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

Apollonij Pergæi nuuntur quidem; ſed non efficiuntur minora interuallo quo parallelæ asymptoti
diſtant inter ſe; ex altera verò parte perueniri poteſt ad interuallum minus
quolibet dato. Et hoc erat faciendum.

235.1.

0272-01
Prop. 10.
addit.
huius.
Lem. 9.
huius.
10. 12.
huius.
Maurol.
lib. 3. de
lin. horar.
ca. 6. 7.
Propoſ. 6.
addit.
huius.
Propoſ. 8.
addit.
huius.

Data hyperbola eadem X præcedentis propoſitionis deſcribere duos ſi-
miles conos, vt idem planum in eis efficiat duas hyperbolas ſimiles da-
tæ ſectioni, quæ asymptoticæ ſint, & ex vtraque parte ſibi ipſis vici-
niores fiant interuallo minori quolibet dato.

235.1.

PROP.
14. Add.
0274-01

In quolibet plano fiat angulus A d G æqualis angulo inclinationis diametri,
& baſis hyperbolæ datæ X, & per G d extenſo quolibet alio plano, ducatur in
eo recta linea B d C perpendicularis ad G d O, & ſumpto quolibet alio puncto
b in recta linea B C in plano per B G O extenſo, centris d, & b, deſcribãtur
duo circuli inter ſe æquales G C O B, & S Q P L ſe ſe ſecantes in duobus punctis
R, a: atq; vt latus rectum ad tranſuerſum ſectionis datæ X, ita fiat quadratũ
G d ad quadratũ d A, & ducatur recta linea A N M parallela ipſi B C, quæ ſecet
b N æquidiſtantẽ d A in N, & coniungantur rectæ lineæ A B, A C, N L, N Q,
& fiant A, & N vertices duorũ conorũ A B C, N L Q, & in eorũ ſuper ficiebus
planum M c T æquidiſtans planis A G O, & N S P efficiat ſectiones H I K,
& T V c, quarum diametri D V I genitæ à triangulis A B C, & N L Q per
axes in eodem plano exiſbentibus ſunt æquidiſtantes axibus conorum A d, N b,
propter planorum æquidiſtantiam: Dico, eas eſſe hyperbolas quæſitas. Qnoniam
(propter æquidiſtantiam oppoſitarum linearum) eſt ſpatium A b parallelogram-
mum; igitur conorum axes A d, N b æquales ſunt inter ſe, & æquè inclinan-
tur ad communem rectam lineam B C Q (propter æquidiſtantiam earundem
A d, N b); ſuntque æqualium circulorum radij d B, d C, b L, b Q æqua-
les inter ſe; igitur triangula A B C, N L Q ſimilia ſunt inter ſe, & ſimili-

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