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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[141.] PROPOSITIO XXXIII. XXXIV.
[142.] PROPOSITIO XXXV.
[143.] PROPOSITIO XXXVI.
[144.] PROPOSITIO XXXVII. XLVI.
[145.] PROPOSITIO XXXVIII.
[146.] PR OPOSITIO XXXIX.
[147.] PROPOSITIO XXXX.
[148.] PROPOSITIO XXXXVII.
[149.] PROPOSITIO XXXXVIII.
[150.] Notæ in Propoſit. XXXII.
[151.] Notæ in Propoſit. XXXIII. XXXIV.
[152.] Notæ in Propoſit. XXXV.
[153.] Notæ in Prop. XXXVI.
[154.] Notæ in Prop. XXXVIII.
[155.] Notæ in Propoſit. XXXIX.
[156.] Notæ in Propoſit. XXXXVIII.
[157.] LIBRI QVINTI FINIS.
[158.] APOLLONII PERGAEI CONICORVM LIB VI. DEFINITIONES. I.
[159.] II.
[160.] III.
[161.] IV.
[163.] VI.
[164.] VII.
[165.] VIII.
[166.] IX.
[167.] NOTÆ.
[168.] MONITVM.
[169.] SECTIO PRIMA Continens Propoſit. I. II. IV. & X. PROPOSITIO I.
[170.] PROPOSITIO II.
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141103Conicor. Lib. V. non ergo perpendicularis C F æqualis erit Trutinæ K, ſed priùs, neque maior
illa erat;
igitur perpendicularis C F neceſſario minor erit Trutina K; quod
erat oſtendendum.
Iiſdem poſitis, ſi in productione breuiſsimæ A I ſumatur quodlibet
11PROP. 8.
Addit.
punctum C citra terminum D perpendicularis D E, à puncto C duci
poterit alter ramus breuiſecans ſupra C A incedens;
& ſi punctum C
ſumatur vltra punctum D poterit ex C duci alter ramus breuiſecans
infra ipſum C A.
126[Figure 126]
Quoniam quælibet recta C F parallela perpendiculari D E interpoſita inter
productionem breuiſsimæ A I, &
axim minor eſt Trutina K nouæ menſuræ B
F (ex præcedenti propoſ.)
propterea ramus principalis C O cadit ſupra ipſum
C A, quando B F minor eſt, quàm B E, &
tunc quidem duci poteſt hyperbola
ex puncto A circa aſymptotos (vt in propoſitione 51.
& 52. factum eſt) quæ pro-
ducta occurret ſectioni B A inter B, &
O, vt in P, & coniuncto radio C P,
2251. 52. 53.
huius.
erunt duo rami C A, &
C P breuiſecantes, quorum infimus eſt C A. Si vero
punctum C ſumatur vltra punctum D, tunc quidem menſura B F maior erit,
quàm B E, &
propterea abſciſſa N B maior, quàm H B, & ideo principalis
ramus C O cadet infra ramum C A;
& denuo facta eadem conſtructione propo-
ſit.
51. & 52. huius, erunt duo rami C P, & C A breuiſecantes, quorũ ſupre-
mus verſus B erit C A, quod erat probandum.
Sit coniſectio, vel ellipſis portio quadrantis B A G, cuius axis B
33PROP. 9.
Addit.
E, perpendicularis E D, euiuſque Trutina L ſit minor perpendiculari
D E, &
centro D, interuallo cuiuslibet rami ſecantis D A circulus Z
A γ deſcribatur, &
ex puncto A ducatur recta A x contingens

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