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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300262Apollonij Pergæi idem diametrum M A; erunt igitur tangentes

347[Figure 347] A D, & M V parallelæ eidem N O, erat au-
tem E B parallela ipſi N O; igitur duæ cir-
culum tangentes A B, & M V parallelæ ſunt
idem E B; & propterea A D, & E B in eo-
dem ſunt plano, vtrumque conum tangente
cum per vertices E, & B ducatur, & per A
D baſis circulum tangentem. Eadem ratione
M V, & E B ineodem plano vtrumque conum
tangente exiſtent. Si verò recta E B plano cir-
culi non æquidiſtat producta alicubi planum
eiuſdem circuli ſecabit extra circulum ipſum,
vt in γ, & tunc quidem à puncto γ extra,
circulum poſito ducantur duæ contingentes γ A,
& γ M. Manifeſtum eſt, rectas lineas A γ,
B E in eodem plano iacere: tranſit verò præ-
dictum planum per vertices B, & E duorum
conorum, atque per γ A tangentem circulum
baſis communis; igitur planum A E B vtrum-
que conum contingit. Eodem modo planum E
B M ex altera parte vtrumq; conum tanget.
Et hoc erat faciendum.

In qualibet coniſectione H A I
11PROP
16.
Addit cuius diameter A L non ſit axis,
per eius verticem A aliam coniſe-
ctionem in eodem plano deſcribere,
quæ priorem abſcindat, atque eadem
recta linea vtramq; ſectionem tangat
in puncto mutuæ earum abſcisſionis.

Sicut in conſtructione prop. 11. & 12.
addit. factum eſt, deſcribatur conus B A
C comprehendens ſectionem H A I, cu
ius vertex B baſis circulus A M C per
ſectionis verticem A ductus, & trian-
gulum per axim B A C efficiat diame-
trum A L: & in duobus circulis æqui-
diſtantibus A C M, & in eo, qui per
ſectionis baſim H I ducitur idẽ planum
ſectionis conicæ deſignet duas parallelas
A D, H I, & planum trianguli per axim
efficiat circulorũ diamctros C A, & eum,
qui per L ducitur æquidiſtantes inter ſe:
ergo ſicuti baſis H I perpendicularis eſt
ad circuli diametrum per L ductam, ſeu
ad baſim trianguli per axim, ita D

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Scan	Original
81	43
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90	52
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