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 contents

< >
[111.] Notæ in Propoſit. LXXII.
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
[113.] PROPOSITO LXXIV.
[114.] PROPOSITO LXXV.
[115.] PROPOSITIO LXXVI.
[116.] PROPOSITIO LXXVII.
[117.] Notæ in Propoſit. LXXIII.
[118.] LEMMA XII.
[119.] Notæ in Propoſ. LXXIV.
[120.] Notæ in Propoſit. LXXV.
[121.] Notæ in Propoſ. LXXVI.
[122.] Notæ in Propoſit. LXXVII.
[123.] COROLLARIVM.
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
[125.] PROPOSITO XXXXII.
[126.] PROPOSITIO XXXXIII.
[127.] Notæ in Propoſ. XXXXI.
[128.] Notæ in Propoſ. XXXXII.
[129.] Notæ in Propoſit. XXXXIII.
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
[133.] PROPOSITIO XX. XXI. & XXII.
[134.] PROPOSITIO XXIII. & XXIV.
[135.] PROPOSITIO XXV.
[136.] Notæ in Propoſit. XIX.
[137.] Notæ in Propoſit. XX. XXI. XXII.
[138.] Notæ in Propoſ. XXIII. XXIV.
[139.] Notæ in Propoſ. XXXV.
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
< >
page |< < (128) of 458 > >|
166128Apollonij Pergæi
PR OPOSITIO XXXIX.
IN ſectione A B elliptica quælibet
162[Figure 162] perpendicularis F D ad lineam
maximam C D, ab eius termino D
in ſectione poſito educta, continget
coniſectionem.
Alioquin ſecet illam, & in eius produ-
ctione D G ſumatur punctum G intra ſe-
11a ctionem:
& educamus B G C, igitur G
C maior eſt, quàm C D, quia ſubtendit
rectum angulum C D G, &
propterea B C multo maior eſt, quàm C D,
quod eſt abſurdum;
igitur educta illa linea eſt tangens; quod erat oſten-
dendum.
PROPOSITIO XXXX.
E Contra ſi fuerit F D tangens, erit perpendicularis ſuper
maximam D C.
Alioquin educamus aliam E D perpendicularem ſuper illam; ergo E
D tangit ſectionem in puncto D (39.
ex 5.) ſed F D ſuppoſita fuit tan-
gens;
igitur duæ D F, & D E tangunt ſectionem in vno puncto, quod
eſt abſurdum (36.
ex I.)
PROPOSITIO XXXXVII.
Q Vælibet linea D E ex puncto
163[Figure 163] contactus D ad axim alicuius
ſectionis A B educta per-
pendicularis ad tangentem D C,
erit linea breuiſſima, aut maxima.
Alioquin educamus D F breuiſſimam,
22Ex 10. & 20. huius. vel maximam;
ergo D C perpendicularis
eſt ſuper D F;
ſed C D ſuppoſita fuit per-
3340. huius. pendicularis ſuper D E;
quod eſt abſur-
dum:
quapropter demonſtratũ eſt, quod
fuerat propoſitum.

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index