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

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

[91.] Notæ in Propoſ. XLV.

[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.

[93.] PROPOSITIO LXX.

[94.] PROPOSITIO LXXI.

[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.

[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.

[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.

[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.

[99.] PROPOSITIO LXVI.

[100.] PROPOSITIO LXVII.

[101.] PROPOSITIO LXXII.

[102.] MONITVM.

[103.] LEMMA IX.

[104.] LEMMA X.

[105.] LEMMA XI.

[106.] Notæ in Propoſ. LXIV. & LXV.

[107.] Notæ in Propoſ. LXVI.

[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.

[109.] Notæ in Propoſ. LXVII.

[110.] COROLLARIVM PROPOSIT. LXVII.

[111.] Notæ in Propoſit. LXXII.

[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.

[113.] PROPOSITO LXXIV.

[114.] PROPOSITO LXXV.

[115.] PROPOSITIO LXXVI.

[116.] PROPOSITIO LXXVII.

[117.] Notæ in Propoſit. LXXIII.

[118.] LEMMA XII.

[119.] Notæ in Propoſ. LXXIV.

[120.] Notæ in Propoſit. LXXV.

9961Conicor. Lib. V.

76[Figure 76] ſimiliter C L ad L E, vt proportio figuræ, & producamus per L ip-
ſam O M parallelam A I F, & per F ipſam G M parallelam C E, & fa-
ciamus ſectionem H C B hyperbolen tranſeuntem per punctum C circa
114. lib. 2. continentes G M, O M, quæ occurret ſectioni A B (in ellipſi quidem vt
2256.
huius. demonſtrauimus) in hyberbola vero eo quod O M parallela axi D A in-
33b clinato ſubtendit, ſi producatur, angulum ſubſequentem continentiæ an-
gulum ſecabit A B, & corda, ſi producatur, occurret ſectioni; Ergo O
M ingreditur ſectionem A B, & ampliatur ſectio A B per extenſionem,
longè à duabus lineis O M, M G, & ſectio B C prope illas ducitur (deci-
4414. lib. 2. moſexta, ex ſecundo) igitur duæ ſectiones A B, C B ſibi occurrunt, vt
in B, & ducamus per B, C lineam occurrentem D F A in I, & G F in G;
Et quia B O æqualis eſt ipſi C G (octaua ex ſecundo) erit O N æqualis
55c ipſi M L, & O L ipſi N M; ergo O L, nempe N M, ſeu K F ad E I eſt,
vt C L ad C E, nempe D F ad D E, ergo K F ad E I eſt, vt D F
ad E D comparando homologorum ſummas in hyperbola, & eorundem
66d77Lem. 3. differentias in ellipſi, & iterum comparando antecedentes ad differen-
88Lem. 1. tias terminorum

77[Figure 77] fiet D K ad K
I, vt D F ad F
E, quæ eſt vt
proportio figu-
ræ; igitur B I eſt
linea breuiſſima
(9. 10. ex quin-
to) & hoc erat
probandum.

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