Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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4 L*IBER* S*TATICÆ*
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æquari columnæbaſis A B C D, altitudinis GE,
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patebit demiſſa O Q perpendiculari in planum
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A B C D: </
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le eſt ſolido cujus baſis A B C D altitudo O Q:
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</
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<
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C O Q ſunt æquales, & </
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<
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cta trajecto perpendicularis, item O Q ei quod
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per C, Q, propterea A E & </
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<
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ideoq́ue parallelepipedum A B C D P O M N,
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parallelepipedo in baſin A B C D altitudine
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A E inſiſtente erit æquale. </
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xml:space
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jam 11 propoſ. </
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">demonſtratum fuit) priſma
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M N P O K L æquatur parallelepipedo baſis
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A B C D altitudinis A G. </
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<
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">quare duo iſta ſolida
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addita conſtituunt priſma A B C D L K N M æquale parallelepipedo dictæ
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baſis A B C D, altitudinis autem G E.</
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">ALTERA DEMONSTRATIO.</
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">Si per A B agas planum horizonti parallelum ipſi A B C D ſimile & </
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</
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">huic incumbet per 10 prop. </
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">põdus aquæ æquale columnæ baſis A B C D, altitu-
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dinis AE: </
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">atqui minimùm tantũ põderis inſidet cuilibet fundo humiliori ipſiq́; </
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æquali: </
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">primùm igitur fundo A B C D incumbit columna baſis dictæ A B C D,
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altitudinis A E. </
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ipſi A B C D formavimus æquale, erit A B in reliquę aqu@ ſummitate, atque
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ideo per 11 prop. </
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<
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xml:space
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">dicto fundo A B C D inſidebit aquea columna baſis A B C D
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altitudinis A B; </
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">quæ ad ſuperiorem addita cõſtituet columnam baſis A B C D,
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altitudinis autem E G, quæ quantitas eſt ponderis fundo A B C D inſidentis.</
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">Fundi regularis A B ſupremum punctum A in aquæ
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ſummo, B ſit in imo; </
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ad C aquæ ſuperficiem extimam, & </
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planum per B imum punctum horizonti parallelũ con-
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tinuata, continuationisq́ue inferioris ſemiſſis eſto A E.
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næ baſis A B altitudinis C E. </
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cedenti ſimilis eſt.</
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punctum, &</
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">Hoc T heoremate, adhibita perpendiculari per ſummum fundipunctum educta, quan-
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tum eſſet pondus regulari plano inſidens demonſtr avimus, ſed fundo non regulari pon-
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dus hoc istiuſmodi perpendiculari non invenitur. </
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">Certum eſt ipſi pondus inſidere æquale
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aqueæ columnæ, cuius baſis iſtud ſit fundum, & </
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fundi puncto ad aquæ ſub qua deliteſcit ſummitatem educta, ſedpræterea jamreliguum
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@llud pondus non æquatur alteri, columnæ cuius baſis ſit idem fundum altitudo dimidiæ
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perpendicularis ab altiſsimo fundi puncto in planum per infimum punctum </
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