457Conicor. Lib. V.
dente in hyperbola, &
deficiente in ellipſi rectangulo F K H ſimile ei, quod la-
teribus recto, & tranſuerſo continetur, ſcilicet G A E, & eſt A F ſemiſsis la-
teris recti, igitur quadratum B G æquale eſt ſummæ in hyperbole, & differen-
tiæ in ellipſi rectanguli G A F bis ſumpti, & rectanguli F K H, quod eſt æqua-
le duplo trianguli F K H: ſed quadrilaterum A G H F æquale eſt aggregato in
hyperbola, & differentiæ in ellipſi rectanguli G A F, & trianguli F K H, ergò
quadratum B G æquale eſt duplo quadrilateri A G H F, ſeù diſſerentiæ triangu-
lorum D A F, & D G H.
teribus recto, & tranſuerſo continetur, ſcilicet G A E, & eſt A F ſemiſsis la-
teris recti, igitur quadratum B G æquale eſt ſummæ in hyperbole, & differen-
tiæ in ellipſi rectanguli G A F bis ſumpti, & rectanguli F K H, quod eſt æqua-
le duplo trianguli F K H: ſed quadrilaterum A G H F æquale eſt aggregato in
hyperbola, & differentiæ in ellipſi rectanguli G A F, & trianguli F K H, ergò
quadratum B G æquale eſt duplo quadrilateri A G H F, ſeù diſſerentiæ triangu-
lorum D A F, & D G H.
IN tertia propoſitione ſimilitèr, quandò ordinata
B H G I cadit infrà centrum D ellipſis, tunc
ducta C L parallela ipſi A E, erunt duo triangula
D A F, & D C L æqualia inter ſe, cum ſint ſimi-
lia, & latera homologa D A, D C ſint æqualia,
quia ſunt ſemiaxes; proptereà differentia triangu-
lorum D G H, & D A F, ſeù D C L erit trapezium
C G H L, quod ſubduplum eſt quadrati ordinatæ
B G.
B H G I cadit infrà centrum D ellipſis, tunc
ducta C L parallela ipſi A E, erunt duo triangula
D A F, & D C L æqualia inter ſe, cum ſint ſimi-
lia, & latera homologa D A, D C ſint æqualia,
quia ſunt ſemiaxes; proptereà differentia triangu-
lorum D G H, & D A F, ſeù D C L erit trapezium
C G H L, quod ſubduplum eſt quadrati ordinatæ
B G.