Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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dum eam, quæ per g ſurſum eleuabitur. </
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<
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">non igitur manebit
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portio ſic inclinata, nec conuertetur ita, ut axis ad ſuperfi-
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ciem humidi ſit perpendicularis: </
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<
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deorſum; </
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<
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">quæ uero ex parte a ſurſum ferentur, ut ex iam de
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monſtratis apparere poteſt. </
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<
s
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">Quòd ſi axis cum ſuperficie
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humidi fecerit angulum minorem angulo b, ſimiliter de-
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monſtrabitur, nõ manere portionem, ſed inclinari, donec
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utique axis cum ſuperficie humidi faciat angulum angulo
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b æqualem.</
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<
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">COMMENTARIVS.</
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f q, quàm b c quadratum: </
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<
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<
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">idcirco linea f q minor eſt,
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quàm b c: </
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<
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">f minor quam b r.</
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<
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">] _Quoniani exceſſus, quo_
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_quadratum b d excedit quadratum b c ad quadratum b d minorem_
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_proportionem habet, quàm exceſſus, quo quadratum b d excedit qua_
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_dratum f q, ad idem quadratum: </
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<
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">erit ex octaua quinti exceſſus, quo_
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_quadratum b d excedit quadratum b c, minor quàm exceſſus, quo ex_
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_cedit quadratum f q. </
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<
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_propterea linea f q minor linea b c. </
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">Sed f q ad f eandem proportionẽ_
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_habet, quam b c ad b r; </
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<
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">utraque enim utriuſque ſeſquialtera est. </
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_igitur f q ſit minor b c, & </
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<
s
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">Et propterea k r ad ſ y maiorem habet, quàm dimidium
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ipſius k r ad ψ b.</
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<
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_dratum ſ y
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: </
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<
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">dimidium lineæ K r ad lineam ψ b, ut quadratum e ψ_
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_ad quadratum ψ b_.</
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<
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">Et s o minor quàm ψ b] _Est enim ſ y dupla ipſius ſ o._</
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<
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_ipſi f_.</
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<
s
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">Habebit ergo tota portio ad eam, quæ eſt extra humi-
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dum proportionem eandem, quam quadratum b d ad qua
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dratum f q.</
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<
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xml:id
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_exceſſus, quo quadratum b d excedit quadratum f q ad b d quadratu
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:_</
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