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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Scan	Original
71	30
72
73	37
74
75	32
76
77	25
78
79	34
80
81	35
82
83	36
84
85	37
86
87	38
88
89	39
90
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100

Scan	Original
71	30
72
73	37
74
75	32
76
77	25
78
79	34
80
81	35
82
83	36
84
85	37
86
87	38
88
89	39
90
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100

Scan	Original
71	30
72
73	37
74
75	32
76
77	25
78
79	34
80
81	35
82
83	36
84
85	37
86
87	38
88
89	39
90
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100