261223Conicor. Lib. VI.
ad axim ducantur rami breuiſſimi O B, Q P præter axim A O, &
ſecent ex-
118. 9. & 10.
lib. 5. ternam curuam in G, E, R, & occurſui Z, vel communi asymptoto I M N,
306[Figure 306]
aut vicinioribus asymptotis I K, M N ſit A G propinquior, quàm E B, &
E B
propinquior, quàm R P: Oſtendendum eſt curuarum diſtantiam A G minorem
eße, quàm B E, & B E, quàm P R. Ducantur interceptæ G S parallela E B,
& E X parallela R P. Et quia in parabola angulus Y D A rectus ſupponitur,
22SCHO-
LIVM.
Prop. 6.
addit.& in hyperbola non eſt minor ſemirecto, ergo quilibet ramus breuiſſimus E B,
vel R P æquidiſtans erit rectæ lineæ diuidenti angulum A D Y in parabsla, &
angulum M I H in hyperbola; ſed duarum parallelarum E B, G S, vel R P,
E X eſt G S vertici propinquior, vel vlterius tendit ad partes asymptoti I K,
quàm E B; ergo G S minor eſt, quàm E B; eſtque G A minor, quàm G S, quia
33Prop. 3. 4.
addit.
7. & 38.
lib. 5. illa eſt portio, vel productio lineæ breuiſſimæ O A; igitur G A adhuc minor erit
307[Figure 307]
quàm E B.
Eadem ratione E B minor oſtendetur, quàm R P.
Poſtea ſi occur-
ſus Z cadit extra duos axes, inter axim A G, & occurſum aut ad partes
118. 9. & 10.
lib. 5. ternam curuam in G, E, R, & occurſui Z, vel communi asymptoto I M N,
propinquior, quàm R P: Oſtendendum eſt curuarum diſtantiam A G minorem
eße, quàm B E, & B E, quàm P R. Ducantur interceptæ G S parallela E B,
& E X parallela R P. Et quia in parabola angulus Y D A rectus ſupponitur,
22SCHO-
LIVM.
Prop. 6.
addit.& in hyperbola non eſt minor ſemirecto, ergo quilibet ramus breuiſſimus E B,
vel R P æquidiſtans erit rectæ lineæ diuidenti angulum A D Y in parabsla, &
angulum M I H in hyperbola; ſed duarum parallelarum E B, G S, vel R P,
E X eſt G S vertici propinquior, vel vlterius tendit ad partes asymptoti I K,
quàm E B; ergo G S minor eſt, quàm E B; eſtque G A minor, quàm G S, quia
33Prop. 3. 4.
addit.
7. & 38.
lib. 5. illa eſt portio, vel productio lineæ breuiſſimæ O A; igitur G A adhuc minor erit
ſus Z cadit extra duos axes, inter axim A G, & occurſum aut ad partes