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

< >
[71.] Demonſtratio ſecundæ partis. PROPOSITIONIS LI.
[72.] Notæ in Propoſ. LII. LIII.
[73.] Secunda pars buius propoſitionis, quam Apollonius non expoſuit hac ratione ſuppleri poteſt.
[74.] Notæ in Propoſ. LIV. LV.
[75.] Notæ in Propoſit. LVI.
[76.] LEMMA VIII.
[77.] Notæ in Propoſ. LVII.
[78.] SECTIO NONA Continens Propoſ. LVIII. LIX. LX. LXI. LXII. & LXIII.
[79.] PROPOSITIO LVIII.
[80.] PROPOSITIO LIX. LXII. & LXIII.
[81.] PROPOSITIO LX.
[82.] PROPOSITIO LXI.
[83.] Notæ in Propoſit. LVIII.
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
[85.] Notæ in Propoſit. LX.
[86.] Notæ in Propoſit. LXI.
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
[88.] PROPOSITIO XXXXIV.
[89.] PROPOSITIO XXXXV.
[90.] Notæ in Propoſ. XXXXIV.
[91.] Notæ in Propoſ. XLV.
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
[93.] PROPOSITIO LXX.
[94.] PROPOSITIO LXXI.
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
[99.] PROPOSITIO LXVI.
[100.] PROPOSITIO LXVII.
< >
page |< < (232) of 458 > >|
270232Apollonij Pergæi317[Figure 317] A B C, & D E F ſimilia, & ſimiliter poſita: poſtea in plano per B C, M K
ducto, diametris B C, &
E F, fiant duo circuli B K C, E L F, qui ſint ba-
ſes duorum conorum, quorum vertices ſint A, &
D, & in eorum ſuper ficie-
bus planum per H I, M K ductum efficiat ſectiones K H M, &
L X S: Dico
eas eſſe quæſitas.
Quoniam duo triangula A B C, D E F ſimilia, & ſimiliter
poſita in eodem ſunt plano, pariterque duo circuli baſium in vno plano exiſtunt;
11Lem. 9.
huius.
ergo duo coni A B C, &
D E F ſimiles erunt; poſtea quia triangula A B C,
&
D E F ſimilia ſunt, & communis ſectionum diameter H X I æque inclina-
tur ad coincidentes baſes M K, S L, &
axi communi A D G æquidiſtat, &
in angulis æqualibus intercipiunt G I communem portionem baſium triangulorum
22Prop. 10.
add.
ſimilium per axes;
igitur hyperbolæ K H M, & L X S æquales ſunt, & ſimi-
les inter ſe, &
earum figuris æqualia ſunt quadrata ex dupla interceptæ G I
deſcripta.
Secundò quia ( propter parallelas A O, & B C ) triangula H O A,
&
A G C ſimilia ſunt; igitur quadratum A G ad quadratum G C, ſeu ad re-
ctangulum B G C eandem proportionem habebit, quàm quadratum H O ad qua-
dratum O A, ſeu quàm latus tranſuerſum ad rectum figuræ Z;
ſed vt quadra-
3312. lib. 1. tum A G ad rectangulum B G C, ita eſt latus tranſuerſum ad rectum hyperbo-
les K H M;
igitur duæ hyperbolæ Z, & K H M, habent figurarum latera,
porportionalia;
ſuntq; prædictæ figuræ æquales cum ſint æquales quadratis ex du-
plis ipsarum A O, &
interceptæ G I: quæ ſunt æquales in parallelogrammo G
O, &
habent angulos à diametris, & baſibus contenti, æquales inter ſe: erunt
4410. 12.
huus.
hyperbolæ K H M, &
Z æquales, & ſimiles inter ſe: & propterea ſectio L X S,
quæ ſimilis, &
æqualis oſtenſa eſt ipſi K H M, erit quoque æqualis, & ſimilis
eidem ſectioni Z.
Tertiò, quia in duobus conis ſimilibus, & ſimiliter poſitis
circa communem axim A D G, ſuperficies nunquàm conueniunt, propterea,
quod latera A B, &
D E, à quibus generantur in tota reuolutione inter

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index