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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[241.] Notæ in Propoſit. XXVIII.
[242.] LEMMAX.
[243.] SECTIO VNDECIMA Continens Propoſit. XXIX. XXX. & XXXI. PROPOSTIO XXIX.
[244.] PROPOSITIO XXX.
[245.] PROPOSITIO XXXI.
[246.] Notæ in Propoſit. XXIX.
[247.] Notæ in Propoſit. XXX.
[248.] Notæ in Propoſit. XXXI.
[249.] LIBRI SEXTI FINIS.
[250.] DEFINITIONES. I.
[251.] II.
[252.] III.
[253.] IV.
[255.] VI.
[256.] VII.
[257.] VIII.
[258.] NOTÆ.
[259.] SECTIO PRIMA Continens Propoſit. I. V. & XXIII. Apollonij. PROPOSITIO I.
[260.] PROPOSITIO V. & XXIII.
[261.] Notæ in Propoſit. I.
[262.] Notæ in Propoſit. V. & XXIII.
[263.] SECTIO SECVNDA Continens Propoſit. II. III. IV. VI. & VII. Apollonij. PROPOSITIO II. & III.
[264.] PROPOSITIO IV.
[265.] PROPOSITIO VI. & VII.
[266.] Notæ in Propoſit. II. III.
[267.] Notæ in Propoſit. IV.
[268.] Notæ in Propoſit. VI. & VII.
[269.] SECTIO TERTIA Continens Propoſit. Apollonij VIII. IX. X. XI. XV. XIX. XVI. XVIII. XVII. & XX.
[270.] Notæ in Propoſit. VIII.
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248210Apollonij Pergæi vltra centrum in eadem asymptoti produ{ct}ione A Z; aut F I ſupra, & G K in-
fra centrum A exiſtat:
In quo libet caſu dicetur, F I vlterius tendere ad partes
centri, vel asymptoti A B, quàm G K.
Non ſecus ſi ab eadem asymptoto A C educantur quatuor rectæ lineæ inter ſe
æquidiſtantes F I, G K, H L, C E, quarum duæ priores F I, G K, centro pro-
pinquiores ſint, quando omnes infra centrum A collocantur;
vel magis à centro
recedant, quando omnes in productione A Z exiſtunt;
aut certe duæ F I, G K
ſupra centrum, &
H L, C E infra centrum exiſtant: Tunc ſimiliter in quoli-
bet caſu dicentur rectæ lineæ F I, G K vlterius tendere ad partes centri, &

asympoti A B, quàm duæ aliæ H L, C E.
285[Figure 285]11PROP.2.
Addit.
Si in vna aſymptoto A C, hyperboles D E ſumantur duo ſegmenta
æqualia F G, H C, &
à punctis diuiſionum ducantur quatuor rectæ
lineæ F I, G K, H L, C E parallelæ inter ſe, vſque ad hyperbolen:
Dico quod differentia duarum æquidiſtantium F I, G K ad partes cen-
tri, &
alterius aſymptoti A B vlterius tendentium, maior erit differen-
tia reliquarum H L, C E.
Ducantnr à punctis E, K rectæ
286[Figure 286] lineæ E S, K R parallelæ asympto-
to A C, quæ efficiant parallelogrã-
ma C S, G R.
Patet I R eſſe dif-
ferentiam æquidiſtantium F I, &

G K;
pariterque L S eſſe differen-
tiam æquidiſtantium H L, C E;
& coniungantur rectæ lineæ E I,
&
K I, ducaturque E O parallela
I K, ſecans H L in O.
Et quia
recta linea E I cadit intra curuam
ſectionem conicam E K I, &
pun-
ctum K eiuſdem conicæ

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