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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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