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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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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