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

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1201204 L*IBER* S*TATICÆ*

2 C*ONSECTARIUM.*

Secundò in aquam ABCD immittitor corpus ſolidum, ſolidavé quot-
cunque materiâ aquæ æquipondiâ, inter quæ, reliqua omnia aqua expulſa,
tantùm comprehendatur IKFELM; quæ cum ita ſint, hæc corpora fundum
EF nec aggravant neque relevant
ab eo pódere quo aqua prius ipſum

166[Figure 166] afficiebat. quare etiamnum ex ſen-
tentia propoſitionis dicimus, fun-
do EF inſidere pondus æquale
aqueo ponderi, magnitudine co-
lumnam æquante, cujus baſis EF,
altitudo perpendicularis GE abaquæ ſummo AB ſeu MI ad imum EF de-
miſſa.

3 C*ONSECTARIUM.*

Sittertiùm ABCD mera aqua, & in ipſa EF fundum horizonti parallelum.
Quibus poſitis, aqua ſub fundo EF tam potenter ipſum ſurſum premit, quam
aqua ſupra inſidens deorſum; ſecus enim per 1 propoſ. infirmius validiori con-
cederet, quod hîc non fit quia utrumque loco ſuo permanet. lam corpus ſoli-
dum iſti aquæ pondere homogeneum ita collocator ut

167[Figure 167] aqua IKEFLM ab inferiori parte preſſet fundum EF,
ut hîc. Quibus poſitis, aqua ſubter EF nunc tam validè
premit fundum EF, ſive ipſum ſolidum, quàm prius
ipſam aquam oppoſitam: ſed impreſſio tanta tunc erat
quanta ſuperioris aquæ ad EF depreſſio, ut ſupra pa-
tuit, ſuperioris autem aquæ depreſſio æqualis erat ponderi columnæ aqueæ
cujus baſis EF, altitudo perpendicularis GE, à ſuperficie AB ſeu MI ad
fundum EF demiſſa. Itaque aquæ ſubter EF conſtitutæ impreſſio erit quoque
tanta.

4 C*ONSECTARIUM.*

Corpora ſolida ſecundi tertiiq́ue conſectatii iſtic ita firmentur, effuſaq́ue
aqua ſpatium IKFELM vacuum nullo amplius pondere afficiet fundũ EF;
unde apparetaqua in vacuum locum rurſum infusâ fundũ EF tam validè pre-
mi, ac ſi integrũ vas ABCD, ſublato iſto corpore ſolido, aquâ repletum foret.

5 C*ONSECTARIUM.*

Atverò quia immiſſa ſolida 2 & 3 conſectarii ſunt ſuo loco defixa, ipſorum
materia extrema nec gravitate nec levitate ulla afficiet fundum EF, quam-
obrem ſublata omni aquam ambiente materia, relinquentur internæ iſtæ aqueæ
figuræ MIKFEL, quales hic vides.

168[Figure 168]

Atque hic etiam ex ſententia propoſitionis dicimus baſe EF ſubnixum

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