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
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
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
160	122

206168Apollonij Pergæi natim ad axium applicatæ, numero pares, quæ ad abſciſſas ſint proportionales,
tum abſcißæ inter ſe: V nde ſequitur poſtrema concluſio, quæ in textu habetur,
quod nimirum rectangulum a L B ad rectangulum a K B eandem proportionem
habeat, quàm abſciſſa, L B ad abſciſſam K B: ſed quotieſcunque duo rectangu-
la eandem proportionem habent, quàm baſes, illa ſunt æque alta: igitur altitu-
dines a L, & a K æquales ſunt inter ſe, pars, & totum: quod eſt absurdum.

Notæ in Propoſit. XIV.

ALioquin ſequitur, quod quadratum R L ad quadratum K P, & c. In
11a propoſitione deficit expoſitio, quæ talis eſt. Sit A B quælibet hyperbolc,
& E F quælibet ellipſis. Dico A B ipſi E

226[Figure 226] F ſimilem non eße. Sint eorum axes late-
ra tranſuerſa, & recta eadem, quæ in præ-
cedenti propoſitione poſita ſunt. Et ſiqui-
dem ſectiones A B, & E F ſimiles credan-
tur, neceßario ex definitione ſecunda, duci
poterunt ad axes ordinatim applicatæ nu-
mero pares proportionales abſciſſis, tum
abſciſſæ inter ſe proportionales: & vt in
præcedenti propoſitione oſtenſum eſt, qua-
dratum R L ad quadratum P K, ſcilicet
rectangulum a L B ad rectangulum a K B in hyperbola eandem proportionem
2221. lib. 1. habebit, quàm quadratum γ N ad quadratum V M, ſeu quàm rectangulum b
33Ibidem. N F ad rectangulum b M F in ellipſi, ergo rectangulum a L B ad rectangulum
a K B eandem proportionem habet, quàm rectangulum b N F ad rectangulum
b M F: ſed eorundem rectangulorum baſes proportionales ſunt, eo quod L B ad
B K erat vt N F ad F M; igitur eorundem altitudines proportionales erunt,
ſcilicet a L ad a K eandem proportionem habebit, quàm b N ad b M, ſed in
hyperqola a L maior eſt, quàm a K; in ellipſi verò contra b N minor eſt, quã
b M; igitur maior a L ad minorem a K eandem proportionem habebit, quàm
minor b N ad maiorem b M. Luod erat abſurdum.

SECTIO QVINTA

Continens ſex Propoſitiones Præmiſſas,
PROPOSITIO I. II. III. IV. & V.

SI in triangulis A B C, D E F in duobus circulorum ſeg-
44I mentis A T C, D G F deſcriptis, à duobus angulis B,
E, educantur duæ rectæ lineæ B T H, E G I efficientes cum
baſibus A C, D F duos angulos H, I æquales (incidentes

Page concordance

Text layer

Text normalization

Search

Scan	Original
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
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
160	122

Scan	Original
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
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
160	122

Scan	Original
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
151	113
152	114
153	115
154	116
155	117
156	118
157	119
158	120
159	121
160	122