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

196158Apollonij Pergæi

MONITVM.

IN principio huius libri monuimus, definitionem ſimilium conicarum
ſectionum, quæ circunfertur, vitioſam eſſe; quod hic oſtendendum
ſuſcepimus: ſed prius hæc demonſtranda ſunt.

LEMMA II.

IN duabus coniſectionibus A B, E F eiuſdem nominis ſint axium
figuræ G B D, K F I ſimiles inter ſe, ideſt tranſuerſa latera G B,
K F proportionalia ſint lateribus rectis B D, F I : duci debent in ſingu-
lis ſectionibus ſeries applicatarum ad axes, ita vt axium abſciſſæ (quæ
proportionales ſunt inter ſe) ad conterminas potentiales non ſint in ĳſdem
rationibus.

Sumantur duæ abſciſſæ B C, F H, quarum C B ad B D habeat maiorem pro-
portionem, quàm habet H F ad F I, & C B, H F ſecentur proportionaliter in
R, V. , & per ea puncta ducantur ad axes ordinatim applicatæ A C, E H, Q
R, T V. Quoniam quadratum A C ad rectangulum G C B eandem proportio-

214[Figure 214] nem babet, quàm latus rectum D B ad tranſuerſum G B, pariterq; quadratum
1121. lib. 5. E H ad rectangulum K H F eſt vt I F ad F K; atq; D B ad B G ex hypotheſi,
eſt vt I F ad F K; ergo quadratum A C ad rectangulum G C B eandem pro-
portionem habet quàm quadratum E H ad rectangulum K H F : & quia G B
ad B D eſt vt K F ad F I, & D B ad B C minorem proportionẽ habet quàm
I F ad F H, ergo ex æquali G B ad B C, minorem proportionem habet quàm
K F ad F H, & componendo in hyperbola, & diuidendo in ellipſi G C ad C B
ſeu rectangulum G C B ad quadratum B C minorem proportionẽ habebit quàm
K H ad H F, ſeu quàm rectangulum K H F ad quadratum F H : erat autem
quadratum A C ad rectangulum G C B vt quadratum E H ad rectangulum K
H F ; igitur ex æquali, quadratum A C, ad quadratum C B minorem propor-
tionem habet quàm quaàratum E H ad quadratum H F, & ideo A C ad C

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