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

119. Notæ in Propoſ. LXXIV.

ERgo E F per centrum non tranſit, cadat ſuper C D, & quia produ-
cti ſunt ex E duo breuiſecantes; ergo C F excedit dimidium erecti,
& E F æqualis eſt Trutinæ (52. ex 5.) patet itaque, vt antea demonſtra-
uimus, quod E G ſit maximus ramorum, & E C minimus, & c. Quoniam in 11. huius oſtenſum eſt, quod ſemiaxis minor ellipſis eſt ramus bre-
uiſsimus, ergo ſi incidentia perpendicularis E F ſuper axim A C, ideſt punctum
F eſt centrum ellipſis educerentur ex concurſu E tres breuiſecantes, nimirum
E H, E G, & E F producta, quæ eſſet axis minor ellipſis: hoc autem eſt con-
tra hypotheſim, cum ducti ſint ex E duo breuiſecantes: ergo eorum vnus E H
menſuram C F ſecat, quæ minor eſſe debet ſemiſſe axis maioris C D; igitur
ex conuerſa propoſitione 50. huius, menſura C F maior erit ſemiſſe lateris re-
cti, & (ex conuerſa propoſ. 52. huius) erit perpendicularis E F æqualis Tru-
tinæ. Demonſtratio huius propoſitionis neglecta ab Apollonio, propterea quod
eodem ferè modo, ac præcedens oſtendi poteſt, breuiſsimè perficietur in hunc
modum.

119.1.

a
0134-01

Quoniam à concurſu E vnicus tantum breuiſecans E H ad quadrantem C B
ducitur; igitur C E minimus eſt omnium ramorum cadentium ad ſectionis pe-
ripheriam C B, & E C vertici B propinquior minor eſt remotiore E H, & E
H minor, quàm E B: rurſus, quia ramorum cadentium ex E ad peripheriam
B G vnus tantummodo breuiſecans E G conſtituit cum tangente N G angulum

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