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

138. Notæ in Propoſ. XXIII. XXIV.

EContra linea maxima, ſi non egredia-
tur ex centro, continet cum mẽſura
angulum acutum, & proportio illius in-
uerſæ ad abſciſſam eius potentialis ex mẽ-
ſura cum origine, eſt vt proportio figuræ
recti. Si verò fuerit extra centrum, erit
perpendicularis ſuper rectum, & c. Mani-
feſtè nõ nulla in textu Arabicc [?] deficiunt; ali-
qua verò immutari debent; alioquin propo-
ſitio vera non eſſet, itaque legendum puto: E
contra ſi maximi rami origo ponatur in axi
minore, & c: Vt in textu babetur.

138.1.

a
0161-01

Sit ſectio A B C elliptica, & E origo, & E F linea maxima, & c. Ad-
didi pariter in bac expoſitione verba, quæ deſiciunt; nimirum: Sit centrum
D, & origo E, quæ ſit in axi minori A C.

138.1.

b

Et ideo D C ad dimidium erecti eſt linea minor, quàm D C, & ſit D
G ad G E, & c. Nonnulla adiungi debent buic textui corruptiſsimo, ne ſint
verba nil prorſus ſignificantia, itaque ſic legendum puto. Et ideo aliqua minor,
quàm D C ad reſiduam vſque ad E eandem proportionem babebit, quàm D C ad
ſemiſſem erecti; & ſit D G ad G E, & c. Quæ verba breuiſsimè more Apollonij
expoſita ſic confirmantur. Quia E C oſtenſa eſt minor dimidio erecti axis mi-
noris C A, fiat C K æqualis dimidio erecti; erit E C minor quàm C K,
& ablata communi D C erit D E minor, quàm K D; & propterea D E ad ean-
dem D C minorem proportionem babebit, quàm K D: fiat E D a d D G, vt K
D ad D C, erit D G minor, quàm D C: & componendo, E G ad G D eandem
proportionem babebit, quàm K C ad C D, & inuertendo, D G ad G E eandem
proportionem babebit, quàm D C ſemiſsis axis recti ad C K ſemiſsim erecti
eiuſdem axis; & ex G ducatur G F perpendicularis ad axim, quàm, dico, oc-
currere ſectioni in F termino maximi rami E F.

138.1.

c

Et ſi maxima fuerit extra centrum, vt D B erit perpendicularis, & c. Textus euidenter corruptus ſic corrigi debet. Si verò ramus maximus educatur
ex centro, vt D B, & c.

138.1.

d

139. Notæ in Propoſ. XXXV.

SI producatur vna linearum maximarum, vt E B ad latus illius originis
E ad punctum F, fiet maxima linearum egredientium ab illo puncto
F G, F H, F I, F A ad ſectionem B I A in directum, & propinquior illi
maior eſt remotiore, & c. Immutaui nonnulla, quæ ad propoſitionis integrita-
tem facerc videbantur: vt in textu babetur.

139.1.

a
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