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

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117117*DE* H*YDROSTATICES ELEMENTIS.*

6 THE OREMA. 7 PROPOSITIO.

In aquis ponderitatis heterogeneæ erit ut ponderitas ma-
teriæ aquæ ponderoſioris ad ponderitatem materiæ aquæ
levioris, ſic pars corporis ſolidi in aquam materiæ levioris
immerſa ad partem ſolidi ejuſdem in aqua graviore de-
merſam.

D*ATVM. * Aqua AB materiæ ſit gravioris quam DC, corpus ſolidum EF
materiâ utrâlibet ipſarum leviore, quod in aquam AB immiſſum parte GF
aquæ inſideat, idemq́ue immiſſum in aquam CD mergatur parte KI.

Q*VAESITVM. * Demonſtrandum materiæ gravitatem aquæ AB, adgra-
vitatem materiæ aquæ CD eſſe, ſicut KI ad GF.

DEMONSTRATIO.

Moles aquæ ex AB æqualis ipſi GF, ponderitate æquabit corpus EF; ſic
item moles aquea ex CD æqualis ipſi KI æquiponderat pci 5 propoſ. corpo-
ri HI ſive EF cum ex hypotheſi ſit unum
idemq́ue corpus; & moles igitur aquæ ex AB

160[Figure 160] ęqualis ipſi GF ponderitate quoque æquat
molem aqueam ex CD ęqualem ipſi KI. Sed
poſitis duabus aquis gravitatis æqualis erit ma-
gnitudinum & materię ponderitatum propor-
tio reciproca, quod neceſſariò deduciturè de-
finitione 5. quare ratio ponderoſitatis materiæ
aquæ AB ad ponderitatem materię aquæ CD eadem erit, quæ magnitudinis
KI ad mag itudinem GF. C*ONCLVSIO. * Itaque in aquis ponderitatis
heterogeneæ ut ponderitas materiæ, & c.

7 THE OREMA. 8 PROPOSITIO.

Corpus ſolidum in aqua levius eſt quàm in aëre, pon-
dere aquæ magnitudine ſibiæqualis.

D*ATVM. * Eſto A corpus ſolidum, aqua BC.

Q*VAESITVM*. Demonſtrato corpus A in aquam immiſſum iſticlevius
eſſe quam in aëre gravitate aqueę molis magnitudine ſibiæqualis.

P*RAEPARATIO. * Sit D vas ſuperficiarium aquæ plenum, ſimile & æqua-
leipſi A.

DEMONSTRATIO.

Vas ſuperficiarium D aqua repletum per 1 propoſ. in ipſa aqua nec gravi-
tatis neque levitatis habet momentum, quare eſſusâ aquâ D vastanto aquę
pondere erit levius, id eſt, perſectè leve; in hocſubſti-
tuito corpus A ipſi congruum, jam vas ſuperficia-

161[Figure 161] rium cum corpore A ſibi inſerto pendet pódus ipſius
A ſimul cum dicta levitate, hoc eſt, pendet pondus
A dempto pondere aquæ prius effuſę, ſed aqua iſta
mole æquat corpus A. Quamobrem A

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