Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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l h eandem habet proportionem, quam e m ad m k, uideli-
<
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cet triplam. </
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<
s
xml:id
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xml:space
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">quare linea l m ipſam e f ſecabit in puncto g:
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</
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<
s
xml:id
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xml:space
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">etenim e g ad g f eſt, ut el ad l h. </
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<
s
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xml:space
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">præterea quoniam h k, l m
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æquidiſtant, erunt triangula h e f, l e g ſimilia: </
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<
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xml:id
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<
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xml:space
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<
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ſe ſimilia f e k, g e m: </
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">ut e fad e g, ita h fad l g: </
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<
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xml:id
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xml:space
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">& </
s
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<
s
xml:id
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xml:space
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">ita f _K_ ad
<
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g m. </
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>
<
s
xml:id
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xml:space
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">ergo uth fadlg, ita f k ad g m: </
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<
s
xml:id
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">permutando uth f
<
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ad f _K_, ita l g ad g m. </
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<
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xml:id
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xml:space
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">ſed cum h ſit centrum trianguli a b d; </
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<
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& </
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<
s
xml:id
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xml:space
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">K triãguli b c d: </
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<
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xml:id
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xml:space
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">punctũ uero f totius quadrilateri a b c d
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centrum: </
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<
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">erit ex 8. </
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<
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xml:space
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">Archimedis de centro grauitatis plano
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rum h fad f
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style
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, ut triangulum b c d ad triangulum a b d: </
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<
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xml:space
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<
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autem b c d triangulum ad triangulum a b d, ita pyramis
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b c d e ad pyramidem a b d e. </
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<
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linea lg ad g m erit, ut pyramis
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b c d e ad pyramidé a b d e. </
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<
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xml:space
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ſequitur, ut totius pyramidis
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a b c d e punctum g ſit grauitatis
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centrum. </
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<
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xml:space
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ſim habens pentagonum a b c d e:
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</
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<
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xml:space
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<
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xml:space
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">axem f g: </
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>
<
s
xml:id
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xml:space
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">axis in pũ
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/>
cto h, ita ut fh ad h g triplam habe
<
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/>
at proportionem. </
s
>
<
s
xml:id
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xml:space
="
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">Dico h grauita-
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tis centrũ eſſe pyramidis a b c d e f. </
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>
<
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xml:space
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<
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/>
iungatur enim e b: </
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<
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xml:space
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">intelligaturq; </
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<
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pyramis, cuius uertex f, & </
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<
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xml:space
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triangulum a b e: </
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<
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xml:space
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<
s
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xml:space
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">alia pyramis
<
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intelligatur eundem uerticem ha-
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bens, & </
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>
<
s
xml:id
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xml:space
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">baſim b c d e quadrilaterũ: </
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<
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<
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ſit autem pyramidis a b e faxis f
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,
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& </
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<
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<
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dis b c d e faxis f m, & </
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<
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<
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uitatis n: </
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<
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<
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m, l n; </
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<
s
xml:id
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xml:space
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<
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/>
quæ per puncta g h tranſibunt. </
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>
<
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xml:id
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<
lb
/>
Rurſus eodem modo, quo ſup ra,
<
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/>
demonſtrabimus lineas K g m, l h n ſibiipſis æ </
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>
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