Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

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50ARCHIMEDIS nea h m ad li-

30[Figure 30] neam fc. at uero
ut h m ad f c, ita
o h ad a f: & ut
quadratum h m
ad quadratú g l,
ita linea h b ad
b g; hoc est b g
ad b f. ex quibus
ſequitur o h ad
a f ita eſſe, ut b g
ad b f: & permu
tando oh ad b g,
ut a f ad f b. ſed
eſt a f dupla ip-
ſius fb: ſunt eni
a b, b f æquales
ex 35 primi libri
conicorum. ergo
& h o ipſius g b
eſt dupla. quod demonſtrare oportebat.

LEMMA IIII.

Iiſdem manentibus, & à puncto m ducta m q uſque
ad diametrum, quæ ſectionem in puncto m conting at;
Dico h q ad q o eandem proportionem habere, quam
habet g h ad c n.

F_IAT_ enim h r æqualis g f. & cumtriangula a f c, o p n ſimi
lia ſint, & p n ſit æqualis f c; eodem modo demonſtrabimus p o, f a
inter ſe æquales eſſe. quare p o ipſius f b dupla erit. Sed eſt h o du
pla g b. ergo & reliqua p h reliquæ f g; uidelicet ipſius r h eſt

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91	40
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94
95	42
96
97	43
98
99	44
100
101	43
102
103
104
105
106
107
108
109
110
111
112
113	1
114
115	2
116
117	3
118
119	4
120

Scan	Original
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100
101	43
102
103
104
105
106
107
108
109
110
111
112
113	1
114
115	2
116
117	3
118
119	4
120

Scan	Original
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100
101	43
102
103
104
105
106
107
108
109
110
111
112
113	1
114
115	2
116
117	3
118
119	4
120