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.

6729Conicor. Lib. V.

SECTIO SEPTIMA

Continens XXVI. XXVII. XXVIII. Propoſ.
Apollonij.

PROPOSITIO XXVI. & XXVII.

ANgulorum ab axi ſectionis A H, & à lineis breuiſſimis F
B, H G contentorum proximiores vertici ſectionis mi-
nores ſunt remotioribus, nempe angulus AFB minor eſt AHG.

44[Figure 44]

SIt itaque centrum D, & ſemi inclinatus axis A D, ſiue ſemitranſuer-
ſus, & dimidium erecti A C: educamus itaque duas perpendiculares
11a GL, BI, & ſi ſectio fuerit parabole, erit FI æqualis LH, quia quælibet
earum æqualis eſt A C (13. ex quinto) & L G maior eſt, quàm BI; an-
22b gulus igitur F minor quàm H; ſi verò ſectio fuerit hyperbole, aut ellipſis,
erit FI ad ID, vt HL ad LD, quia quælibet earum eſt, vt AC ad AD
33c (14. 15. ex quinto) & permutando, erit I D ad L D nempe B I ad M L,
44d vt I F ad L H, & anguli I, & L ſunt recti; igitur duo triangula BIF, M
L H ſunt ſimilia, ideoque angulus A H G maior eſt, quàm angulus A F
B, & hoc erat propoſitum.

PROPOSITIO XXVIII.

Hinc patet, lineas breuiſſimas ſibi occurrere ad partes axis
ſectionis.

QVia angulus AFB minor eſt, quàm angulus AHG; quare ſibi oc-
5526. 27. h.66e currunt ad partes F, H, & hoc erat oſtendendum.

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