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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page |< < (348) of 458 > >|
387348Apollonij Pergæi H erit vt M H ad H D: & comparando homologorum differentias erit
M G ad M D, vt G H ad H M:
& propterea duplum G H in M D, ſeu
quadruplum H D in D M eſt æquale duplo G M in M H:
& propterea
duplum G M in M H maius erit quàm duplum G E in M H;
ponatur
communiter duplum E M in H M cum quadruplo quadrati M D, &
fiat
D d æqualis D M, fiet duplum E d in M H maius quadrato H M cum
457[Figure 457] quadrato M G;
igitur d E in E M bis ſumptum ad duplum E d in M H.
nempe E M ad M H minorem proportionem habebit, quàm duplum d
E in E M ad duo quadrata ex M G, &
ex M H: & componendo E H
ad M H, ſeu E H in H A ad M H in H A minorem proportionem habe-
bit, quàm duplum d E in E M vna cum quadratis ex M H, &
ex
M G, quæ æqualia ſunt duobus quadratis H E, &
G E ad duo quadra-
ta ex M G, &
ex H M. Et ſic pariter oſtendetur, quod quadratum H
A ad H E in H A minorem proportionem habebit, quàm duo quadrata
ex H A, &
ex A G ad duo quadrata ex H E, & ex E G. Atque de-
monſtrabitur quemadmodum antea dictum eſt, quod quadratum

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