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

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1281284 L*IBER* S*TATICÆ* æquari columnæbaſis A B C D, altitudinis GE,
177[Figure 177] patebit demiſſa O Q perpendiculari in planum
A B C D:
nam priſma A B C D P O M N æqua-
le eſt ſolido cujus baſis A B C D altitudo O Q:
ſed quia rectæ A H, O C, itemq́ue anguli HAE,
C O Q ſunt æquales, &
AE plano per H, E, pun-
cta trajecto perpendicularis, item O Q ei quod
per C, Q, propterea A E &
æquatur ipſi O Q:
ideoq́ue parallelepipedum A B C D P O M N,
parallelepipedo in baſin A B C D altitudine
A E inſiſtente erit æquale.
At (quemadmodum
jam 11 propoſ.
demonſtratum fuit) priſma
M N P O K L æquatur parallelepipedo baſis
A B C D altitudinis A G.
quare duo iſta ſolida
addita conſtituunt priſma A B C D L K N M æquale parallelepipedo dictæ
baſis A B C D, altitudinis autem G E.
ALTERA DEMONSTRATIO.
Si per A B agas planum horizonti parallelum ipſi A B C D ſimile & æquale;
huic incumbet per 10 prop. põdus aquæ æquale columnæ baſis A B C D, altitu-
dinis AE:
atqui minimùm tantũ põderis inſidet cuilibet fundo humiliori ipſiq́;
æquali:
primùm igitur fundo A B C D incumbit columna baſis dictæ A B C D,
altitudinis A E.
remota igitur aqua iſta quæ ſuperiori fundo inſidet quodque
ipſi A B C D formavimus æquale, erit A B in reliquę aqu@ ſummitate, atque
ideo per 11 prop.
dicto fundo A B C D inſidebit aquea columna baſis A B C D
altitudinis A B;
quæ ad ſuperiorem addita cõſtituet columnam baſis A B C D,
altitudinis autem E G, quæ quantitas eſt ponderis fundo A B C D inſidentis.
2 Exemplum.
178[Figure 178]
Fundi regularis A B ſupremum punctum A in aquæ
ſummo, B ſit in imo;
perpendicularis A C ab A ſurſum
ad C aquæ ſuperficiem extimam, &
deorſum in D ad
planum per B imum punctum horizonti parallelũ con-
tinuata, continuationisq́ue inferioris ſemiſſis eſto A E.
Ajo tantum pondus fundo inſidere, quantum eſt colum-
næ baſis A B altitudinis C E.
cujus demonſtratio ante-
cedenti ſimilis eſt.
C*ONCLVSIO*. Itaqueſi fundi regularis ſupremum
punctum, &
c.
NOTATO.
Hoc T heoremate, adhibita perpendiculari per ſummum fundipunctum educta, quan-
tum eſſet pondus regulari plano inſidens demonſtr avimus, ſed fundo non regulari pon-
dus hoc istiuſmodi perpendiculari non invenitur.
Certum eſt ipſi pondus inſidere æquale
aqueæ columnæ, cuius baſis iſtud ſit fundum, &
altituào perp endicularis à ſupremo cius
fundi puncto ad aquæ ſub qua deliteſcit ſummitatem educta, ſedpræterea jamreliguum
@llud pondus non æquatur alteri, columnæ cuius baſis ſit idem fundum altitudo dimidiæ
perpendicularis ab altiſsimo fundi puncto in planum per infimum punctum

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