Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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1161164 L*IBER* S*TATICÆ*
5 THE OREMA. 5 PROPOSITIO.
Corpus ſolidum materiæ levioris quamaqua cuiinnatat,
ponderitate æquale eſt tantæ aqueæ moli, quantâ ſui
parte demergitur.
D*ATVM. * AB corpus ſolidum materiam habeat leviorem aqua BC in
quam immittiur, ſolidi autem ſuperficies AB, pars in aquam immerſa EB.
Q*VAESITVM*. Demonſtrato ſolidum AB pondere æquari aquæ EB
quæ æqualis eſt parti in aquam CD immerſæ.
DEMONSTRATIO.
In vaſe ſuperficiario AB loco ſolidi corporis AB ſubſtituitor aquæ copia
tanta, quę ipſum eadem altitudine qua priùs in aquam immer-
gat. quibus poſitis, aqua EB (cujus ſuperſicies eſt in ſuperfi-
158[Figure 158] cie reliquæ aquæ cum vas ſuperficiarium nullius ſit ponderita-
tis) contenta vaſe ſuperficiario EB per 3 poſtul. æquiponde-
rabit ſolido corpori AB quia vas idem eadem altitudine im-
mergunt. C*ONCLVSIO. * Itaque ſolidum corpus materia
leviore quam aqua in quam immittitur æquiponderat tantæ
aqueæ moli, quantâ ſui parteaquæ immergitur.
1 PROBLEMA. 6 PROPOSITIO.
*Corpore ſolido ſui partenotæ magnitudinis in aquam*
*cognitæ ponderitatis immerſo, totius ſolidi pondus in-*
*venire. *
D*ATVM. * ABCD ſolidum corpus formæ contingentis, EF aqua cujus
pes cubicus ponderet 65 ℔, nam experientia edoctus Delfenſem pedem Del-
fenſis aquæ tanti ponderis eſſe cognovi, ſicq́ue deinceps in ſequentibus exem-
plis uſurpabimus; ſolidi corporis pars aquæ immerſa ACD, cujus magni-
tudo ſit 10000 pedum cubicorum. Q*VAESITVM*. Quantum pondus ſit
univerſi corporis ABCD quæq́; illo vel continentur velinnituntur invenien-
dum eſto.
CONSTRVCTIO.
Multiplicatis 10000 cum 65 ℔ efficiuntur pro quęſito 650000 ℔.
DEMONSTRATIO.
159[Figure 159]
Vniverſum ſolidum ABCD æquiponderat per
5 propoſ. aquæ æquali corpori ACD, ſed tanta
aquæ moles pendet 650000 ℔, itaque etiam corpus
ABCD erit librarum totidem.
C*ONCLVSIO. * Quamobrem corpore ſolido
ſui parte notæ magnitudinis in aquam cognitæ pon-
deritatis immerſo, etiam totius ponderitatem inveni-
mus. Quod oportuit.

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