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
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82
121	83
122	84
123	85
124	86
125	87
126	88
127	89
128	90
129	91
130	92

226188Apollonij Pergæi ad A E, vt O C ad C F, ſuntque anguli E, & F æquales, vt dictum eſt. Et
hoc erat propoſitum.

Notæ in Propoſit. XVII.

DEinde ſint ſectiones hyperbolicæ, aut ellipticæ, & reliqua in ſuo
11a ſtatu, & c. Ideſt. Supponantur ſectiones hyperbolicæ, vel ellipticæ A B,
& C D ſimiles inter ſe, ſcilicet figuræ axium V B, & γ D ſint ſimiles inter ſe,
atque à verticibus A, & C duarum diametrorum A M, & C O ductæ ſint re-

254[Figure 254] ctæ lineæ contingentes A E, & C F, efficientes cum axibus angulos A E B, &
C F D æquales, ſintque H G, & K I ordinatim ad diametros applicatæ, ſcili-
cet æquidiſtantes contingentibus verticalibus; & habeat abſciſſa M A ad portio-
nem contingentis A E eandem proportionem, quàm abſcißa O C habet ad por-
tionem contingentis C F; Dico ſegmenta H A G, & K C I ſimlia eſſe inter ſe.

Ergo Y c C ſimile eſt V a A, & c. Quoniam duæ ordinatim ad axes ap-
22b plicatæ A a, & C c perpendiculares ſunt ad axes, erunt in triangulis A a E,
& C c F duo anguli a, & c recti: atque ex hypotheſi duo reliqui anguli E, &
F æquales quoque ſunt; igitur tertius angulus a A E æqualis eſt tertio angulo c
C F, cumque in duobus triangulis V A E, atque γ C F ab eorum verticibus A,
& C ducuntur ad baſes V E, & γ F duæ rectæ lineæ A a, & C c continentes
cum baſibus angulos æquales, nempe rectos, & rectangulum V a E ad quadra-
tum a A eandem proportionem habet, quàm rectangulum γ c F ad quadratum
c C, vt in textu oſtenſum eſt: atq; duo anguli a A E, & c C F æquales oſten-
33ex 37.
lib. 1. ſi ſunt inter ſe; igitur erunt triangula V A E, & γ C F ſimilia inter ſe; ergo
44Propoſ. 6
præmiſſ. angulus V æqualis eſt angulo γ, atque angulus E A V æqualis erit angulo F

Page concordance

Text layer

Text normalization

Search

Scan	Original
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82
121	83
122	84
123	85
124	86
125	87
126	88
127	89
128	90
129	91
130	92

Scan	Original
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82
121	83
122	84
123	85
124	86
125	87
126	88
127	89
128	90
129	91
130	92

Scan	Original
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82
121	83
122	84
123	85
124	86
125	87
126	88
127	89
128	90
129	91
130	92