. An encyclopaedia of architecture, historical, theoretical, & practical. New ed., rev., portions rewritten, and with additions by Wyatt Papworth. rdinates to the circlet-and to the figure of the section, of the same time. By the similar triangles APL and AHN, AP : PL:: AH : HN; And by the similar triangles BPK and BHQ, BP : PK::BH : HaTherefore, taking the rectangles of the corresjjonding terms, AP x BP ; BII ; UN X in the circle, PL x PK= PM^ and HN x HQ- HI2 ;Therefore AP x BP ; PM^:: AH x BH : HPi, Or, alternately, PMi : HI^:: AP : PB : AH : Theouem II. In the hyperbola, as
. An encyclopaedia of architecture, historical, theoretical, & practical. New ed., rev., portions rewritten, and with additions by Wyatt Papworth. rdinates to the circlet-and to the figure of the section, of the same time. By the similar triangles APL and AHN, AP : PL:: AH : HN; And by the similar triangles BPK and BHQ, BP : PK::BH : HaTherefore, taking the rectangles of the corresjjonding terms, AP x BP ; BII ; UN X in the circle, PL x PK= PM^ and HN x HQ- HI2 ;Therefore AP x BP ; PM^:: AH x BH : HPi, Or, alternately, PMi : HI^:: AP : PB : AH : Theouem II. In the hyperbola, as the square of the transverseaxis is to the square (f the conjugate axis, su is the rectangle of the abscissasto the sqriare of their ordinate. Let AB (j?//. 431.) be the transverse axis, GE the conjugate axis,C being the centre of th*> opposite curves; also let HI and PM be or-dinates as before ; then will AB2: GE2::PA x pb : vu\Or CA2 : CEJ:: PA X PB : PM^, Bv Theor. 1., PA x PB : HA x HB:: PM^ : U\-, Altfernateh, PA x PB : PM^:: H A x H B :: II!?!. / I \ Mut ? HA X HB : HI2::AB2 : GE^; ^J^^^ Thenfor(! A B- : G E ^:: PA x PB : rM^.. (^,11 A p. I. CONIC SECTIONS. 311
Size: 900px × 2777px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, booksubjectarchitects, booksubjectarchitecture
