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

Apollonij Pergæi ſarum in vna ſectionum ad homologa abſciſſa alterius eſt eadem ( 12. ex
6. ), & anguli compræhenſi à potentibus, & abſciſſis ſunt æquales; quia
æquales ſunt duobus angulis R A L, S C N æqualibus, & propterea duo
ſegmenta ſunt ſimilia.

213.1.

0217-01
37. lib. I.
12. huius.
b
6. præmiſ.
huius.
50. lib. I.
c
0217-02
Defin. 7.
huius.

Poſtea oſtendetur, quod ſi duo ſegmenta fuerint ſimilia, erit
angulus F æqualis E, & A M ad A E, vt O C ad C F.

Quia propter ſimilitudinem duorum ſegmentorum continebunt poten-
tes cum ſuis abſciſſis angulos æquales, & erit proportio potentium ad ab-
ſciſſas eadem, & proportio abſciſſarum, in vna earum ad ſua homologa in
altera, erit eadem. Et quia V a in a E ad quadratũ a A eandem propor-
tionem habet, quàm Y c in c F ad quadratum c C, & duo anguli a, & c
ſunt recti; atque angulus C, nempe O æqualis eſt A, nempe M, propter
ſimilitudinem ſegmentorum: ergo triangulum A E V ſimile eſt C F Y,
& angulus V æqualis eſt angulo Y; pariterque angulus E æqualis eſt F,
& A V ad A E eandem proportionem habet, quàm Y C ad C F. Po-
namus iam P A ad duplam A E, vt Q C ad duplam C F; ergo ex æqua-
litate A T diameter ad A P erectum eius eſt, vt C X diameter ad C Q
erectum eius ( 53. 54. ex I. ) & T M in M A ad quadratum M G eandẽ
proportionem habet, quàm X O in O C ad quadratum O I: at ſuppoſi-
tum eſt quadratum A M ad quadratum M G, vt quadratum C O ad qua-
dratum O I; ergo ex æqualitate T M in M A ad quadratum A M, nem-
pe T M ad M A, eandem proportionem habet, quàm X O in O C ad

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