Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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<
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xml:space
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<
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enim b K duplam eſſe ipſius K d. </
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<
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ut tria ad unum; </
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<
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<
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erat ut quídecim
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ad quatuor. </
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<
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b d ad d c, ut quin
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decim ad nouem:
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</
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">& </
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<
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">per conuerſio
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nem rationis, con
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uertendôq; </
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<
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b d, ut ſex ad quí
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decim.</
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<
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b d, ita e b ad
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b a, & </
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d a.</
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">] _Nam cum_
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_triangula c b e,_
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_d b a ſint ſimilia,_
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_erit ut c b ad b e,_
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_ita d b, ad b a & </
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_ut b c ad c e, ita b d ad d a: </
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_eſt d z ei æqualis ad d a._</
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_quidem l a duplam eſſe ipſius d a, cum b d ſit portionis diameter,_
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_manifeſte conſtat. </
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">At uero l i ipſius d z dupla hoc pacto demon-_
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_ſtrabitur. </
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_uertendo, diuidendôq; </
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<
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_rurſus diuidendo i d ad d z, ut
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m ad duo. </
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">erat autem z d ad_
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_d a, hoc eſt ad d l, ut duo ad quinque. </
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">ergo ex æquali, conuertendóq;_
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</
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<
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<
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">per conuerſionem rationis d l ad_
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_li, ut quinque ad quatuor. </
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_ergo rurſus ex æquali d z ad l i, ut duo ad quatuor. </
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">dupla eſt igitur_
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_l i ipſius d z. </
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</
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<
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">Et a d ad d i eam proportionem habet, quã quinque
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