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

146. PR OPOSITIO XXXIX.

IN ſectione A B elliptica quælibet
perpendicularis F D ad lineam
maximam C D, ab eius termino D
in ſectione poſito educta, continget
coniſectionem.

146.1.

0166-01

Alioquin ſecet illam, & in eius produ-
ctione D G ſumatur punctum G intra ſe-
ctionem: & educamus B G C, igitur G
C maior eſt, quàm C D, quia ſubtendit
rectum angulum C D G, & propterea B C multo maior eſt, quàm C D,
quod eſt abſurdum; igitur educta illa linea eſt tangens; quod erat oſten-
dendum.

146.1.

a

147. PROPOSITIO XXXX.

E Contra ſi fuerit F D tangens, erit perpendicularis ſuper
maximam D C.

Alioquin educamus aliam E D perpendicularem ſuper illam; ergo E
D tangit ſectionem in puncto D (39. ex 5.) ſed F D ſuppoſita fuit tan-
gens; igitur duæ D F, & D E tangunt ſectionem in vno puncto, quod
eſt abſurdum (36. ex I.)

148. PROPOSITIO XXXXVII.

Q Vælibet linea D E ex puncto
contactus D ad axim alicuius
ſectionis A B educta per-
pendicularis ad tangentem D C,
erit linea breuiſſima, aut maxima.

148.1.

0166-02

Alioquin educamus D F breuiſſimam,
vel maximam; ergo D C perpendicularis
eſt ſuper D F; ſed C D ſuppoſita fuit per-
pendicularis ſuper D E; quod eſt abſur-
dum: quapropter demonſtratũ eſt, quod
fuerat propoſitum.

148.1.

Ex 10. & 20. huius.
40. huius.

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