Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Table of figures

< >
[Figure 161]
[Figure 162]
[Figure 163]
[Figure 164]
[Figure 165]
[Figure 166]
[Figure 167]
[Figure 168]
[Figure 169]
[Figure 170]
[Figure 171]
[Figure 172]
[Figure 173]
[Figure 174]
[Figure 175]
[Figure 176]
[Figure 177]
[Figure 178]
[Figure 179]
[Figure 180]
[Figure 181]
[Figure 182]
[Figure 183]
[Figure 184]
[Figure 185]
[Figure 186]
[Figure 187]
[Figure 188]
[Figure 189]
[Figure 190]
< >
page |< < (98) of 458 > >|
13698Apollonij Pergæi120[Figure 120] te ellipſis C B ducuntur à concurſu E duo breuiſecantes E I, E H; igitur (ex
propoſitione 72.
huius) erit breuiſecans E I vertici A propinquior maximus om-
nium ramorum cadentium ex concurſu E ad ellipſis peripheriam C H;
& pro-
pinquior maximo E I maior erit remotiore, ſed non omnium ramorũ cadentium
ad quadrantem C B, ſed eorum ſolummodo, qui inter verticem C, &
infimum
breuiſecantem E H, &
aliquorum propè ipſum; nam rami ſecantes cadentes pro-
pè punctum H hinc inde ſucceſsiuè augentur, vt dictum eſt in notis propoſ.
67.
in eiuſque Corollario.
Nec non, quia H M, G N ſunt duæ breuiſſimæ, conſtat, vt dictũ eſt, quod
11c G E ſit maximus ramorũ egredientiũ ex vtroque latere eius ad A H, &
c.
Quorũ verborũ ſenſus hic eſt. Quiaex concurſu E ducuntur duæ breuiſecantes E G
&
E H ad ſemiellipſim A B C, quarum E G ſecat vtrumq; axim, at E H ſecat
tantummodo menſuram;
ergo, ſicuti in præcedenti propoſ. 74. oſtenſum eſt, erit
ramus E G maximus omniũ cadentiũ ad peripheriam H A, &
c. At quia dubitari
poſſet de certitudine huius conſequentiæ, quandoquidem hypotheſes non ſunt om-
nino eædem;
in propoſitione enim 74. non tres, ſed duo tantummodo breuiſecan-
tes ex concurſu E ad ſectionem C B A ducebãtur, hic vero etiam tertia breui-
ſecans ducitur:
ſed ſi conſideretur progreſſus Apollonij, eandem concluſionem ex
vtraque hypotheſi deduci poſſe percipitur;
nam (ex propoſitione 72. huius) bre-
uiſecans E H, infra breuiſecantem, E I poſitus, minimus eſt omnium ramorum
cadentium ex E ad peripheriam H B ellipſis, &
propinquior minimo E H mi-
nor eſt remotiore, reliquorum vero ramorum cadentium ad quadrantem B A ma-
ximus eſt breuiſecans E G, vt oſtenſum eſt in præcedenti propoſit.
74. ex Lemma-
te 12.
huius, & ex Corollario propoſit. 67, atque propinquior ramus maximo
E G eorum, qui ad quadrantem B A cadunt maior eſt remotiore;
quapropter ra-
mus E G maximus eſt omnium ramorum ex E ad ellipſis peripheriam H A ca-
dentium.

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index