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

< >
[201.] COROLLARIVM I.
[202.] COROLLARIVM II.
[203.] Notæ in Propoſit. XI.
[204.] Notæ in Propoſit. XII.
[205.] Notæ in Propoſit. XIII.
[206.] Notæ in Propoſit. XIV.
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
[208.] PROPOSITIO Præmiſſa VI.
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
[210.] Notæ in Propoſit. Præmiſſ. VI.
[211.] SECTIO SEXTA Continens Propoſit. XV. XVI. & XVII. PROPOSITIO XV.
[212.] PROPOSITIO XVI.
[213.] PROPOSITIO XVII.
[214.] Notæ in Propoſit. XV.
[215.] MONITVM.
[216.] LEMMA VI.
[217.] LEMMA VII.
[218.] LEMMA VIII.
[219.] Notæ in Propoſit. XVI.
[220.] Notæ in Propoſit. XVII.
[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
[222.] Notæ in Propoſit. XVIII. & XIX.
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
[224.] PROPOSITIO XXI.
[225.] PROPOSITIO XXII.
[226.] PROPOSITIO XXIII.
[227.] PROPOSITIO XXIV.
[228.] Notæ in Propoſit. XX.
[229.] Notæ in Propoſit. XXI.
[230.] Notæ in Propoſit. XXII.
< >
page |< < (46) of 458 > >|
8446Apollonij Pergæi
Et ponamus quamlibet duarum proportionum C F ad F D, & I S ad S C,
11b vt proportio figuræ, &
educamus ex E, S, & c. Ideſt fiat diſtantia ex centro
vſque ad perpendicularem E D ad eius portionem D F in hyperbola, vt ſumma late-
ris tranſuerſi, &
recti ad latus rectum, & vt eorum differentia in ellipſi ad latus
rectum ita fiat C D ad eius productionem D F;
tunc enim C F ad F D diuidendo in
hyperbola, &
compo-
61[Figure 61] nendo in ellipſi habe-
bit eandem propor-
tionem, quàm latus
tranſuerſum ad re-
ctum;
pariterq; fiat
E K ad K D in eadẽ
proportione figuræ,
&
ex E, K educamus
rectas E I, K S pa-
rallelas axi A C D,
ſecantes I C, &
L F
parallelas ipſi E D
in I, S, L, &
M.
Immutaui poſtremã
partem conſtructio-
nis, vt manifeſte er-
roneã in textu Ara-
bico;
Si enim I C ad
libitum ſumpta ſeca-
tur in S in ratione
C F ad F D non ca-
det neceſſariò E L
parallela C D ſuper
punctum I.
Et interponamus
22c inter F C, C A du-
as C N, C O pro-
portionales illis duabus, &
c. Textum corruptum ſic reſtituo: Interponamus in-
ter F C, &
A C duas medias proportionales, itaut F C, N C, C O, C A ſint continuè
proportionales, quod fieri poſſe conſtat ex lemmate 7.
huius librt.
Et ponamus proportionem lineæ alicuius, vt eſt Q compoſitam, & c. Vo-
33d catur Trutina in hyperbola, &
ellipſi linea recta Q, quæ ad B O compoſitam propor-
tionem habet ex C D ad D F, &
ex ratione F O ad O C.
Producatur priùs E B ſecans axim in H, & c. Producatur priùs E B ſecans
44e axim in H, &
rectam S K in R, nec non rectam I C in puncto T.
Ergo E D ad B O, quæ componitur ex E D ad D K, & c. Nam poſita inter-
55f media D K, proportio E D ad B O compoſita erit ex ratione E D ad D K, &
ex ra-
tione D K ad B O;
eſt verò I C ad C S, vt E D ad D K (propter parallelas I E, S K,
C D) atque D K eſt æqualis G O in parallelogrammo G D;
ergo proportio E D ad B O
componitur ex ratione I C ad C S, &
ex ratione G O ad O B.
Sed E D ad D K eſt, vt CD ad DF, quia quælibet earum vt proportio
66g

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index