Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

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76ARCHIMEDIS

Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
ipſis ſectionibus in eandem proportionem ſecari. eſt enim
diuidendo, conuertendoque cm ad mb, & cf ad fb, ut
ce ad ea.

LEMMA III.

Sed & illud constare potest; lineas, quæ in portioni-
bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
les angulos contineant, ab ipſis ſimiles quoque portiones
abſcindere: hoc eſt, ut in propoſita figura, portiones h b c,
m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
ſimiles eſſe.

D_ividantvr_ enim ch, cm bifariam in punctis p q: & per
ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes. erit portio-
nis b s c diameter p s, & portionis m u c diameter q u. Itaque fiat
ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
quæ ſit s x: & ut quadratum c t ad quadratum c q, ita fiat f o ad
u y. iam exĳs

47[Figure 47] quæ demóſtra
uimus in com-
mentarĳs in
quartam pro-
poſitioné. Ar-
chrmedis de co
noidibus, &
ſphæroidibus,
patet quadra-
tum c p æqua-
le eſſe rectan-
gulo p s x:

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65	27
66
67	22
68
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75	32
76
77	25
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Scan	Original
61	25
62
63	26
64
65	27
66
67	22
68
69	29
70
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

Scan	Original
61	25
62
63	26
64
65	27
66
67	22
68
69	29
70
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