Stevin, Simon - Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis

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119119*DE* H*YDROSTATICES ELEMENTIS.*

Tertium quoddam exemplum excogitari potuit, cum ratio ponderitatum
utriuſque materiæ aqueæ ſcilicet & ſolidę ęqualis erit: ſed eo caſu, normam for-
mamq́ue antecedentis pragmatiæ ſecutus, deprehendes ſolidum corpus in tali
aqua nec grave eſſe neque leve. demonſtratio autem omniũ horum per 8 prop.
manifeſta eſt. C*ONCLVSIO. * Itaq; corporis ſolidi gravitate, ejuſdemq́; ma-
teriæ ponderitatis ad ponderitatem aqueam ratione data; ejus ſitus gravitatem
in aqua invenimus. Quod faciendum erat.

8 THE OREMA. 10 PROPOSITIO.

Aquæ fundo horizonti parallelo tantum inſidet pon-
dus, quantum eſt aqueæ columnæ cujus baſis fundo, alti-
tudo perpendiculari ab aquæ ſuperſicie ſumma ad imam
demiſſæ æqualis ſit.

D*ATVM. * ABCD aquæ figura ſolida rectangula, AB ſuperficies ſumma,
EF pars fundi horizonti paralleli, GE perpendicularis à ſumma ad imam aquæ
ſuperficiem, columna GHFE comprehenſa ſub baſi EF & altitudine EG.

Q*VAESITVM. * Demonſtrato baſe ſeu fundo EF ſuſtineri pondus æqua-
le columnæ aqueæ GHFE.

DEMONSTRATIO.

Sifundo EF plus ponderis inſideat quàm aquæ GHFE, id erit ab aqua
finitima, atque ideò ſi ſieri poſſit eſto ab AGED & HBCF; quibus poſitis
fundo DE quoque, propter aquam finitimam GHFE
(cum utrobiq; ſit parratio) plus pó deris incumbet quàm

164[Figure 164] ſit aquæ AGED, perinde quoque baſi FC plusinſi-
det ponderis quam aquæ HBCF; quare toti fundo
DC majus quoddam pondus inſidet quam aquæ totius
ABCD, quod tamen, cum ABCD corpus rectan-
gulum ſit, abſurdum ſuerit. Eadem ratione evinces fun-
do EF non minus pondus ſuſtentari quam ſit aquæ GHFE; quare tantun-
dem duntaxat ponderis neceſſario ipſi incumbet.

1 C*ONSECTARIVM.*

Immittito in aquam ABCD hujus propoſitionis corpus ſolidum IKLM,
materiæ levioris quam aqua, quodque ideo ipſi innatet parte NOLM
immersâ, reliquâ NOKI ſupereminente, ut in ſubjecta ſigura apparet. Iam
ſolidum IKLM per 5 propoſ. gravitate æquale eſt tan-

165[Figure 165] tæ aqueæ moli, quanta eſt pars ſui demerſa NOLM;
quare ſolidum IKLM cum reliqua ipſum ambiente
aqua pondere æquat corpus aqueum magnitudinis
ABCD. Itaque etiamnum aſſerimus ſecundùm pro-
poſitionis ſententiam, ſundo EF inniti pondus æquale
corpori aqueo magnitudinis columnæ, cujus baſis ſit
EF, altitudo perpendicularis GE à ſumma ſuperficie
aquæ AB adimum fundum EF demiſſa. Vnde efficitur à materia qualibct
aquæ innatante fundum nec magis nec minus affici, quam ab aqua in eadem
altitudine conſtituta.

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