Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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pla. </
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<
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">ex quo fit ut pr, rh, fg inter ſe ſint æquales; </
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<
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">itémq; </
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<
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">æquales
<
lb
/>
rg, pf. </
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<
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xml:id
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xml:space
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">eſt enim pg utrique r p, gf communis. </
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<
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xml:space
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">Quoniam igitur
<
lb
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hb ad bg est, ut
<
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gb ad bf; </
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<
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">per c
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<
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uerſionem ratio-
<
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mis erit b h ad
<
lb
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h g, ut b g ad gf.
<
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/>
</
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<
s
xml:id
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echoid-s1158
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xml:space
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">eſt autem q h ad
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h b, ut h o ad gb. </
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<
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nam ex 35 primi
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libri conicorum,
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cum linea qm có
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tingat ſectionem
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in punctom; </
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<
s
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h b, bq æquales; </
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& </
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dupla. </
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<
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">ergo ex æ-
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quali q h ad hg,
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ut ho ad g f; </
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eſt ad hr: </
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mutando q h ad
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h o, ut g h ad h r. </
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>
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<
lb
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rurſus per conuerſionem rationis h q ad qo, ut h g ad g r; </
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>
<
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xml:id
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xml:space
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">hoc eſt
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p f: </
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">& </
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<
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">propterea ad ipſam cn, quod demonstrandum fuerat.</
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<
s
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">His igitur explicatis, iam adid, quod propoſitum fue
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rat, accedamus. </
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">Itaque dico primum nc ad c k eandem
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proportionem babere, quam h g ad g b.</
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<
s
xml:id
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xml:space
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">Quoniam enim h q ad qo eſt, ut h g ad c n, hoc eſt ad a o ipſi
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lb
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cn æqualem; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">erit reliqua gq ad reliquam q a, ut h q ad q o: </
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>
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="
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">& </
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<
lb
/>
ob eam cauſſam lineæ a c g l productæ ex ijs, quæ ſupra demonſtra
<
lb
/>
uimus in linea q m conueniunt. </
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>
<
s
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xml:space
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