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 271]
[Figure 272]
[Figure 273]
[Figure 274]
[275] Cc 2
[Figure 276]
[Figure 277]
[Figure 278]
[Figure 279]
[Figure 280]
[Figure 281]
[Figure 282]
[Figure 283]
[Figure 284]
[Figure 285]
[Figure 286]
[287] Dd 2
[Figure 288]
[Figure 289]
[Figure 290]
[Figure 291]
[Figure 292]
[Figure 293]
[Figure 294]
[Figure 295]
[Figure 296]
[Figure 297]
[Figure 298]
[Figure 299]
[Figure 300]
< >
page |< < (236) of 458 > >|
274236Apollonij Pergæi nuuntur quidem; ſed non efficiuntur minora interuallo quo parallelæ asymptoti
diſtant inter ſe;
ex altera verò parte perueniri poteſt ad interuallum minus
quolibet dato.
Et hoc erat faciendum.
Data hyperbola eadem X præcedentis propoſitionis deſcribere duos ſi-
11PROP.
14. Add.
miles conos, vt idem planum in eis efficiat duas hyperbolas ſimiles da-
tæ ſectioni, quæ asymptoticæ ſint, &
ex vtraque parte ſibi ipſis vici-
niores fiant interuallo minori quolibet dato.
320[Figure 320]
In quolibet plano fiat angulus A d G æqualis angulo inclinationis diametri,
&
baſis hyperbolæ datæ X, & per G d extenſo quolibet alio plano, ducatur in
eo recta linea B d C perpendicularis ad G d O, &
ſumpto quolibet alio puncto
b in recta linea B C in plano per B G O extenſo, centris d, &
b, deſcribãtur
duo circuli inter ſe æquales G C O B, &
S Q P L ſe ſe ſecantes in duobus punctis
R, a:
atq; vt latus rectum ad tranſuerſum ſectionis datæ X, ita fiat quadratũ
G d ad quadratũ d A, &
ducatur recta linea A N M parallela ipſi B C, quæ ſecet
b N æquidiſtantẽ d A in N, &
coniungantur rectæ lineæ A B, A C, N L, N Q,
&
fiant A, & N vertices duorũ conorũ A B C, N L Q, & in eorũ ſuper ficiebus
planum M c T æquidiſtans planis A G O, &
N S P efficiat ſectiones H I K,
&
T V c, quarum diametri D V I genitæ à triangulis A B C, & N L Q per
axes in eodem plano exiſbentibus ſunt æquidiſtantes axibus conorum A d, N b,
propter planorum æquidiſtantiam:
Dico, eas eſſe hyperbolas quæſitas. Qnoniam
(propter æquidiſtantiam oppoſitarum linearum) eſt ſpatium A b parallelogram-
mum;
igitur conorum axes A d, N b æquales ſunt inter ſe, & æquè inclinan-
tur ad communem rectam lineam B C Q (propter æquidiſtantiam earundem
A d, N b);
ſuntque æqualium circulorum radij d B, d C, b L, b Q æqua-
les inter ſe;
igitur triangula A B C, N L Q ſimilia ſunt inter ſe, &

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index