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
page |< < (225) of 458 > >|
263225Conicor. Lib. VI. I M ad partes O A M; ideoque interceptæ R P, f h parallelæ erunt alicui re-
ctæ lineæ diuidenti angulum D A O ab axe interioris parabola, &
vertices
coniungente contentum, vel angulum I M L ab asymptoto interioris hyperbolæ,
&
centra coniungente contentum; igitur R P propinquior verticibus, vel vlte-
113. 4. addit. rius tendens ad partes reliquæ asymptoti M N maior erit quàm f h;
eſtque f h
309[Figure 309] maior f e quæ eſt productio rami breuiſſimi;
ergo diſtãtia R P propinquior maximæ
2238. lib. 5. E B maior erit, quàm f e.
E contra quia breuiſſimus ramus i l m cadit inter
duas parallelas E B, &
D A, & ſecat ramũ breuiſſimum E B ad partes O i;
3328. lib. 5. ergo l m occurrit A D, vel M I ad partes D, vel I; ideoque intercepta m l,
&
ei parallela G S erunt æquidiſtantes alicui rectæ lineæ diuidenti angulum Y
D A, in parabolis, vel H I M in hyperbolis:
& propterea G S propinquior ver-
443. 4. addit. tici parabolæ, vel vlterius tendens ad partes reliquæ asymptoti M N minor
erit, quàm m l;
eſtque G A productio rami breuiſſimi minor quàm G S; ergo
5538. lib. 5. m l maior erit, quàm G A;
& ſic vlterius G A maior erit C F, quando oc-
curſus Z ſectionum cadit vltra interceptam F C ad partes T V;
vt in prima
parte oſtenſum eſt.
Iiſdem manentibus: dico poſtea, quod vltra diſtantiam maximam E B ad
partes R P, diſtantiæ, licet ſemper diminuantur non efficiuntur minores inter-
uallo diametrorum æquidiſtantium D Y, A O in parabolis, vel interuallo asym-
ptotorum collateralium I H, M L in hyperbolis, vt facile deducitur ex 3.
& 4.
additarum. At ad partes asymptotorum congruentium hyperbolæ ad ſe ſe ipſas
propius accedunt, interuallo minori quolibet dato:
Nam in locum ab hyperbole
B A C, &
asymptoto M N contentum extenditur altera hyperbole E D F; ſed
diſtantia hyperbolæ B A C ab asymptoto M N efficitur minor qualibet data:
igi-
tur diſtantia hyperbolæ D G F compræhenſæ ab hyperbole intercipiente minor erit
qualibet data diſtantia.

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index