264226Apollonij Pergæi
Tandem ijſdem poſitis ducantur ex altera parte concurſus Z rami breuiſſimi
O C, Q T, qui eſſiciant diſtantias F C, T V. Dico F C propinquiorem con-
curſui Z minorem eße, quàm T V. Quoniam angulus Y D A, vel Y I M ſup-
310[Figure 310]
ponitur acutus;
ſuntque I D Y, M A O inter ſe, parallelæ;
ergo angulus D A O,
vel I M O, & multo magis I M N erit obtuſus; ſed quilibet ramus breuiſſimus
1113. 14.
lib. 5. Q V T parallelus F a eſſicit cum axi A O angulũ acutũ; igitur ramus breuiſſimus
Q T, & ei parallelus F a ſunt æquidiſtantes alicui rectæ lineæ diuidenti angu-
lum D A O, vel I M N; ideoque F a propinquior concurſui, vel vlterius ten-
22Propoſ. 3.
& 4. add. dens ad partes reliquæ asymptoti I H minor eſt, quàm T V; eſtque F C minor
quàm F a (quia illa eſt portio rami breuiſſimi) ergo F C minor eſt, quàm T V.
Quod erat propoſitum.
3312. lib. 5.O C, Q T, qui eſſiciant diſtantias F C, T V. Dico F C propinquiorem con-
curſui Z minorem eße, quàm T V. Quoniam angulus Y D A, vel Y I M ſup-
vel I M O, & multo magis I M N erit obtuſus; ſed quilibet ramus breuiſſimus
1113. 14.
lib. 5. Q V T parallelus F a eſſicit cum axi A O angulũ acutũ; igitur ramus breuiſſimus
Q T, & ei parallelus F a ſunt æquidiſtantes alicui rectæ lineæ diuidenti angu-
lum D A O, vel I M N; ideoque F a propinquior concurſui, vel vlterius ten-
22Propoſ. 3.
& 4. add. dens ad partes reliquæ asymptoti I H minor eſt, quàm T V; eſtque F C minor
quàm F a (quia illa eſt portio rami breuiſſimi) ergo F C minor eſt, quàm T V.
Quod erat propoſitum.
In duabus hyperbolis C A D,
44PROP. 9.
Addit.
311[Figure 311]
H G I ſimilibus, concentricis,
& ſimiliter poſitis circa com-
munem axim B A G, ideſt
conſiſtant circa cõmunes asym-
ptotos E B F: Dico ſectionum
C A D, H G I interualla sẽ-
per minui, quo magis ab axis
vertice recedunt; atque effici
poſſe minora interuallo quolibet
dato.
44PROP. 9.
Addit.
& ſimiliter poſitis circa com-
munem axim B A G, ideſt
conſiſtant circa cõmunes asym-
ptotos E B F: Dico ſectionum
C A D, H G I interualla sẽ-
per minui, quo magis ab axis
vertice recedunt; atque effici
poſſe minora interuallo quolibet
dato.
Deſcribatur hyperbole M G N
5512. huius.
& ex 53.
lib. 1. æqualis, ſimilis, & ſimiliter
5512. huius.
& ex 53.
lib. 1. æqualis, ſimilis, & ſimiliter
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib