# Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Conicor. Lib. VI. lum H I K ad quadratum I K, vt H I ad I K ſeu vt C A ad A D; eſtque
rectangulum C I A æquale rectangulo H I K; igitur rectangulum C I A ad qua-
dratum I K eandem proportionem habet, quàm C A ad A D; componitur verò
proportio rectanguli C I A ad quadratum I K ex duabus proportionibus laterum
C I ad I K, & A I ad I K: & propter parallelas N O, I K, atque K N, & C I, & latus commune C O K duo triangula C I K, & K O N ſimilia ſunt; igitur K N ad N O eſt, vt C I ad I K; & quia in parallelogrammo I N la-
tera oppoſita ſunt æqualia K N ad N A eandem proportionem habebit quàm A I
ad I K; quapropter duæ rationes K N ad N O, & K N ad N A componunt
gulum A N O eandem proportionem habebit, quàm A G ad A D. Si igitur
fiat conus, cuius vertex K baſis circulus diametro A O deſcriptus, cuius pla-
num perpendiculare ſit ad planum A K C; atque per rectam A C æquidiſtan-
tem ipſi K N planum ducatur perpendiculare ad idem planum A K C genera-
bitur ellipſis, cuius axis tranſuerſus erit A C, & latus rectum A D. Textus
igitur corrigi debere ex dictis manifeſtum eſt.

### 248.1.

b

Et quia angulus H K C nempe A O K æqualis eſt H A C, & angulus
C H A æqualis eſt C K A remanet angulus H C A æqualis O A K erit
H C A ſimile F E G ſimile quoque O K A; ergo, & c. Quoniam ex con-
ſtructione ſegmentum A H C capax eſt anguli æqualis angulo F erit angulus A
H C æqualis angulo F; & quia peripheria A H C ſecta eſt bifariam in H; ergo
ſubtenſa latera A H, & H C æqualia ſunt: & propterea triangulum A H C
iſoſcelium, & ſimile erit triangulo E F G; propterea quod anguli verticales æ-
quales ſunt inter ſe; ſunt verò duo anguli A H C, & A K C in eodem circuli
ſegmento; ergo æquales ſunt inter ſe; pariterque duo anguli C A H, & C K H
in eodem circuli ſegmento conſtituti, æquales ſunt inter ſe, & propter paralle-

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