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

Scan	Original
121	83
122	84
123	85
124	86
125	87
126	88
127	89
128	90
129	91
130	92
131	93
132	94
133	95
134	96
135	97
136	98
137	99
138	100
139	101
140	102
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112

12183Conicor. Lib. V. ſunt D A V, D L G, D B I, D Q O, D C P, oſtenſus eſt ramus D A minor
quàm D B, & D B propinquior vertici A, minor ramo D C remotiore.

Notæ in Propoſ. LXVII.

POſtea repetamus figuram vtrã-

102[Figure 102]11a que hyperboles, & c. Lego;
Repetamus figuras paraboles, & hy-
perboles, & ſupponantur denuo eædem
lineæ æductæ ex concurſu D ad ſectio-
nem; & perpendicularis D E, atque
Trutina F, & omnium ramorum ſe-
cantium vnicus tantummodo D B ſit
breuiſecans.

Et illi propinquiores ſint maio-
22b res remotioribus, & c. Sed mendo-
sè; legi debet: Et illi propinquiores
ſint minores remotioribus.

Quia educitur ex D vnus tantum breuiſecans, & c. Legi debet. Quia
33Conuerſ.
51. 52.
huius.44c educitur ex concurſu D vnus tantum breuiſecans, erit menſura E A maior di-
midio erecti, & D E perpendicularis ad axim æqualis erit Trutinæ F.

Inde conſtat D G maiorem eſſe, quàm D A, & c. Quia ex concurſu D
55d ad ſectionem A C vnicus ramus D B breuiſecans ſupponitur igitur omnes rami
cadentes inter A, & B præter infimum D B conſtituunt cum tangentibus ſectio-
nem, ab eorum terminis ductis, angulos reſpicientes verticem A acutos; & pro-
66Lem. 10. pterea ramus terminatus D A minor eſt quolibet ramo D G infra ipſum, & ſu-
pra ramum D B poſito; atque ramus D G minor eſt quolibet alio à vertice re-
77Coro 11.
64. 65.
huius. motiore ducto ex D ad peripheriam A B. Dico iam, quod ramus D B maior
eſt quolibet ramo D G, poſito infra verticem A, & ſupra breuiſecantem D B;
Si enim hoc verum non eſt, erit D B æqualis, aut minor, quàm D G, & tunc
ducto quolibet ramo D H ad ſectionem G B infra ramum D G, erit D H re-
88Ibidem. motior à vertice A maior propinquiore D G, & propterea ramus D B adhuc
minor erit ramo D H.

Ergo D M nempe D I, & c. Quia D M, vt remotior à vertice A, eſt ma-
99e ior, quàm propinquior D H eſt vero D L, atque D I æqualis D M cum ſint
1010Ibidem. radĳ eiuſdem circuli; ergo D I portio maior eſt, quàm totum D H, quod eſt
abſurdum; quare D B maior eſt quolibet ramo D G infra verticem A, & ſu-
pra ramum D B poſito; & propterea D B multo maior erit, quàm D A.

Ergo D N minor eſt, quàm D C, & c. Dubitare quis poſſet, an ramus
1111f D N, quia propinquior eſt vertici A ſit minor remotiore ramo D C, vt in pro-
poſitione 64. & 65. verificabatur; & ratio eſt, quia hypotheſes ſunt diuerſæ,
nam ibi nullus ramus breuiſecans à concurſu D ad ſectionem A C duci poſſe
ſupponebatur, in hac vero propoſitione 67. ponitur vnicus breuiſecans D B, at
ſcrupulus omnis tolletur, ſi dicatur, non quidem ex propoſitionibus 64. & 65.
ſed ex demonſtratione ibi allata, ſeu ex Corollario in fine notarum

Page concordance

Text layer

Text normalization

Search

Scan	Original
121	83
122	84
123	85
124	86
125	87
126	88
127	89
128	90
129	91
130	92
131	93
132	94
133	95
134	96
135	97
136	98
137	99
138	100
139	101
140	102
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112

Scan	Original
121	83
122	84
123	85
124	86
125	87
126	88
127	89
128	90
129	91
130	92
131	93
132	94
133	95
134	96
135	97
136	98
137	99
138	100
139	101
140	102
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112

Scan	Original
121	83
122	84
123	85
124	86
125	87
126	88
127	89
128	90
129	91
130	92
131	93
132	94
133	95
134	96
135	97
136	98
137	99
138	100
139	101
140	102
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112