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 |< < (140) of 458 > >|
178140Apollonij Pergæi 179[Figure 179]
Quoniam facta conuenienti ſuperpoſitione axis A M ſuper axim D
O, cadet quoque ſectio A B ſuper ſectionem D E:
ſi enim non cadit ſu-
per illam, ſumatur (ſi fieri poteſt) eius punctum B, extra ſectionem.
D E cadens; & producatur ad axim perpendicularis B L vſque ad P: &
perficiatur planum A P applicatum comparatum;
& ſecetur D N æqua-
lis A L, &
erigatur per N ad axim perpendicularis N E, & producatur
vſque ad R, perficiendo planum D R applicatum comparatum;
Et quia
A I æqualis eſt D K, &
A L æqualis D N: erit planum I L, æquale pla-
no K N;
cumque G I, H K ſint duæ figuræ ſimiles, & æquales, pariter-
11b que I P, K R;
ergo duo plana A P, D R ſunt æqualia: & propterea E
N, B L, quæ illa ſpatia poſſunt (13.
14. ex 1.) ſunt æquales. Si autem
2212. 13.
lib. I.
ſuperponatur axis axi cadet B L ſuper E N, eoquod duo anguli N, &
L
ſunt æquales;
igitur B cadit ſuper E, quod prius cadere non concedeba-
tur:
& hoc eſt abſurdum. Quapropter ſectio ſectioni æqualis eſt.
Deinde ponamus duas ſe-
180[Figure 180] ctiones æquales, vtique con-
gruet ſectio A B ſectioni D E,
&
axis A L axi D N, quia ſi
non cadit ſuper illum, eſſent
33c in hyperbola duo axes, &
in
ellipſi tres axes, quod eſt ab-
ſurdum (52.
53. ex 2.) Et fi-
4448. lib. 2. at A L æqualis D N, &
reli-
qua perficiantur, vt prius ca-
dent duo puncta L, B ſuper
N, E;
ideoque B L æqualis
55d erit E N;
& poterunt æqua-
lia rectangula A P, D R applicata ad æquales A L, D N (13.
14. ex 1.)
6612. 13.
lib. 1.
ergo L P æqualis eſt N R.
Similiter ponatur A M æqualis D O, & edu-
cantur C M Q, F O S duæ ordinationes, oſtendetur, quod M Q æqua-
lis eſt O S, &
L M æqualis N O; & propterea duo plana P Q, R S ſunt
æqualia, &
ſimilia; igitur duo plana G P, H R ſunt æqualia, & ſimilia,
&
L P oſtenſa eſt æqualis N R: ergo G L æqualis eſt H N, & A L æ-
qualis D N;
& propterea G A æqualis eſt D H, & A I æqualis D K.

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index