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
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
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82

9456Apollonij Pergæi

Sit ſectio ellipſis
11b A C B tranſuerſa A

70[Figure 70] B, & c. Lego; Sit ſe-
ctio ellipſis A C B, &
axis maior A B, cen-
trum D, & perpendi-
cularis E F ſecans a-
xim in F inter cen-
trũ ellipſis D, & ver-
ticem A.

Et ducamus per
22c punctum E ſectionẽ
hyperbolicam E M
C circa duas eius continentes, & c. Ideſt circa duas asymptotos I L, I H per
E deſcribatur hyperbole E M C, quæ ſecet axim A B æquidiſtantem alteri asym-
3312. & 13.
lib. 2. ptoton in aliquo puncto vt in M; oſtendetur punctum M ſuper ellipſis centrum
D cadere.

Ergo E H prima in proportione in IH ſubſequentem, nempe G F ſub-
44d ſequens ipſam M G quartam, æquale eſt ſubſequenti D G ſecundæ in,
I G nempe F H tertiam. Ergo punctum N, & c. Textus corruptus ſic reſti-
tui poſſe cenſeo; Ergo E H prima proportionalium in H I, nempe G F quartam
æquale eſt D G ſecundæ in I G, nempe F H tertiam, & c. Propterea quod E H ad
F H, atque D G ad G F poſitæ fuerunt, vt latus tranſuerſum ad rectum; ergo re-
ctangulum ſub D G, & H F, ſeu I G, extremis quatuor proportionalium, æqua-
le eſt rectangulo ſub intermedĳs E H, & F G, ſeu H I, eſt que punctum E in,
hyperbola E M C cuius aſymptoti K I, L I; ergo punctum D in eadem hyperbola
exiſtit; ſed erat prius in ellipſis diametro A B, ſcilicet in centro; quare in eorum
communi ſectione exiſtet: erat autem punctum M communis ſectio hyperboles
E C, & axis ellipſis A B; igitur puncta M, & D coincidunt, & hyperbole E D C
tranſit per centrũ ſectionis ellipticæ A C B, & ideo hyperbole E D C, quæ in infinitũ
558. lib. I. extendi, & dilatari poteſt neceſſario ſecabit finitam ellipſim alicubi, vt in C.

Et producamus per E C lineam, & c. Et producamus per E C rectam li-
66e neam, quæ occurrat continentibus in L, K, & ſecet axim ellipſis in P.

Erit G F æqualis O N, quare F O, & c. Quia duæ rectæ lineæ A O, L K
ſecantur à parallelis I L, F E, C N, K O proportionaliter, & ſunt K C, L E
æquales, ergo O N, F G inter ſe æquales erunt, & addita communiter N F erit
778. lib. 2. F O æqualis N G; Et quoniam E H ad H F eſt vt E K ad K P (propter pa-
rallelas K I, O A) nempe vt F O, ſeu ei æqualis G N ad O P (propter paral-
lelas E F, O K) ſed eandem proportionẽ habet D G ad G F, quàm E H ad H F;
ergo G N ad O P eandem proportionem habet quàm D G ad G F, & compa-
rando homologorum differentias D N ad N P erit vt D G ad G F, ſeu vt latus
88Lem. 3.
10. huius. tranſuerſum ad rectum; & ideo C P eſt breuiſsima.

Quia in ſequenti propoſitione 57; & in alĳs adhibetur propoſitio non adhuc
demonſtrata; nimirum poſita C P linea breuiſsima, pariter que I D ſemiſsi axis
recti minoris etiam breuiſsima (ex II. huius) quæ occurrant vltra axim in,
M deducuntur ea omnia, quæ in propoſitionibus 51. & 52. ex hypotheſi

Page concordance

Text layer

Text normalization

Search

Scan	Original
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
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82

Scan	Original
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
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82

Scan	Original
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
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82