Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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eam proportionem babebit, quam a f ad a e. </
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<
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<
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">eandem habet
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a s ad a r. </
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<
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xml:space
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">quare a s ipſi a x eſt æqualis, pars toti, quod fieri non
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poteſt. </
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<
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xml:space
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tra lineam a c. </
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<
s
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xml:space
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">neceſſarium igitur est, ut in ipſam a c cadat. </
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<
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demonſtrandum propoſuimus.</
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<
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head
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<
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<
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">atque eam cŏtingen
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tes rectæ lineæ a c, b d; </
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<
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xml:space
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">a c quidem in puncto c, b d ue
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ro in b: </
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<
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xml:space
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">& </
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<
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">per c ductis duabus lineis; </
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<
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">quarum alter a c e
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diametro æquidiſtet, alter a c f æquidiſtet ipſi b d: </
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<
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tur quod uis punctum g in diametro: </
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<
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">fiatque ut f b, ad
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b g, ita b g ad b h: </
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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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">per g h ducantur g k l, h e m,
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æquidiſtantes b d: </
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<
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æquidistans, quæ diametrum ſecet in o: </
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<
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">per n ducta
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n p uſque ad diametrum, ipſi b d æquidistet. </
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<
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ipſius g b duplam eſſe.</
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<
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">V_EL_ igitur linea m n o ſccat diametrum in g, uel in alijs pun-
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ctis: </
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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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">ſi quidem ſecat in g, unum at que idem punctum duabus li-
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teris go notabitur. </
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<
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">Itaque quoniam f c, p n, h e m ſibiipſis æqui
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distant: </
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<
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xml:space
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<
s
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">ipſi a c æquidiſtat m n o: </
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<
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">fient triangula a f c, o p n,
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o h m inter ſe ſimilia. </
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<
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">quare erit o h ad h m, ut a f ad fc: </
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xml:space
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<
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<
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note
>
mut ando o h ad a f, ut h m ad fc. </
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<
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xml:space
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">est autem quadratum h m ad
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quadratum g l, ut linea h b ad lineam b g, ex uigeſima primi libri
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conicorum: </
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<
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<
s
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xml:space
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">quadratum g l ad quadratum fc, ut linea g b ad
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ipſam b f: </
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<
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<
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">22. ſexti.
<
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cor. 20. ſe
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xti.</
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go & </
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<
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">quadrata h m, g l, f c, & </
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<
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">ipſorum latera proportionalia
<
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erunt. </
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<
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xml:space
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">atque idcirco ut quadratum h m ad quadratum g l, ita </
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