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 151]
[Figure 152]
[Figure 153]
[Figure 154]
[Figure 155]
[Figure 156]
[Figure 157]
[Figure 158]
[Figure 159]
[Figure 160]
[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]
< >
page |< < (83) of 458 > >|
12183Conicor. Lib. V. ſunt D A V, D L G, D B I, D Q O, D C P, oſtenſus eſt ramus D A minor
quàm D B, &
D B propinquior vertici A, minor ramo D C remotiore.
Notæ in Propoſ. LXVII.
POſtea repetamus figuram vtrã-
102[Figure 102]11a que hyperboles, &
c. Lego;
Repetamus figuras paraboles, & hy-
perboles, &
ſupponantur denuo eædem
lineæ æductæ ex concurſu D ad ſectio-
nem;
& perpendicularis D E, atque
Trutina F, &
omnium ramorum ſe-
cantium vnicus tantummodo D B ſit
breuiſecans.
Et illi propinquiores ſint maio-
22b res remotioribus, &
c. Sed mendo-
sè;
legi debet: Et illi propinquiores
ſint minores remotioribus.
Quia educitur ex D vnus tantum breuiſecans, & c. Legi debet. Quia
33Conuerſ.
51. 52.
huius.
44c educitur ex concurſu D vnus tantum breuiſecans, erit menſura E A maior di-
midio erecti, &
D E perpendicularis ad axim æqualis erit Trutinæ F.
Inde conſtat D G maiorem eſſe, quàm D A, & c. Quia ex concurſu D
55d ad ſectionem A C vnicus ramus D B breuiſecans ſupponitur igitur omnes rami
cadentes inter A, &
B præter infimum D B conſtituunt cum tangentibus ſectio-
nem, ab eorum terminis ductis, angulos reſpicientes verticem A acutos;
& pro-
66Lem. 10. pterea ramus terminatus D A minor eſt quolibet ramo D G infra ipſum, &
ſu-
pra ramum D B poſito;
atque ramus D G minor eſt quolibet alio à vertice re-
77Coro 11.
64. 65.
huius.
motiore ducto ex D ad peripheriam A B.
Dico iam, quod ramus D B maior
eſt quolibet ramo D G, poſito infra verticem A, &
ſupra breuiſecantem D B;
Si enim hoc verum non eſt, erit D B æqualis, aut minor, quàm D G, & tunc
ducto quolibet ramo D H ad ſectionem G B infra ramum D G, erit D H re-
88Ibidem. motior à vertice A maior propinquiore D G, &
propterea ramus D B adhuc
minor erit ramo D H.
Ergo D M nempe D I, & c. Quia D M, vt remotior à vertice A, eſt ma-
99e ior, quàm propinquior D H eſt vero D L, atque D I æqualis D M cum ſint
1010Ibidem. radij eiuſdem circuli;
ergo D I portio maior eſt, quàm totum D H, quod eſt
abſurdum;
quare D B maior eſt quolibet ramo D G infra verticem A, & ſu-
pra ramum D B poſito;
& propterea D B multo maior erit, quàm D A.
Ergo D N minor eſt, quàm D C, & c. Dubitare quis poſſet, an ramus
1111f D N, quia propinquior eſt vertici A ſit minor remotiore ramo D C, vt in pro-
poſitione 64.
& 65. verificabatur; & ratio eſt, quia hypotheſes ſunt diuerſæ,
nam ibi nullus ramus breuiſecans à concurſu D ad ſectionem A C duci poſſe
ſupponebatur, in hac vero propoſitione 67.
ponitur vnicus breuiſecans D B, at
ſcrupulus omnis tolletur, ſi dicatur, non quidem ex propoſitionibus 64.
& 65.
ſed ex demonſtratione ibi allata, ſeu ex Corollario in fine notarum

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index