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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[251.] II.
[252.] III.
[253.] IV.
[255.] VI.
[256.] VII.
[257.] VIII.
[258.] NOTÆ.
[259.] SECTIO PRIMA Continens Propoſit. I. V. & XXIII. Apollonij. PROPOSITIO I.
[260.] PROPOSITIO V. & XXIII.
[261.] Notæ in Propoſit. I.
[262.] Notæ in Propoſit. V. & XXIII.
[263.] SECTIO SECVNDA Continens Propoſit. II. III. IV. VI. & VII. Apollonij. PROPOSITIO II. & III.
[264.] PROPOSITIO IV.
[265.] PROPOSITIO VI. & VII.
[266.] Notæ in Propoſit. II. III.
[267.] Notæ in Propoſit. IV.
[268.] Notæ in Propoſit. VI. & VII.
[269.] SECTIO TERTIA Continens Propoſit. Apollonij VIII. IX. X. XI. XV. XIX. XVI. XVIII. XVII. & XX.
[270.] Notæ in Propoſit. VIII.
[271.] Notæ in Propoſit. IX.
[272.] Notæ in Propoſit. X.
[273.] Notæ in Propoſit. XI.
[274.] Notæ in Propoſit. XV.
[275.] Notæ in Propoſit. XIX.
[276.] Notæ in Propoſit. XVI.
[277.] Notæ in Propoſit. XVIII.
[278.] Notæ in Propoſit. XVII.
[279.] Notæ in Propoſit. XX.
[280.] SECTIO QVARTA Continens Propoſit. Apollonij XII. XIII. XXIX. XVII. XXII. XXX. XIV. & XXV.
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302264Apollonij Pergæi& per rectam B E extendatur aliud planum E N O B inter duo plana contin-
gentia
prope verticem A vbicumq;
cadens, quod ſecet vtrumque conum, & cir-
culum
baſis in recta linea N O, &
ſuperficies duorum conorum in lateribus B
N
Q, E N, B O, E O R, quarum B N occurret ſemiſectioni A H in quolibet
eius
puncto Q prope verticem A, eo quod portio A H, &
peripheria A N C ex
cepto
puncto eius A totæ inter duo plana conos tangentia intercipiuntur;
& eadem
ratione
E O occurret ſemiſectioni A G in quolibet eius puncto R vltra verticem
A
ad partes G.
Et quoniam in eo-
349[Figure 349] dem plano trianguli E N B (ſcili-
cet
plani B N O E ſecantis vtrum-
que
conum) à puncto E ducitur re-
cta
linea E O intra angulum N E B;
ergo vlterius producta ſecabit latus
B
N ſubtendentem angulum N E B
inter
puncta N, &
B, vt in X, &
propterearecta
linea N X intra triã-
gulum
E N O, &
ideo intra conum
E
A C intercepta erit;
ſimiliter re-
cta
linea O X intra triangulum B N
O
, &
intra conum B A C interclu-
ſa
erit:
quare quodlibet aliud punctũ
Qlateris
conici B N citra, vel vltra
interclusã
portionẽ N X cadet neceſ-
ario
extra ſuperficiem coni E A C,
&
ideo quodlibet punctum Q in pro-
ductione
lateris coni B N ſumptum
&
in ſemiſſe ſectionis conicæ H A
prope
verticem A cadet extra ſemiſ-
ſem
ſectionis F A, quæ in ſuperfi-
cie
coni E A C exiſtit, &
ad eaſ-
dem
partes vergit.
Pari modo quod-
libet
aliud punctum R lateris conici
E
O citra, vel vltra intercluſam
portionẽ
X O cadet extra ſuperſiciem
coni
B A C, &
ideo quodlibet punctũ
R
ſumptum in medietate ſectionis
conicæ
A G prope verticem A cadet
extra
medietatem ſectionis A I, quæ
in
ſuperficie coni B A C exiſtit, &

ad
eaſdem partes vergit.
Igitur ſe-
ctio
H A I abſcindit coniſectionem
F
A G in vertice communi A, vbi
ambo
tanguntur ab eadem recta li-
nea
A D.
Quod erat faciendum.

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