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

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              <pb o="127" file="527.01.127" n="127" rhead="*DE* H*YDROSTATICES ELEMENTIS.*"/>
            ſuperficie, pondusipſi inſidens æquatur columnæaqueæ,
              <lb/>
            cujus baſis ſit huic fundo æqualis, altitudo ſemiſsi perpen-
              <lb/>
            dicularis à fundi ſummo in planum per imum ejus pun-
              <lb/>
            ctum horizonti æquidiſtanter eductum, demiſſæ.</s>
            <s xml:id="echoid-s3726" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s3727" xml:space="preserve">Lua formula poſtremam partem buius 12 propoſitionis efferemus.</s>
            <s xml:id="echoid-s3728" xml:space="preserve"/>
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        <div xml:id="echoid-div519" type="section" level="1" n="372">
          <head xml:id="echoid-head389" xml:space="preserve">10 THEOREMA. 12 PROPOSITIO.</head>
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            <s xml:id="echoid-s3729" xml:space="preserve">Si fundi regularis ſupremum punctum infra ſummam
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            aquæ ſuperficiem deliteſcat, pondus ipſi inſidens æquatur
              <lb/>
            columnæaqueæ cujus baſis huicſundo, altitudo perpendi-
              <lb/>
            culariab aquæ ſummo in planum per ſummũ ſundi pun-
              <lb/>
            ctum horizonti parallelum, demiſſæ, atque inſuper ſemiſsi
              <lb/>
            perpendicularis indidem in alterum planũ perimum fun-
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            di punctum, horizonti parallelum, continuatæ.</s>
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        <div xml:id="echoid-div520" type="section" level="1" n="373">
          <head xml:id="echoid-head390" xml:space="preserve">I Exemplum.</head>
          <p>
            <s xml:id="echoid-s3731" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3732" xml:space="preserve">Fundum regulare A B C D primùm quadrangulum parallelo-
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            grammum latere ſummo A B infra aquam abditum horizonti parallelum ſumi-
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            tor, perpendicularis E A per ſummum A utrimque continuata illic aquæ ſum-
              <lb/>
            mo, hic plano per D C horizonti parallelo occurrat in F, ſitq́ue AG ipſius in-
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            ferioris continuationis ſemiſsis.</s>
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          <figure number="176">
            <image file="527.01.127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.127-01"/>
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            <s xml:id="echoid-s3734" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3735" xml:space="preserve">Pondus aquaæ
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            molis nixæ fundo A B C D colum-
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            næ cujus baſis dicto fundo, altitudo
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            rectæ E G æqualis ſit, æquari demõ-
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            ſtrato. </s>
            <s xml:id="echoid-s3736" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s3737" xml:space="preserve">Latera
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            D A, C B uſque ſuperam aquæ ſu-
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            perficiem in H, I continuata conne-
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            ctantur recta H I; </s>
            <s xml:id="echoid-s3738" xml:space="preserve">hinc C K, D L æ-
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            quales lateri C I & </s>
            <s xml:id="echoid-s3739" xml:space="preserve">horizonti paral-
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            lelæ acta L K compleant parallelo-
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            grammum C D L K & </s>
            <s xml:id="echoid-s3740" xml:space="preserve">jungantur rectę I K, H L; </s>
            <s xml:id="echoid-s3741" xml:space="preserve">denique B M, A N lateri
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            C O, item M O, N P ipſi B C æquales & </s>
            <s xml:id="echoid-s3742" xml:space="preserve">parallelæ conſtituantur.</s>
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            <s xml:id="echoid-s3744" xml:space="preserve">Tumq́ue altera figura huic aqueæ ſimilis, magnitudine autem & </s>
            <s xml:id="echoid-s3745" xml:space="preserve">pondere
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            æqualis deformetur C D H I K L, hac lege ut C K horizontiad perpendicu-
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            lum immineat. </s>
            <s xml:id="echoid-s3746" xml:space="preserve">ut hic.</s>
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        <div xml:id="echoid-div521" type="section" level="1" n="374">
          <head xml:id="echoid-head391" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s3748" xml:space="preserve">Eadem eſt corporis ſolidi C D H I K L ſecundi diagrammatis per 11 propoſ.
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            <s xml:id="echoid-s3749" xml:space="preserve">in C D H I fundum impreſsio, quæ humidi primæ figuræ in fundum ſuum
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            C D H I, & </s>
            <s xml:id="echoid-s3750" xml:space="preserve">conſequenter qualis preſſus eſt in illius parte A B C D, talis in hu-
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            jus parte A B C D quoque erit: </s>
            <s xml:id="echoid-s3751" xml:space="preserve">ſed impreſsio illius in A B C D eſt ſolidum
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            A B C D L K M N æquale columnę cujus baſis A B C D; </s>
            <s xml:id="echoid-s3752" xml:space="preserve">altitudo G E: </s>
            <s xml:id="echoid-s3753" xml:space="preserve">quare
              <lb/>
            aquæ põdus inſidens primæ figuræ fundo A B C D æquatur quoque columnę
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            baſis quidem H B C D, altitudinis verò G E. </s>
            <s xml:id="echoid-s3754" xml:space="preserve">Corpus autĕ A B C D L K N </s>
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