Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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*DE* H*YDROSTATICES ELEMENTIS.*
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<
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<
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xml:space
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">Tertium quoddam exemplum excogitari potuit, cum ratio ponderitatum
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utriuſque materiæ aqueæ ſcilicet & </
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<
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<
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xml:space
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">ſed eo caſu, normam for-
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mamq́ue antecedentis pragmatiæ ſecutus, deprehendes ſolidum corpus in tali
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aqua nec grave eſſe neque leve. </
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<
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xml:space
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">demonſtratio autem omniũ horum per 8 prop.
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</
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<
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<
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<
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<
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xml:space
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teriæ ponderitatis ad ponderitatem aqueam ratione data; </
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<
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">ejus ſitus gravitatem
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in aqua invenimus. </
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<
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<
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<
s
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xml:space
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">Aquæ fundo horizonti parallelo tantum inſidet pon-
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dus, quantum eſt aqueæ columnæ cujus baſis fundo, alti-
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tudo perpendiculari ab aquæ ſuperſicie ſumma ad imam
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demiſſæ æqualis ſit.</
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<
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">D*ATVM.</
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<
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">* ABCD aquæ figura ſolida rectangula, AB ſuperficies ſumma,
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EF pars fundi horizonti paralleli, GE perpendicularis à ſumma ad imam aquæ
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ſuperficiem, columna GHFE comprehenſa ſub baſi EF & </
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<
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<
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le columnæ aqueæ GHFE.</
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<
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finitima, atque ideò ſi ſieri poſſit eſto ab AGED & </
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<
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<
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fundo DE quoque, propter aquam finitimam GHFE
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(cum utrobiq; </
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<
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">ſit parratio) plus pó deris incumbet quàm
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ſit aquæ AGED, perinde quoque baſi FC plusinſi-
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det ponderis quam aquæ HBCF; </
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DC majus quoddam pondus inſidet quam aquæ totius
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ABCD, quod tamen, cum ABCD corpus rectan-
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gulum ſit, abſurdum ſuerit. </
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<
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xml:space
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">Eadem ratione evinces fun-
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do EF non minus pondus ſuſtentari quam ſit aquæ GHFE; </
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<
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dem duntaxat ponderis neceſſario ipſi incumbet.</
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">Immittito in aquam ABCD hujus propoſitionis corpus ſolidum IKLM,
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materiæ levioris quam aqua, quodque ideo ipſi innatet parte NOLM
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immersâ, reliquâ NOKI ſupereminente, ut in ſubjecta ſigura apparet. </
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ſolidum IKLM per 5 propoſ. </
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<
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tæ aqueæ moli, quanta eſt pars ſui demerſa NOLM;
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</
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<
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">quare ſolidum IKLM cum reliqua ipſum ambiente
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aqua pondere æquat corpus aqueum magnitudinis
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ABCD. </
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<
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xml:space
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">Itaque etiamnum aſſerimus ſecundùm pro-
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poſitionis ſententiam, ſundo EF inniti pondus æquale
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corpori aqueo magnitudinis columnæ, cujus baſis ſit
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EF, altitudo perpendicularis GE à ſumma ſuperficie
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aquæ AB adimum fundum EF demiſſa. </
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<
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aquæ innatante fundum nec magis nec minus affici, quam ab aqua in eadem
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altitudine conſtituta.</
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