Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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ducta fuerìnt, ira ut in unum punctum y coeant, erunt triã
<
lb
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gala u y l, x y p, t y _k_ inter ſe ſimilia: </
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<
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xml:space
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<
s
xml:id
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xml:space
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">ſimilia etiam triangu
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la l y r, p y s, _k_ y q. </
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<
s
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xml:space
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">quare ut in 19 huius, demonſtrabitur
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x p, ad p s: </
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<
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<
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xml:space
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">t k ad _k_ q èandem habere proportionẽ,
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quam u l ad l r. </
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<
s
xml:id
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xml:space
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">Sed ut u l ad l r, ita eſt triangulum a b c ad
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triangulum a c d: </
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<
s
xml:id
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xml:space
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<
s
xml:id
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echoid-s4637
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xml:space
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">ut t k ad K q, ita triangulum e f g ad
<
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triangulum e g h. </
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<
s
xml:id
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echoid-s4638
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xml:space
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">Vt autem triangulum a b c ad triangu-
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lum a c d, ita pyramis a b c y ad pyramidem a c d y. </
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<
s
xml:id
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xml:space
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<
s
xml:id
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xml:space
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">ut
<
lb
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triangulum e f g ad triangulum e g h, ita pyramis e f g y
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ad pyramidem e g h y; </
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<
s
xml:id
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echoid-s4641
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xml:space
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">ergo ut pyramis a b c y ad pyramidẽ
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a c d y, ita pyramis e f g y ad pyramidem e g h y. </
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<
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igitur fruſtũ l f ad reliquum fruſtũ l h eſt ut pyramis a b c y
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ad pyramidem a c d y, hoc eſt ut u l ad l r, & </
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<
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</
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<
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xml:space
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">Quòd cum fruſti l f centrum grauitatis ſit s: </
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<
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xml:id
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xml:space
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<
s
xml:id
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xml:space
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">fruſti l h ſit
<
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centrum x: </
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<
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xml:id
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xml:space
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">conſtat punctum p totius fruſti a g grauitatis
<
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<
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medis.</
note
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eſſe centrum. </
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">Eodem modo fiet demonſtratio etiam in
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aliis pyramidibus.</
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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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">Sit fruſtum a d à cono, uel coni portione abſciſſum, cu-
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lb
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ius maior baſis circulus, uel ellipſis circa diametrum a b;
<
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</
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<
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xml:id
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xml:space
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">minor circa diametrum c d: </
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xml:id
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xml:space
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<
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xml:id
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xml:space
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">axis e f. </
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<
s
xml:id
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xml:space
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">diuidatur autẽ e f
<
lb
/>
in g, ita ut e g ad g f eandem proportionem habeat, quam
<
lb
/>
duplum diametri a b unà cum diametro c d ad duplum c d
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lb
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unà cum a b. </
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<
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xml:id
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">Sitq; </
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<
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">g h quarta pars lineæ g e: </
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xml:space
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<
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xml:space
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">ſit ſ K item
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quarta pars totius f e axis. </
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<
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xml:space
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">Rurfus quam proportionem
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habet fruſtum a d ad conum, uel coni portionem, in eadẽ
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baſi, & </
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<
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">æquali altitudine, habeat linea _k_ h ad h l. </
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ctum l fruſti a d grauitatis centrum eſſe. </
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xml:space
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teſt, ſit m centrum: </
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<
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">l m extra fruſtum in n: </
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& </
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<
s
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xml:space
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">ut n l ad l m, ita fiat circulus, uel ellipſis circa diametrũ
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a b ad aliud ſpacium, in quo ſit o. </
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>
<
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xml:space
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">Itaque in circulo, uel
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lb
/>
ellipſi circa diametrum a b rectilinea figura plane deſcri-
<
lb
/>
batur, ita ut quæ relinquuntur portiones ſint o ſpacio mi-
<
lb
/>
nores: </
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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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">inteiligatur pyramis a p b, baſim habens rectili-
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lb
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neam figuram in circulo, uel ellipſi a b deſcriptam: </
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>
<
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xml:id
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xml:space
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