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

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[141.] PROPOSITIO XXXIII. XXXIV.
Page: 163 (125)
[142.] PROPOSITIO XXXV.
Page: 163 (125)
[143.] PROPOSITIO XXXVI.
Page: 164 (126)
[144.] PROPOSITIO XXXVII. XLVI.
Page: 164 (126)
[145.] PROPOSITIO XXXVIII.
Page: 165 (127)
[146.] PR OPOSITIO XXXIX.
Page: 166 (128)
[147.] PROPOSITIO XXXX.
Page: 166 (128)
[148.] PROPOSITIO XXXXVII.
Page: 166 (128)
[149.] PROPOSITIO XXXXVIII.
Page: 167 (129)
[150.] Notæ in Propoſit. XXXII.
Page: 167 (129)
[151.] Notæ in Propoſit. XXXIII. XXXIV.
Page: 167 (129)
[152.] Notæ in Propoſit. XXXV.
Page: 168 (130)
[153.] Notæ in Prop. XXXVI.
Page: 169 (131)
[154.] Notæ in Prop. XXXVIII.
Page: 169 (131)
[155.] Notæ in Propoſit. XXXIX.
Page: 170 (132)
[156.] Notæ in Propoſit. XXXXVIII.
Page: 170 (132)
[157.] LIBRI QVINTI FINIS.
Page: 170 (132)
[158.] APOLLONII PERGAEI CONICORVM LIB VI. DEFINITIONES. I.
Page: 171 (133)
[159.] II.
Page: 171 (133)
[160.] III.
Page: 171 (133)
[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)
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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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