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

Conicor. Lib. V. D C, quad [?] ratum igitur, & c. Textum corruptum ſic corrigendum puto; & eſt
r C æqualis D C, atque γ F æqualis ſummæ in hyperbola, & differentiæ in elli-
pſi laterum D C, & C F.

40.1.

g

Exemplar ſimile plano rectanguli C D in Y F in hyperbola, & Y C in
ellipſi, & c. Hæc poſtrema verba expungenda duxi, tanquam ſuperuacanea.

Poteſt etiam ad imitationem Euclidis reperiri multitudo ramorum inter ſe-
æqualium, qui ex origine duci poſſunt in eadem coniſectione. Itaque quoties
menſura fuerit comparata, ſcilicet aqualis ſemiſsi lateris recti, tunc duo tan-
tum rami inter ſe æquales a puncto originis ad vtraſque partes axis duci poſ-
ſunt in qualibet coniſectione, eruntque illi, qui ad terminos L l cuiuslibet or-
dinatim applicatæ L l ducuntur ab origine
I, nam efſiciuntur duo triangula I M L, & I M l, quæ circa angulos æquales ad M, nẽ-
pe rectos, habent latera æqualia, ſcilicet L
M, & l M medietates ordinatim applicatæ,
& ſegmentum axis I M inter ordinatam, & originem eſt latus commune; ergobaſes, ſeu
rami I L, & I l ſunt æquales. Reliquiverò
rami ſupra, vel infra terminum eiuſdem ordinatim applicatæ minores, aut ma-
iores ſunt ramo ad eius terminum ducto; quare duo tantum rami ad vtraſque
partes axis inter ſe æquales duci poſſunt.

40.1.

PROP. I.
Additar.
0049-01

Rurſus quadratum rami I A remotioris a comparata ſuperat quadratum ra-
mì I L propinquioris (in parabola quidem) rectangulo ſub differentia, & ſub
aggregato abſciſſarum eorundem ramorum; in reliquis verò ſectionibus rectan-
gulo ſub differentia abſciſſarum, & ſub recta linea, ad quam ſumma abſcißa-
rum eandem proportionem habet, quam latus tranſuerſum ad ſummam in hy-
perbola, & ad differentiam in ellipſi laterum tranſuerſi, & recti.

40.1.

PROP.
II.Add.

Et primò in parabola, quia quadratum I A æquale eſt quadrato I C cum qua-
drato abſciſſæ C E; pariterque quadratum I L æquale eſt quadrato eiuſdem I C
cum quadrato abſciſſæ C M; ergo exceſſus quadrati I A ſupra quadratum I L
æqualis eſt differentiæ quadratorum E C, & C M; ſed exceſſus quadrati E C
ſupra quadratum M C æqualis eſt rectangulo, cuius baſis æqualis eſt ſummæ la-
terum E C, & C M; altitudo verò æqualis eſt E M differentiæ laterum eorun-
dem quadratorum (vt de-
ducitur ex elementis) igitur
exceſſus quadrati I A ſupra
quadratum I L æqualis eſt
rectangulo, cuius baſis eſt
ſumma abſciſſarum E C, C
M, altitudo verò E M dif-
ferentia earundem abſciſſa-
rum.

40.1.

4. huius.
ibidem.
0049-02

Secundò in hyperbola, & ellipſi fiat exemplar N T ap-
plicatum ab abſciſſam C E. Et quia quadratum I A æ-
quale eſt quadrato eiuſdem

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