Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Apollonij Pergæi nempe e, f ſunt æquales: deinde ducantur V Z, Y a ad axes ordinatæ; ergo (propter ſimilitudinem duarum ſectionum) T Z in Z e ad quadra-
tum Z V eandem proportionem habebit, quam X a in a f ad quadratum
a Y, & angulus e æqualis eſt angulo f; igitur V e T ſimile eſt Y f X, & pariter O T R, Q X S; & propterea O e ad R V eandem proportionem
habebit, quàm Q f ad Y S, & propter ſimilitudinem duarum ſectionum
B I ad I A eſt, vt E K ad K D, & A I ad I O, vt D K ad K Q propter
ſimilitudinem duorum triangulorum; ergo (ex æqualitate, & comparan-
do antecedentes ad ſummas vel differentias terminorum) erit B I ad B O,
vt E K ad E Q, ſed B T ad B I erat, vt X E ad E K (propter ſimilitu-
dinem duarum ſectionum)
ergo ex æqualitate, & rurſus
comparando antecedẽtes ad
ſummas vel differentias ter-
minorum B T ad T O erit,
vt X E ad X Q, cumque T
Z in Z e ad quadratum V Z
ſit vt X a in a f ad quadra-
tum a Y (39. ex 1.) & qua-
dratum V Z ad quadratum
Z e eſt, vt quadratum a Y ad
quadratũ a f erit T Z in Z e,
ad quadratũ Z e, nempe T Z
ad Z e vt X a in a f ad quadra
tum a f nempe G a ad a f, & comparãdo antecedentes ad
differnntias terminorũ in hy-
perbola, & ad eorum ſummas
in ellipſi, fiet Z T ad T e, nẽ-
pe quadratum B T (quod eſt
æquale ipſi Z T in T e (39 ex 1.) ad quadratnm T e eſt, vt X a ad X f,
nempe a X in X f, quod eſt æquale quadrato E X (39. ex 1.) ad qua-
dratum X f; ergo B T ad T e potentia eſt, vt E X ad X f; & propterea


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