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

Si fuerint quotcunque coni
ſuper circulum communem ba-
ſis deſcripti, habentes latus com-
mune indefinitè extenſum in-
triangulis per axes ad baſes
perpendicularibus, atque per ter-
minum lateris communis duca-
tur planum efficiens coni ſectio-
nes tangentes baſim: habebunt
illæ latera recta æqualia inter
ſe, eritquè ſectio ſingularis, ſi
fuerit par abole, vel circulus: ſi verò fuerit ellipſis, aut hy-
perbole erunt infinitæ.

248.1.

PROP.
17.
Addit.
0303-01

Sit conus A D C ſingularis, & A B C ſit multiplex, habentes cir-
culum A C baſeos communem, & latus A B D productum commu-
ne ſumptum ſit in triangulis per
axes conorum perpendicularibus ad
circulum baſis B C, atque à ter-
mino A ducatur planũ ſecans cir-
culi A C planum in recta linea,
quæ perpendicularis ſit ad diame-
trum C A, quod efficiat in cono
quidem A B C ſectionem A N,
cuius latus rectum ſit X, & latus
tranſuerſum A F: in cono verò
A D C efficiat ſectionem A M, cu-
ius latus rectum Z, & diameter
communis A E; ſitque ſectio A N
hyperbole, circulus, aut ellipſis
circa axim maiorem, aut mino-
rem; Sectio verò ſingularis A M in cono D A C ſit parabole, & ducatur B H
parallela diametro ſectionis A E ſecans circuli diametrum A C in H: & du-
catur C O parallela D A ſecans A E in O. Dico latus rectum Z paraboles A M
æquale eſſe lateri recto X cuiuſlibet alterius ſectionis A N; & ſupponantur tres
parabolæ A M inter ſe æquales earumq; latera recta Z æqualia, quæ in tribus fi-
guris apponẽtur, vt confuſio euitetur. Quoniam vt latus rectum X ad tran-
ſuerſum A F ſectionis A N, ita eſt rectangulum A H C ad quadratum B H: hæc verò proportio componitur ex ratione C H ad H B, & ex ratione A H ad
H B: eſtque C A ad A F, vt C H ad H B (propter parallelas F A, H B, & ſimilitudinem triangulorum) & vt A H ad H B, ita eſt A C ad C D, ſeu ad

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