tense parallel to SP; C the centerof the ellipse, join PC and produceit to meet the
. The first three sections of Newton's Principia; with an appendix, and the ninth and eleventh sections. Edited by John H. Evans . OR P V 1Since .^,|^=_.— , and by similar triangles, QTV, SPY, . limit QV SP- QT SY- SPSA QR 1 QT- ~ -iSA 2h^ 1 CP4SA SECTION III. OS THK MOTION Of HOD IKS IN CONIC SECTIONS, ABOUT ACENTPIR OF KOKCK IN ONE OF THE Pitoi. XI. A hod}/ hi /in ellipse, to Jind thelaw of force tending to our of the fori. liCt the focus S be the centerof force, PQ an arc, QR a sub-tense parallel to SP; C the centerof the ellipse, join PC and produceit to meet the ellipse in G; parallel to the tangent PR,cutting SP, CP in .r, r; and QT,PF respectively perpendicular toSP, and the senii-conjugatc diameter CD: and Jet jE be thepoint, in which SP cuts CD, then PE = AC the ^ axismajor. By similar triangles. \ PEF,Qy PE _ AC .uul b\ n projurtv of the ellipse, Ir _ CPQr~ vGTCD also by similar triangles. PaV, PEC, _ PE^ ACPr ~ PC~ PC 43 Now Px = Q7?, Qw ultimately = Qv, and vG ulti-mately = 2CP; hence multiplying the above quantities to-gether, and taking the limits of the products, limit QR AC . CP A(y iCP . CJr . PF 2AC-. BC AC2BC ^ 2h ,. QR 2 k L SP SP- SP Peop. XII. A body moves in an hyperbola, to Jind thelaw of force tending to one of the foci. Let the center of force be in the focus .S*, an
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