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

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[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.
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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, &

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