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 contents

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[171.] PROPOSITIO IV.
[172.] PROPOSITIO X.
[173.] Notæ in Propoſit. I.
[174.] Notæ in Propoſit. II.
[175.] Notæ in Propoſit. IV.
[176.] Notæ in Propoſit. X.
[177.] SECTIO SECVNDA Continens Propoſit. III. VI. VII. & IX. PROPOSITIO III.
[178.] PROPOSITIO VI.
[179.] PROPOSITIO VII.
[180.] PROPOSITIO IX.
[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.
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214176Apollonij Pergæi237[Figure 237] tum potentialis I B, vt H L in L O, ſeu L V in L D ad quadratum L
D, eò quod quælibet ex dictis proportionibus eadem eſt proportioni fi-
guræ K A, &
M C (39. ex 1.) , ergo T I ad I B eſt, vt V L ad L D, &
1137. lib. 1. angulus I, qui æqualis eſt ipſi R A G æqualis eſt angulo L, qui æqualis
eſt S C H;
igitur angulus G æqualis etiam eſt angulo H: & propterea
22Propoſ. 2.
præmiſſ.
G A R ſimile eſt H C S, &
pariter G A P, H C Q ſunt ſimilia, quia P, Q
ſunt recti, vnde A P R, C Q S ſunt etiã ſimilia, &
proportio vniuſcuiuſq;
eorum, nempe G P, P R ad P A, eſt, vt proportio H Q, S Q ad C Q;
33c igitur G P in P R ad quadratum P A, nempe B E ad erectum illius (39.
ex 1.) eſt vt H Q in Q S ad quadratum C Q, nempe D F ad erectum
illius (39.
ex 1.) ; igitur
4437. lib. 1.238[Figure 238] figuræ duorum axiũ ſunt
ſimiles, &
duæ ſectiones
ſimiles ſunt (12.
ex 6. (
ſed oportet in ellipſi, vt
duæ diametri, ideoque
duo axes ſint ſimul aut
tranſuerſi, aut ſimul re-
cti.
Et hoc erat propoſi-
tum.

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