Apollonius <Pergaeus> - Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

339300Apollonij Pergæi

XXI. Deinde ſit A C æqualis QR in hyperbola fiet A C æqualis ere-
cto, & conuenient duo puncta H, & G in puncto D, eritque A C ad
11b

392[Figure 392] Q R vt A D ad ſe ipſam, ſiue vt A C ad ſe ipſam, quæ eſt vt D E ad
ſe ipſam, & hæc oſtenſa eſt, vt quadratum I L ad quadratum N O; igi-
22Prop. 6.
huius. tur I L, & N O ſunt æquales, & ſic demonſtrabitur, quod S T, V X ſunt
æquales, & hoc erat propoſitum.

PROPOSITIO XXVI

At in ellipſi fieri po-

393[Figure 393] teſt, vt H E ſit æ-
qualis E G, ſi nimirum
punctum B cadat in Q, &
tunc B E cadetſuper Q D,
& erit diameter I L æqua-
lis ſuæ coniugatæ; & vo-
cabo eas æquales.

Quia C G ad C H, nempe
quadratum A C ad ſuam fi-
guram maiorem proportionem
habet in primis figuris, & mi-
norem in ſecunda ellipſi, quàm
C G ad G E, nempe quàm
quadratum A C ad figuram
ipſius I L ( 18. ex 7. ) & C
G ad G E in primis figurisma-
iorem proportionem habet, &

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