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
61	23
62	24
63	25
64	26
65	27
66	28
67	29
68	30
69	31
70	32
71	33
72	34
73	35
74	36
75	37
76	38
77	39
78	40
79	41
80	42
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52

12082Apollonij Pergæi

Notæ in Propoſ. LXVI.

QVia ſi caderet inter C, D ducipoſ-

100[Figure 100]11a ſet, & c. Quotieſcumq; enim perpen-
dicularis E F cadit ſuper centrũ
D, vel ſecat ſemiaxim D C inter D, & C, tũc
ex concurſu E vnicus ramus breuiſecans du-
ci poteſt ad ſectionem B A, qui nimirum ca-
2245. 56.
huius. dit inter verticem remotiorem A, & axim
minorem D B: ſed ex hypotheſi nullus ra-
mus ex concurſu E ad quadrantem ellipſis A
B duci poteſt, qui ſit breuiſecans; igitur per-
pendicularis E F ſecat ſemiaxim A D in
puncto F poſito inter A, & D.

Deinde patet, quemadmodum demon-
ſtrauimus in vtraque hyperbola, & c. Permuto particulam [vtraque] vt
manifeſtè erroneam, legi enim debet in parabola, & hyperbola. Quod vero ra-
mus terminatus E A minimus ſit omnium ramorum ſecantium manifeſtum eſt
ex demonſtratione propoſitionis 64. 65. , quæ compræhendit etiam ellipſim,
quando menſura F A minor eſt ſemiaxi A D, vt ex propoſitione 52. patet. Et ſi-
militer ramorũ ſecantium ex concurſu E ad ſectionem A B ductorum propinquio-
res vertici A minores ſunt remotioribus ex eadem demonſtratione 64. 65. huius.

Ex demonſtratione præmiſſa propoſitionum 64. & 65.
deduci poteſt conſectarium, à quo notæ ſubſe-
quentes breuiores reddantur.

COROLLARIVM PROPOSIT.
LXIV. & LXV.

SI in aliqua peripheria cuiuslibet coniſectio-

101[Figure 101] nis omnes rami ſecantes, qui à concurſu
duci poſſunt, cum tangentibus ab eorum ter-
minis ductis conſtituunt angulos, qui verti-
cem reſpiciunt, acutos; rami proximiores ver-
tici ſectionis minores erunt remotioribus.

Ex eo enim, quod ïn propoſitionibus 64. &
65. , omnes rami D A, D L, D B, D Q, D
C, & reliqui omnes, qui duci poſſunt ex con-
curſu D ad ſectionem A B C efficiunt cum
tangentibus ſectionẽ à terminis A, L, B, Q, C
angulos, verticem A reſpicientes, acutos,

Page concordance

Text layer

Text normalization

Search

Scan	Original
61	23
62	24
63	25
64	26
65	27
66	28
67	29
68	30
69	31
70	32
71	33
72	34
73	35
74	36
75	37
76	38
77	39
78	40
79	41
80	42
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52

Scan	Original
61	23
62	24
63	25
64	26
65	27
66	28
67	29
68	30
69	31
70	32
71	33
72	34
73	35
74	36
75	37
76	38
77	39
78	40
79	41
80	42
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52

Scan	Original
61	23
62	24
63	25
64	26
65	27
66	28
67	29
68	30
69	31
70	32
71	33
72	34
73	35
74	36
75	37
76	38
77	39
78	40
79	41
80	42
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52