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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[11.] PRÆFATIO AD LECTOREM.
[12.] INDEX
[13.] APOLLONII PERGAEI CONICORVM LIB. V. DEFINITIONES. I.
[14.] II.
[15.] III.
[16.] IV.
[17.] V.
[18.] VI.
[19.] VII.
[20.] VIII.
[21.] IX.
[22.] X.
[23.] XI.
[24.] XII.
[25.] XIII.
[26.] XIV.
[27.] XV.
[28.] XIV.
[29.] NOTÆ.
[30.] SECTIO PRIMA Continens propoſitiones I. II. & III. Apollonij. PROPOSITIO I.
[31.] PROPOS. II.
[32.] PROPOS. III.
[33.] Notæ in Propoſitionem primam.
[34.] Notæ in Propoſitionem ſecundam.
[35.] Notæ in Propoſitionem tertiam.
[36.] SECTIO SECVNDA Continens propoſitiones IV. V. VI. Apollonij.
[37.] PROPOSITIO IV.
[38.] PROPOSITIO V. & VI.
[39.] Notæ in pro poſitionem quartam.
[40.] Notæ in propoſitionem quintam.
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page |< < (88) of 458 > >|
12688Apollonij Pergæi
SECTIO DECIMAQVARTA
Continens Propoſ. LXXIII. LXXIV. LXXV.
LXXVI. & LXXVII.
PROPOSITIO LXXIII.
SI ex concurſu E non exiſtente ſuper rectum minorem elli-
11a pſis A B C ducatur ad ſectionem A B vnicus ramus vtrum-
que axim ſecans, cuius portio G I inter ſectionem, &
axim
maiorem A C ſit breuiſſima, vel duo breuiſecantes;
vtique ra-
morum ſecantium ex illo concurſu egredientium maximus erit
breuiſecans, qui ſectionis rectum ſecat, nempe E G, &
illi
proximior maior eſt remotiore;
minimus verò eorum eſt, qui
terminatur à vertice ſectionis proximiori concurſui, nempe E
C, &
illi propinquiores minores ſunt remotioribus, nempe in-
ter C G.
Si autem egrediantur ex illo tres breuiſecantes, &
duo illorum ſecuerint menſuram, &
vnus ſecuerit rectum, vtique
qui rectum ſecat eſt maximus ramorum ſecantium:
& ramorum
inter mediam breuiſecantem, &
remotiorem verticem ſectionis
à concurſu cadentium, proximior illi, eſt maior remotiore, &

maximus duorum reliquorum breuiſecantium eſt ille, qui vertici
proximus eſt, &
ramorum, inter proximiorem verticem ſectio-
nis, &
intermedium breuiſecantem cadentium, vicinior illi, ma-
ior eſt remotiore.
109[Figure 109]

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