A Treatise On the Construction Properties And Analogies of the Three Conic Sec

B Bewick Bridge

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Hence PV : PO ( -- )i: PP : P E(iC), PV=™-^. A, B„H, extremity of the minor axis) the semi-conjugate becomes equal to AC ; hence the chord of curvature passing from B through the 2 AC 2 focus S=^=2AC.
(130. ) At A (the extremity of the major axis) the diameter of (2CD 2, v 2RC 2 ___. _ j=___ r = latus-rectum ;* at B (the extremity 2AC 2 of the minor axis) it is equal to -^^ ; it is therefore least at A, and greatest at B ; hence, by Art. 122, the curvature is greatest at the extremity of the ma...jor axis, and least at the extremity of the minor axis. At the intermediate points between the extremities of the axes, the curvature varies inversely as the cube of the normal. !
rectum, i. E. 2AC : 2BC : : 2BC : latus-rectum * For by Art. 39, major axis : minor axis : : minor axis : latus- 4BC 8 = 2BC 2 2AC AC* CD 8 t The radius of curvature ==^^ . Now by Art. 58, (PI being the Pr normal) PIxPF=BC 2 = a constant quantity, . -. Plac^^. By Art. 62. CDxPF=ACxCB= a constant quantity, . -. CDoc^; Pr 1 CD 2 / 1 \ hence PI acCD.

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