214176Apollonij Pergæi
237[Figure 237]
tum potentialis I B, vt H L in L O, ſeu L V in L D ad quadratum L
D, eò quod quælibet ex dictis proportionibus eadem eſt proportioni fi-
guræ K A, & M C (39. ex 1.) , ergo T I ad I B eſt, vt V L ad L D, &
1137. lib. 1. angulus I, qui æqualis eſt ipſi R A G æqualis eſt angulo L, qui æqualis
eſt S C H; igitur angulus G æqualis etiam eſt angulo H: & propterea
22Propoſ. 2.
præmiſſ. G A R ſimile eſt H C S, & pariter G A P, H C Q ſunt ſimilia, quia P, Q
ſunt recti, vnde A P R, C Q S ſunt etiã ſimilia, & proportio vniuſcuiuſq;
eorum, nempe G P, P R ad P A, eſt, vt proportio H Q, S Q ad C Q;
33c igitur G P in P R ad quadratum P A, nempe B E ad erectum illius (39.
ex 1.) eſt vt H Q in Q S ad quadratum C Q, nempe D F ad erectum
illius (39. ex 1.) ; igitur
4437. lib. 1.
238[Figure 238]
figuræ duorum axiũ ſunt
ſimiles, & duæ ſectiones
ſimiles ſunt (12. ex 6. (
ſed oportet in ellipſi, vt
duæ diametri, ideoque
duo axes ſint ſimul aut
tranſuerſi, aut ſimul re-
cti. Et hoc erat propoſi-
tum.
D, eò quod quælibet ex dictis proportionibus eadem eſt proportioni fi-
guræ K A, & M C (39. ex 1.) , ergo T I ad I B eſt, vt V L ad L D, &
1137. lib. 1. angulus I, qui æqualis eſt ipſi R A G æqualis eſt angulo L, qui æqualis
eſt S C H; igitur angulus G æqualis etiam eſt angulo H: & propterea
22Propoſ. 2.
præmiſſ. G A R ſimile eſt H C S, & pariter G A P, H C Q ſunt ſimilia, quia P, Q
ſunt recti, vnde A P R, C Q S ſunt etiã ſimilia, & proportio vniuſcuiuſq;
eorum, nempe G P, P R ad P A, eſt, vt proportio H Q, S Q ad C Q;
33c igitur G P in P R ad quadratum P A, nempe B E ad erectum illius (39.
ex 1.) eſt vt H Q in Q S ad quadratum C Q, nempe D F ad erectum
illius (39. ex 1.) ; igitur
4437. lib. 1.
ſimiles, & duæ ſectiones
ſimiles ſunt (12. ex 6. (
ſed oportet in ellipſi, vt
duæ diametri, ideoque
duo axes ſint ſimul aut
tranſuerſi, aut ſimul re-
cti. Et hoc erat propoſi-
tum.
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