Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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humidum ſecundum perpendicularem, quæ per z ad hu-
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midi ſuperficiem ducta fuerit: </
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dum ſecundum eam, quæ per gintra humidum feretur. </
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ergo manebit portio ſic inclinata, ut ponitur: </
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ſtituecur recta: </
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<
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">quoniam perpendicularium per z g ducta
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rum, quæ quidem per z ducitur ad eas partes cadit, in qui
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bus eſt l; </
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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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">quæ per g ad eas, in quibus eſt a. </
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<
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xml:space
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">quare ſequi-
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tur centrum z ſurſum ferri: </
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<
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xml:space
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<
s
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xml:space
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">g deorſum. </
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<
s
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xml:space
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">ergo partes to
<
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tius ſolidi, quæ ſunt ad a deorſum, quæ uero ad l ſurſum
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ferentur. </
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<
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<
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xml:space
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">axis autem
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portionis cum ſuperficie humidi angulum faciat minorẽ
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eo, qui eſt ad b. </
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<
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dratum p i ad quadratum i y, quàm quadratum e ψ ad
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ψ b quadratum: </
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">quare k r ad i y minorem proportionẽ
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habet, quàm dimidium k r ad ψ b: </
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xml:space
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">& </
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<
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xml:space
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">propterea i y maior
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eſt, quam dupla ψ b. </
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<
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xml:space
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<
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ipſa ψ b maior e-
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rit. </
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æqualis ipſi r b:
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</
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xml:space
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<
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xml:space
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">reliqua ω i mi-
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nor quàm ψ r. </
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re & </
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>
<
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xml:space
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">p h minor e-
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rit, quàm f. </
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<
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cum m p ipſi f q
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ſit æqualis, cõſtat
<
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/>
p m maiorẽ eſſe,
<
lb
/>
quàm ſeſquialterã
<
lb
/>
ipſius p h: </
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<
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<
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xml:space
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minorem, quam
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duplam h m. </
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p z ipſius z m du
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pla. </
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<
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">Rurſus to-
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tius quidem ſolidi centrum grauitatis erit pũctum t; </
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uero partis, quæ intra humidum z: </
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<
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xml:space
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