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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[181.] Notæ in Propoſit. III.
[182.] Notæ in Propoſit. VI.
[183.] Notæ in Propoſit. VII.
[184.] Notæ in Propoſit. IX.
[185.] LEMMAI.
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
[187.] PROPOSITIO VIII.
[188.] Notæ in Propoſit. V.
[189.] Notæ in Propoſit. VIII.
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
[191.] PROPOSITIO XII.
[192.] PROPOSITIO XIII.
[193.] PROPOSITIO XIV.
[194.] MONITVM.
[195.] LEMMA II.
[196.] COROLLARIVM.
[197.] LEMMA III.
[198.] LEMMA IV.
[199.] COROLLARIVM.
[200.] LEMMAV.
[201.] COROLLARIVM I.
[202.] COROLLARIVM II.
[203.] Notæ in Propoſit. XI.
[204.] Notæ in Propoſit. XII.
[205.] Notæ in Propoſit. XIII.
[206.] Notæ in Propoſit. XIV.
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
[208.] PROPOSITIO Præmiſſa VI.
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
[210.] Notæ in Propoſit. Præmiſſ. VI.
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156118Apollonij Pergæi
Quoniam proportio E G ad G I facta eſt, vt E C ad C F, nempè E
11b G ad G V, erit G V æqualis G I;
& propterea quadratum G I æquale.
eſt duplo trianguli G I V, & quadratum G B æquale eſt duplo trapezij
G F (1.
ex 5.) ergo quadratum I B æquale eſt duplo trianguli I C S cum
147[Figure 147] duplo trianguli F S V;
& ſic conſtat, quod quadratum I K æquale eſt du-
plo trianguli I C S cum duplo trapezij S L;
& propterea quadrati I B ex-
ceſſus ſupra quadratũ I K æqualis erit duplo trianguli L T V, quæ æqua-
lia ſunt exemplari applicato ad G P (6.
ex 5.) atque ſic oſtendetur, quod
I B potentia ſuperat I H;
eſtque exceſſus exemplar applicatum ad G O,
&
ſuperat quoque I A poteſtate, eſtque exceſſus æqualis exemplari ap-
plicato ad G Q;
eſt vero G O maior, quàm G P; ergo I B maior eſt quã
I K, &
quàm I H; & ſic oſtendetur, quod I B maior ſit, quàm I A; &
hoc erat oſtendendum.
PROPOSITIO XXIII. & XXIV.
EContra, ſi maximi rami origo
148[Figure 148]22a ponatur in axi minore, at non in
cẽtro ellipſis, nec ſit menſura continet
cum ipſa menſura angulum acutum,
&
eius inuerſa ad abſciſſam à poten-
tiali cum origine habet eandem pro-
portionem figuræ axis recti minoris:
ſi vero educatur ex centro, erit per-
pendicularis ſuper rectum.
Sit ſectio elliptica A B C centrum D, & E origo, quæ ſit in axi mino-
33b ri C A, &
E F ramus omnium maximus; erit vtique E C, vel

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