Newton's principia, first book sections I, II, III, with notes and illustrations and a collection of problems, principally intended as examples of Newton's methods (1900)
ment ABG:: dmn : [m -f nf. LEMMA Xh 105 For, by Cor. 5, Lemma XI. seg AB i seg AJSG :i AB: ABC :: m*: {m + n^ seg BG : seg ABG :: rf : (m + w); .*. seg AB + seg BG: seg ABG :: m^ + n^: {m ■\- ny^ and A ABG = seg ABG - seg ^B - seg BG\ .*. A ^^(7 : seg ABG:: 3 (wz-w + mri) : (w + nf :: 3??2n : (m +… … A /STt ySPi: 57?t \Bp::Bp: BG] .-. ^ST: ^P^:: 8P: ^(7^ since Bm = SP, .-. yST^^O = SP^ and (^F - 8Y) BG = >SP - SPj .-. )SP-/SP : /Sr-^ST t: 2SY.BG: 3/SfP ulti-mately; .-. by Art. 86, chord of curvature : 25^:: 2SP: SSY-, therefore the chord of curvature through S = ^SP. XII. 1. Prove that the…
Mechanics · Celestial mechanics
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