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

[81.] PROPOSITIO LX.

[82.] PROPOSITIO LXI.

[83.] Notæ in Propoſit. LVIII.

[84.] Notæ in Propoſit. LIX. LXII. & LXIII.

[85.] Notæ in Propoſit. LX.

[86.] Notæ in Propoſit. LXI.

[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.

[88.] PROPOSITIO XXXXIV.

[89.] PROPOSITIO XXXXV.

[90.] Notæ in Propoſ. XXXXIV.

[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.

5820Apollonij Pergæi ſed potius ex vndecima libri primi;

29[Figure 29] eſt enim quadratum H N æquale re-
ctangulo contento ſub abſciſſa H C,
& ſub latere recto, eſtque rectangu-
lum ſub H C, & ſub ſemierecto C G
ſemiſsis illius; igitur quadratum H
N æquale eſt duplo rectanguli H C G.

11d

Hoc autem eſt æquale duobus
quadratis I H, H Q, & I H in H
Q bis, & c. Poſt hæc verba ſubiun-
go claritatis gratia, atque C H in H
I bis æquale eſt duplo C Q in H I
vna cum duplo Q H in H I.

Ergo quadratum B I æquale eſt
22e I C in I H bis, & c. Hìc pariter, vt
clarior reddatur demõſtratio, ſubiun-
go, ſcilicet duplo rectãguli C H I vna
cum duplo quadrati H I; erat autem
quadratum N I æquale duplo rectan-
guli C H I, & vnico quadrato H I,
ergo, & c.

Et quia quadratum OR æqua-
33f le eſt C R in I H bis, & c.

30[Figure 30] Subiungo hanc declarationem.
Scilicet duplo rectanguli C H
I, & duplo quadrati H I cum
duplo rectanguli R I H. Qua-
re quadratum I O æquale eſt
quadrato R I, duplo quadrati
H I, duplo rectanguli R I H,
& duplo rectanguli C H I: ſed
quadratũ H R æquale eſt qua-
drato R I, quadrato I H cum
duplo rectanguli R I H. Ergo
quadratum I O æquale eſt qua-
drato H R, quadrato H I cum duplo rectanguli C H I; erat autem prius qua-
dratum I N æquale quadrato I H cum duplo rectanguli C H I. Igitur exceßus
quadrati I O ſupra quadratum I N eſt quadratum H R.

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