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

9860Apollonij Pergæi

SECTIO NONA
Continens Propoſ. LVIII. LIX. LX. LXI.
LXII. & LXIII.

I Am ex puncto dato C extra, vel intra ſectionem A B (quod
11a in axi I A non ſit) poſſumus rectam lineam ducere, cuius
portio intercepta inter ſectionem, & axim ſit linea breuiſſima.

PROPOSITIO LVIII.

Sit ſectio parabole, & producamus perpendicularem C E ſu-
per I E A, & ponamus E F æqualem dimidio erecti, & du-
camus G F parallelam ipſi C E, & per C ducamus hyperbolen
224. lib. 2.33b H C B circa duas continentes illam G F, I F, quæ occurat ſe-
ctioni A B in B, & per B, C producatur linea occurrens con-
tinenti I A in I, & continenti G F in G: Dico, quod B I eſt
linea breuiſsima.

75[Figure 75]

Producatur perpendicularis B K. Quoniam C I æqualis eſt B G (sexta
44C ex ſecundo) erit E I æqualis K F, & E F, K I erunt æquales, atque ſup-
558. lib. 2. poſita, eſt E F æqualis dimidio erecti; ergo K I ita eſt pariter; Quare
B I eſt breuiſsima, (octaua ex quinto) & hoc erat probandum.

PROPOSITIO LIX. LXII. & LXIII.

D Einde fit ſectio hyperbole, aut ellipſis, cuius centrum D, & lineis,
66a atque ſignis in eodem ſtatu manentibus, ponamus D F ad F E, &

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