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
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

195157Conicor. Lib. VI. lis alicui earum (ſi poſ-
11b ſibile eſt) ergo poſſu-

212[Figure 212] mus educere in ſingulis
ſectionibus potentes,
quæ habeant ad ſua ab-
ſciſſa axium eaſdẽ pro-
portiones, & abſciſſæ in
ter ſe ſint proportiona-
les; ſintque illæ V M,
Y N, P K, R L. Quia
Y N ad N F poſita fuit,
vt R L ad L B, & N F
ad F M, vt L B ad BK,
& F M ad M V, vt B
K ad K P; ergo Y N ad
M V in potentia, nem-
pe N F ad M F (cum
ſectio ſit parabola 19.
ex 1.) nempe L B ad B K ex contructione erit, vt R L ad K P potentia,
2220. lib. 1. quæ eandem proportionem habent, quàm a L in L B ad a K in K B;
3321. lib. 1. quia ſectio eſt hyperbolæ, aut ellipſis (20. ex 1.) quare a L in L B ad a
K in K B eſt, vt L B ad B K; quare a L eſt æqualis a K: quod eſt abſur-
dum. Igitur parabole non eſt ſimilis vlli reliquarum ſectionum. Et hoc
erat probandum.

PROPOSITIO XIV.

ET ſic oſtendetur, quod hyperbolæ non eſt ſimilis ellipſi.

Alioquin ſequitur, quod quadratum

213[Figure 213]44a R L ad quadratum K P, nempe a L in
L B ad a K in K B in hyperbola eſt, vt
quadratum Y N ad quadratum M V,
ſeu vt b N in N F ad b M in M F in el-
lipſi. His poſitis: quia L B ad B K po-
5521. lib. 1. ſita fuit, vt N F ad M F; ergo a L ad
a K eandem proportionem habet, quàm
b N ad b M: & hoc eſt abſurdum. Qua-
re ſectio A B non eſt ſimilis E F; vt fue-
rat propoſitum.

Page concordance

Text layer

Text normalization

Search

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72