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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12587Conicor. Lib. V. te O N angulum acutum L N O ver-

107[Figure 107]11Lem. 11. ticem A reſpicientem; eſtque G C or-
dinatim applicata ad diametrum N
225. lib. 2. M parallela tangenti verticali O N;
ergo angulus L P G externus æqua-
lis erit angulo L N O interno, & op-
poſito, & ad eaſdem partes conſtitu-
to; & ideo angulus G P L acutus
quoque erit, at in triangulo P M
L angulus internus L M P, & oppo-
ſitus minor eſt externo L P G acuto;
igitur angulus L M P acutus pariter
erit, & L M C obtuſus; ſuntq; intrian-
gulis L M G, & L M C circa an-
gulos inæquales, latera G M, M C
æqualia, & L M commune; ergo L
C maior eſt, quàm L G, quod erat
faciendum.

E contra fieri poteſt, vt infimus
breuiſecans ramus L C æqualis, aut
minor ſit ramo aliquo ſupra breuiſe-
cantem reliquum B L poſito. Nam L C minor eſt, quàm B L, & maior effici
poteſt ramo non vltra ſectionis verticem A collocato ex prima parte huius pro-
poſitionis, ſed rami à concurſu L educti cadentes inter puncta A, & B ſucceſ-
ſiuè augentur quo magis à vertice A recedunt; Ergo ramus L C æqualis,
aut minor erit aliquo ramo ab eodem concurſu L educto inter puncta
A, & B cadente; igitur manifeſtum eſt ramum breuiſecantem
C L infimum duorum breuiſecantium, non eſſe ſemper
minimum omnium ramorum cadentium ex concurſis
L ad peripheriam ſectionis A B C, ſed tan-
tummodo minorem eſſe eorum, qui inter
duo breuiſecantes B L, C L cadunt,
& reliquorum infra ramum
C L cadentium, atque
aliquorum in pe-
pheria
A N exiſtentium propè maximum L B;
quapropter exiſtimandum eſt, in-
curia alicuius verba illa non
ſine Apollonĳ iniuria
textui irrepſiſſe.

108[Figure 108]

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