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

Table of handwritten notes

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443404Archimedis tur inter duas lineas æquales ſibi oc-
516[Figure 516] 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.
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
517[Figure 517] 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

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