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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151113Conicor. Lib. V. educamus F E quouſque ſecet D M perpendicularem ad axim in M, &
F I occurrat D M in N, & ducantur ad axim perpendiculares H O T S,
K P V, B E, L Q, A R: & ſit in prima figura C I minor recto, in ſecun-
da æqualis, in tertia vero maior. Conſtat, quemadmodum demonſtra-
11b uimus in propoſitione ſexta huius, quod quadratum I C æquale ſit du-
plo trianguli I C F; at quadratum O H duplum eſt trapezij O T F C
(1. ex 5.) & quadratum I O duplum eſt trianguli O I S; ergo quadra-
tum I C, nempe duplum trianguli I F C excedit quadratum I H duplo
trianguli F T S, quod eſt æquale rectangulo T a: & conſtat, vti dictum
22c

138[Figure 138] eſt, quod ſit exemplar applicatum ad O C; ergo quadratum I C excedit
quadratum I H exemplari applicato ad O C abſciſſam ipſius I H. Patet
etiam, quod quadratum I C excedit quadratum I K exemplari applica-
to ad P C; idemque conſtat in I B; igitur I C maior eſt, quàm I H, &
33d I H, quàm I K, & I K, quàm I B: poſtea, in figura prima, & tertia. ,

139[Figure 139] quia triangulum F C E æquale eſt triangulo D E M; ergo quadratum.
44e I C æquale eſt duplo trianguli N F M cum duplo trianguli D I N, qua-
dratum vero I D æquale eſt duplo trianguli D I N; igitur quadratum.

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