Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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*DE* H*YDROSTATICES ELEMENTIS*.
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<
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xml:space
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">3 THEOREMA. 3 PROPOSITIO.</
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<
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<
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xml:space
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">Corpus ſolidum materiæ ponderoſioris quàm aqua ad
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fundum uſque demergitur.</
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<
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<
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<
s
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xml:space
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<
s
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xml:space
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">Efto corpus ſolidum A materiâ ponderoſiore quàm aqua B C,
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cujus ſuperſicies ſumma B D, ima E C. </
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<
s
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<
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xml:space
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">A aquæ B C im-
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poſitum ad fundum E C uſque deſcendere demonſtrator.</
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<
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</
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<
s
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xml:space
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">P*RÆPARATIO*. </
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>
<
s
xml:id
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xml:space
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">Vas ſuperſiciatium F G aqua plenum ipſi A ſimile & </
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æquale deſormato, cujus ſuperſicies ſumma F H in plano B D collocetur.</
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<
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xml:space
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<
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<
s
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xml:space
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">Cum A materiæ quidem ponderoſioris ſit ex hy potheſi quam aqua F G,
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magnitudinis verò æ qualis; </
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<
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xml:space
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<
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xml:space
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">Iam ſi in locum
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aquæ F G ſubſtituatur ipſi pro pter fab team congruum corpu; </
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<
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xml:space
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">A attamen, ut
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patet, illo ponderoſius, vas ſuperſiciarium F G per 3 poſtul. </
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<
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xml:space
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">ab A corpore al-
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tius demergetur quam ab aqua F G. </
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<
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xml:space
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">demonſiravimus igitur corpus A mergi;
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</
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<
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xml:space
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">fed ad fundum E C uſque demergi ita evincam. </
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xml:space
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dat ad E C, ſed interinedio loco hæreat ut in I. </
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<
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xml:space
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vas ejus ſuperſiciarium aquâ compleatur, eodem loco per I propoſ. </
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fed æ qua hæc levior eſt iſto ſolido; </
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<
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leviusq́ue in humido eodem hærebuntloco, quod abſur
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dum 3 poſtulato repugnat. </
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<
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xml:space
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E C, ſummam imamq́ue ſuperſiciem conſiſtere nequit,
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ac neceſſariò deſcendet donec ſundo ſubjecto E C im-
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pactum quieſcat. </
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tur materiæ ponderoſioris quam aqua ad fundum uſque demergitur. </
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demonſtraſſe oportuit.</
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<
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inaqua locum ſervat.</
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BC. </
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xml:space
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">Corpus A ubicunque in aqua ſtatuetur ſubſiſtere de-
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monſtrato. </
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">P*RAEPARATIO*. </
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xml:space
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">Eſto vas ſuperſiciarium D, ipſi A æquale & </
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ſimile.</
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<
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">DEMONSTRATIO.</
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<
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<
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">Cum A materię ponderitate & </
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">corporis mole æquale ſit aquæ D, ideo
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D ipſi A pondere quoque æquatur. </
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ſubſtituitor corpus A ipſi propter fabricam per omnia congruum, quare per
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3 poſſul. </
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<
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gis nec minus demergetur quam ab aqua D; </
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D per 1 propoſ datum ſibi locum ſervat. </
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<
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ſolidum corpus A in aqua B C tributum ſibi locum
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retinebit, neque aliò delabetur.</
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<
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materies ponderitate aquæ eſt æqualis, datum ſervat locum. </
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monſtrandum.</
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