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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[161.] IV.
Page: 171 (133)
[162.] V.
Page: 171 (133)
[163.] VI.
Page: 171 (133)
[164.] VII.
Page: 171 (133)
[165.] VIII.
Page: 172 (134)
[166.] IX.
Page: 172 (134)
[167.] NOTÆ.
Page: 172 (134)
[168.] MONITVM.
Page: 175 (137)
[169.] SECTIO PRIMA Continens Propoſit. I. II. IV. & X. PROPOSITIO I.
Page: 176 (138)
[170.] PROPOSITIO II.
Page: 177 (139)
[171.] PROPOSITIO IV.
Page: 179 (141)
[172.] PROPOSITIO X.
Page: 179 (141)
[173.] Notæ in Propoſit. I.
Page: 179 (141)
[174.] Notæ in Propoſit. II.
Page: 180 (142)
[175.] Notæ in Propoſit. IV.
Page: 182 (144)
[176.] Notæ in Propoſit. X.
Page: 182 (144)
[177.] SECTIO SECVNDA Continens Propoſit. III. VI. VII. & IX. PROPOSITIO III.
Page: 184 (146)
[178.] PROPOSITIO VI.
Page: 185 (147)
[179.] PROPOSITIO VII.
Page: 185 (147)
[180.] PROPOSITIO IX.
Page: 186 (148)
[181.] Notæ in Propoſit. III.
Page: 187 (149)
[182.] Notæ in Propoſit. VI.
Page: 187 (149)
[183.] Notæ in Propoſit. VII.
Page: 187 (149)
[184.] Notæ in Propoſit. IX.
Page: 188 (150)
[185.] LEMMAI.
Page: 188 (150)
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
Page: 190 (152)
[187.] PROPOSITIO VIII.
Page: 191 (153)
[188.] Notæ in Propoſit. V.
Page: 192 (154)
[189.] Notæ in Propoſit. VIII.
Page: 192 (154)
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
Page: 192 (154)
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166128Apollonij Pergæi
PR OPOSITIO XXXIX.
IN ſectione A B elliptica quælibet
162[Figure 162] perpendicularis F D ad lineam
maximam C D, ab eius termino D
in ſectione poſito educta, continget
coniſectionem.
Alioquin ſecet illam, & in eius produ-
ctione D G ſumatur punctum G intra ſe-
11a ctionem: & educamus B G C, igitur G
C maior eſt, quàm C D, quia ſubtendit
rectum angulum C D G, & propterea B C multo maior eſt, quàm C D,
quod eſt abſurdum; igitur educta illa linea eſt tangens; quod erat oſten-
dendum.
PROPOSITIO XXXX.
E Contra ſi fuerit F D tangens, erit perpendicularis ſuper
maximam D C.
Alioquin educamus aliam E D perpendicularem ſuper illam; ergo E
D tangit ſectionem in puncto D (39. ex 5.) ſed F D ſuppoſita fuit tan-
gens; igitur duæ D F, & D E tangunt ſectionem in vno puncto, quod
eſt abſurdum (36. ex I.)
PROPOSITIO XXXXVII.
Q Vælibet linea D E ex puncto
163[Figure 163] contactus D ad axim alicuius
ſectionis A B educta per-
pendicularis ad tangentem D C,
erit linea breuiſſima, aut maxima.
Alioquin educamus D F breuiſſimam,
22Ex 10. & 20. huius. vel maximam; ergo D C perpendicularis
eſt ſuper D F; ſed C D ſuppoſita fuit per-
3340. huius. pendicularis ſuper D E; quod eſt abſur-
dum: quapropter demonſtratũ eſt, quod
fuerat propoſitum.

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