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

Archimedis tur inter duas lineas æquales ſibi oc-
currentes in aliquo puncto, vti ſunt
duæ lineæ C D, C E, duæ lineæ ſe
mutuo ſecantes, vti ſunt duæ lineæ
D F, E F, & ſuerit angulus ab illis
contentus vt eſt angulus F æqualis
duobus angulis, qui occurrunt dua-
bus [lineis] ſe inuicem ſecanti-
bus, vti ſunt duo anguli E, D ſimul,
erit linea egrediens à puncto con-
curſus ad punctum ſectionis, vti eſt
linea C F æqualis cuilibet linearum
ſibi occurrentium, vt C D, vel C
E, propterea erit C F æqualis ipſi
C D, ergo angulus C F D eſt æqua-
lis angulo C D F, nempe angulo
D A G, ſed angulus C F D cum an-
gulo D F G eſt æqualis duobus re-
ctis, ergo angulus D A G cum angulo D F G æqualis eſt duobus rectis,
& remanent in quadrilatero A D F G duo anguli A D F, A G F æqua-
les duobus rectis, ſed angulus A D B rectus eſt, ergo angulus A G C
eſt rectus, & C G perpendicularis ad A B, & hoc eſt quod voluimus.

375.1.

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376. SCHOLIVM ALMOCHTASSO.

DIcit Doctor de demonſtratione, quàm citat ex tractatu
de figuris quadrilateris. Sint duæ lineæ æquales ſibi oc-
currentes A B, A C, & punctum concurſus A, & ſe inuicem
ſecantes B D, D C, & punctum ſectionis D, & ſit angulus B
D C æqualis duobus angulis A B D, A C D, & iungamus A
D; Dico quod ſit æqualis A B.

Alioquin vel eſt minor A B, vel maior
illa, & ſit maior, & abſcindatur A E æqua-
lis A B, & iungamus B E, ergo duo anguli
A E B, A B E ſunt æquales; ſed angulus
A E B maior eſt angulo A D B, & pariter
angulus A E C, qui eſt æqualis A C E ma-
ior eſt angulo A D C, omnes ergo anguli
B E C, vel duo anguli ſimul A B E, B C E
maiores ſunt duobus angulis A B D, A C
D, pars ſuo toto, quod eſt abſurdum. Dein-
de ſit A D minor quàm A B, & ponamus
A F æqualem A B, & iungamus B F, F C,
remanet, vt dictum eſt, quod angulus F,

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