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

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157119Conicor. Lib. V. ſemierecto, aut æqualis, aut minor illo; ſed ſi eſſet æqualis, aut maior eſ-
ſet quoque E C maximus ramorum (16.
17. 18. 19. ex 5.) ergo C E mi-
nor eſt dimidio erecti, &
ideo aliqua minor, quàm D C ad reſiduam vſq;
11c ad E eandem proportionẽ habebit, quàm D C ad ſemiſſim erecti; & ſit D G
ad G E, &
ex G ad axim ducamus perpendicularem: hanc, dico, occur-
rere ſectioni in F;
alioquin occurrat ei in H, & iungamus E H; igitur E
H eſt maximus ramus (20.
ex 5.) & propterea maior, quàm E F, qui
maximus ſuppoſitus fuit, &
hoc eſt abſurdum; igitur occurrit ſectioni in
F;
& quia G eſt rectus angulus, erit F E G acutus. Siverò ramus maxi-
22d mus educatur ex cẽtro, vt D B erit perpendicularis ſuper A C;
alioquin
educatur D I perpẽdicularis ad axim;
igitur D I eſt ſemiſsis axis tranſuer-
ſi (11.
ex 5.) & propterea eſt ramus omnium maximus, ſed D B ſuppo-
ſitus fuit maximus, quod eſt abſurdum, vti dictum eſt;
quare patet pro-
poſitum.
PROPOSITIO XXV.
SI in ellipſi ramus
33a149[Figure 149] maximus E B mẽ-
ſuram ſecans vltra ori-
ginem E, in axe eius
minori exiſtentem, pro-
ducatur ad F, fiet F B
maximus omniũ ramo-
rum F G, F H, FI, ab
eodem puncto, ad ſe-
ctionem A B C caden-
tium, &
propinquior
maximo maior eſt remotiore.
Educamus B G, B H, H I, I A, E G, E H, E I; & quia E B maior
44b eſt, quàm E H, erit angulus B H E maior, quàm E B H;
igitur angulus
B H F multo maior erit, quàm H B F, &
propterea B F maior, eſt quàm
F H;
atque ſic demonſtrabitur, quod H F maior ſit, quàm F I, & F I,
quàm F A;
& hoc erat oſtendendum.
Notæ in Propoſit. XIX.
SI vero fuerit menſura E C ex recto duorum axium ellipſis A B C,
55a fed ſit maior comparata, &
c. Similiter bic declarari debet, quod axis
rectus ſit minor;
& propterea lego: Si menſura E C ſumatur in axe minori
ellipſis, &
c.

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