248210Apollonij Pergæi
vltra centrum in eadem asymptoti produ{ct}ione A Z;
aut F I ſupra, &
G K in-
fra centrum A exiſtat: In quo libet caſu dicetur, F I vlterius tendere ad partes
centri, vel asymptoti A B, quàm G K.
fra centrum A exiſtat: In quo libet caſu dicetur, F I vlterius tendere ad partes
centri, vel asymptoti A B, quàm G K.
Non ſecus ſi ab eadem asymptoto A C educantur quatuor rectæ lineæ inter ſe
æquidiſtantes F I, G K, H L, C E, quarum duæ priores F I, G K, centro pro-
pinquiores ſint, quando omnes infra centrum A collocantur; vel magis à centro
recedant, quando omnes in productione A Z exiſtunt; aut certe duæ F I, G K
ſupra centrum, & H L, C E infra centrum exiſtant: Tunc ſimiliter in quoli-
bet caſu dicentur rectæ lineæ F I, G K vlterius tendere ad partes centri, &
asympoti A B, quàm duæ aliæ H L, C E.
æquidiſtantes F I, G K, H L, C E, quarum duæ priores F I, G K, centro pro-
pinquiores ſint, quando omnes infra centrum A collocantur; vel magis à centro
recedant, quando omnes in productione A Z exiſtunt; aut certe duæ F I, G K
ſupra centrum, & H L, C E infra centrum exiſtant: Tunc ſimiliter in quoli-
bet caſu dicentur rectæ lineæ F I, G K vlterius tendere ad partes centri, &
asympoti A B, quàm duæ aliæ H L, C E.
Addit.
Si in vna aſymptoto A C, hyperboles D E ſumantur duo ſegmenta
æqualia F G, H C, & à punctis diuiſionum ducantur quatuor rectæ
lineæ F I, G K, H L, C E parallelæ inter ſe, vſque ad hyperbolen:
Dico quod differentia duarum æquidiſtantium F I, G K ad partes cen-
tri, & alterius aſymptoti A B vlterius tendentium, maior erit differen-
tia reliquarum H L, C E.
æqualia F G, H C, & à punctis diuiſionum ducantur quatuor rectæ
lineæ F I, G K, H L, C E parallelæ inter ſe, vſque ad hyperbolen:
Dico quod differentia duarum æquidiſtantium F I, G K ad partes cen-
tri, & alterius aſymptoti A B vlterius tendentium, maior erit differen-
tia reliquarum H L, C E.
Ducantnr à punctis E, K rectæ
286[Figure 286]
lineæ E S, K R parallelæ asympto-
to A C, quæ efficiant parallelogrã-
ma C S, G R. Patet I R eſſe dif-
ferentiam æquidiſtantium F I, &
G K; pariterque L S eſſe differen-
tiam æquidiſtantium H L, C E;
& coniungantur rectæ lineæ E I,
& K I, ducaturque E O parallela
I K, ſecans H L in O. Et quia
recta linea E I cadit intra curuam
ſectionem conicam E K I, & pun-
ctum K eiuſdem conicæ
to A C, quæ efficiant parallelogrã-
ma C S, G R. Patet I R eſſe dif-
ferentiam æquidiſtantium F I, &
G K; pariterque L S eſſe differen-
tiam æquidiſtantium H L, C E;
& coniungantur rectæ lineæ E I,
& K I, ducaturque E O parallela
I K, ſecans H L in O. Et quia
recta linea E I cadit intra curuam
ſectionem conicam E K I, & pun-
ctum K eiuſdem conicæ
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