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.
Page: 199 (161)
[202.] COROLLARIVM II.
Page: 199 (161)
[203.] Notæ in Propoſit. XI.
Page: 203 (165)
[204.] Notæ in Propoſit. XII.
Page: 204 (166)
[205.] Notæ in Propoſit. XIII.
Page: 205 (167)
[206.] Notæ in Propoſit. XIV.
Page: 206 (168)
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
Page: 206 (168)
[208.] PROPOSITIO Præmiſſa VI.
Page: 209 (171)
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
Page: 209 (171)
[210.] Notæ in Propoſit. Præmiſſ. VI.
Page: 212 (174)
[211.] SECTIO SEXTA Continens Propoſit. XV. XVI. & XVII. PROPOSITIO XV.
Page: 213 (175)
[212.] PROPOSITIO XVI.
Page: 215 (177)
[213.] PROPOSITIO XVII.
Page: 216 (178)
[214.] Notæ in Propoſit. XV.
Page: 219 (181)
[215.] MONITVM.
Page: 221 (183)
[216.] LEMMA VI.
Page: 221 (183)
[217.] LEMMA VII.
Page: 222 (184)
[218.] LEMMA VIII.
Page: 224 (186)
[219.] Notæ in Propoſit. XVI.
Page: 225 (187)
[220.] Notæ in Propoſit. XVII.
Page: 226 (188)
[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
Page: 229 (191)
[222.] Notæ in Propoſit. XVIII. & XIX.
Page: 230 (192)
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
Page: 231 (193)
[224.] PROPOSITIO XXI.
Page: 233 (195)
[225.] PROPOSITIO XXII.
Page: 235 (197)
[226.] PROPOSITIO XXIII.
Page: 236 (198)
[227.] PROPOSITIO XXIV.
Page: 236 (198)
[228.] Notæ in Propoſit. XX.
Page: 237 (199)
[229.] Notæ in Propoſit. XXI.
Page: 241 (203)
[230.] Notæ in Propoſit. XXII.
Page: 243 (205)
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page |< < (246) of 458 > >|
284246Apollonij Pergæi
Notæ in Propoſit. XXVIII.
DEinde ſit ſectio elliptica, vt A B, & axis eius tranſuerſus B D, &
11a erectus illius B E; & ſit triãgulum coni H F I, & circumducamus
circa illum circulum, & educamus ex F lineam F L K occurrentem ipſi
extra circulum in K; & occurrat circulo in L ita vt ſit F K ad K L, vt
D B ad B E; & eſt facile ( vti demonſtrauimus in 59. ex I.) , & c.
331[Figure 331]
Senſus propoſitionis hic erit. In cono recto, cuius triangulum per axim H F I
reperire ſectionem æqualem datæ ellipſi A B, cuius axis tranſuerſus D B, &
latus rectum B E. In conſtructione poſtea duci debet recta linea F L K extra
circulum, & triangulum ad vtraſque partes, alias conſtructio non eſſet perfecta.
Lemma verò, quod repoſuiſſe, dicit Arabicus interpres in I. libro, ab hoc
ſequenti for ſam diuerſum non erit.
LEMMAX.
SEcetur latus F I in S, vt ſit F I
332[Figure 332] ad I S in eadem ratione, quàm
habet axis tranſuerſus D B ad latus re-
ctum B E: & ducatur S L æquidiſtans
trianguli baſi H I, quæ ſecet circulum ex
vtraque parte in L, & coniungantur re-
ctæ lineæ F L, producanturque quoſquè
ſecent baſim H I in punctis K.
Quoniam in triangulo F I K ducitur recta
linea S L æquidiſtans baſi I K, erit F I

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