Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0053
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53
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DE IIS QVAE VEH. IN AQVA.
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<
s
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xml:space
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">Producatur enim u s ad lineam qm in x: </
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<
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xml:space
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">& </
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<
s
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xml:space
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">à puncto x duca
<
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tur ad diametrum x y ipſi bd æquidistans. </
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<
s
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">erit gt minor quàm
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gy, quoniam u s minor eſt quàm ux: </
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<
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xml:space
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">& </
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<
s
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xml:space
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">ex primo lemmate yg
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ad uc erit, ut h g ad n c; </
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<
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">uidelicet ut g b ad c k, quod proxime de
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monstrauimus: </
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<
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<
s
xml:id
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xml:space
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">permutando yg ad gb, ut uc ad c k. </
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<
s
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xml:space
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">Sed t g
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cum ſit ipſa y g minor, habet ad g b proportionem minorem, quàm
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y g ad eandem. </
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<
s
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xml:space
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">ergo u c ad c K maiorem proportioné habet, quàm
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t g ad g b. </
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<
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">quod demonstraſſe oportuit. </
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<
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">Itaque poſitione data g K
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unum duntaxat erit in ſectione punctum, uidelicet m, à quo ductis
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duabus lineis m e h, mno, habeat n c ad c K proportionem ean-
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dem, quam h g ad g b. </
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<
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xml:space
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">nam ſi ab alijs omnibus ducantur, ſemper
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ea, quæ inter a c, & </
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<
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xml:space
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">lineam ipſi æquidistantem interijcitur, ad c K
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proportionem maiorem habebit, quàm quæ inter g K atque ei æqui
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diſtantem, ad ipſam g b. </
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<
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">Conſtat igitur id, quod ab Archimede di-
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ctum est; </
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">nempe lineam pi ad p h uel eandem, quam n ω ad ω o,
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uel maiorem habere proportionem.</
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</
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<
s
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">Quare p h ipſius h i aut dupla eſt, aut minor quàm du
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pla.</
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0053-01
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_minor, quàm du-_
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_pla, ſit pt dupl. </
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_ti. </
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">erit centrum_
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_grauitatis eius,_
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_quod in humido_
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_est, punctumt. </
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<
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_uero p h ſit ip-_
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_ſius h i dupla,_
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_erit h grauitatis_
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_centrum: </
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<
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</
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<
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_ad centrum eius,_
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_quod est extra humidum, uidelicct ad g, alia ſimiliter demonstra-_
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_buntur. </
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<
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">atque idem intelligendum est in propoſitione, quæ ſe_-
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_quitur._</
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<
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">Reuoluetur ergo ſolidum a p o l, & </
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