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
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
160	122
161	123
162	124
163	125
164	126
165	127
166	128
167	129
168	130
169	131
170	132

141103Conicor. Lib. V. non ergo perpendicularis C F æqualis erit Trutinæ K, ſed priùs, neque maior
illa erat; igitur perpendicularis C F neceſſario minor erit Trutina K; quod
erat oſtendendum.

Iiſdem poſitis, ſi in productione breuiſsimæ A I ſumatur quodlibet
11PROP. 8.
Addit. punctum C citra terminum D perpendicularis D E, à puncto C duci
poterit alter ramus breuiſecans ſupra C A incedens; & ſi punctum C
ſumatur vltra punctum D poterit ex C duci alter ramus breuiſecans
infra ipſum C A.

126[Figure 126]

Quoniam quælibet recta C F parallela perpendiculari D E interpoſita inter
productionem breuiſsimæ A I, & axim minor eſt Trutina K nouæ menſuræ B
F (ex præcedenti propoſ.) propterea ramus principalis C O cadit ſupra ipſum
C A, quando B F minor eſt, quàm B E, & tunc quidem duci poteſt hyperbola
ex puncto A circa aſymptotos (vt in propoſitione 51. & 52. factum eſt) quæ pro-
ducta occurret ſectioni B A inter B, & O, vt in P, & coniuncto radio C P,
2251. 52. 53.
huius. erunt duo rami C A, & C P breuiſecantes, quorum infimus eſt C A. Si vero
punctum C ſumatur vltra punctum D, tunc quidem menſura B F maior erit,
quàm B E, & propterea abſciſſa N B maior, quàm H B, & ideo principalis
ramus C O cadet infra ramum C A; & denuo facta eadem conſtructione propo-
ſit. 51. & 52. huius, erunt duo rami C P, & C A breuiſecantes, quorũ ſupre-
mus verſus B erit C A, quod erat probandum.

Sit coniſectio, vel ellipſis portio quadrantis B A G, cuius axis B
33PROP. 9.
Addit. E, perpendicularis E D, euiuſque Trutina L ſit minor perpendiculari
D E, & centro D, interuallo cuiuslibet rami ſecantis D A circulus Z
A γ deſcribatur, & ex puncto A ducatur recta A x contingens

Page concordance

Text layer

Text normalization

Search

Scan	Original
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
160	122
161	123
162	124
163	125
164	126
165	127
166	128
167	129
168	130
169	131
170	132

Scan	Original
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
160	122
161	123
162	124
163	125
164	126
165	127
166	128
167	129
168	130
169	131
170	132

Scan	Original
141	103
142	104
143	105
144	106
145	107
146	108
147	109
148	110
149	111
150	112
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
160	122
161	123
162	124
163	125
164	126
165	127
166	128
167	129
168	130
169	131
170	132