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

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              <pb o="136" file="527.01.136" n="136" rhead="4 L*IBER* S*TATICÆ*"/>
            tra A B interſecet A D in I, & </s>
            <s xml:id="echoid-s4022" xml:space="preserve">ſegmento A B H I incumbat pondus aquæ 24
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            pedum cubicorum. </s>
            <s xml:id="echoid-s4023" xml:space="preserve">diviſis 24 per 3, quæ femiſſis eſt lateris A B, quotus erit 8:
              <lb/>
            </s>
            <s xml:id="echoid-s4024" xml:space="preserve">tumq́ue invenito duos numeros in ratione A F 3 ad A E 4 quorum planus ſit
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            dictus octonarius; </s>
            <s xml:id="echoid-s4025" xml:space="preserve">numeriq́ue iſti erunt √ 6 & </s>
            <s xml:id="echoid-s4026" xml:space="preserve">√ 10 {2/3}, poſterior hic definiet
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            quantitatem A G: </s>
            <s xml:id="echoid-s4027" xml:space="preserve">namque G H parallela ex G contra A B auferet planum
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            A B H I cui per 1, propoſ. </s>
            <s xml:id="echoid-s4028" xml:space="preserve">molcsaquea 24 pedum innitetur.</s>
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        <div xml:id="echoid-div581" type="section" level="1" n="420">
          <head xml:id="echoid-head437" xml:space="preserve">NOTATO.</head>
          <p style="it">
            <s xml:id="echoid-s4030" xml:space="preserve">Tribus deinceps continuis propoſitionibus, ex ſententia Breviarii, agendum nobis de
              <lb/>
            centris gravitatis preſſuum in fundis collectorum Vbi jure funda borizonti parallela
              <lb/>
            primum ſibi locum depoſcerent, ſed quia ipſorum gravitatis centra (quæ ex ſecundi li-
              <lb/>
            bri doctrina pateſcunt) à centris preſſuum diverſa non ſint, brevitatis ſtudio novum
              <lb/>
            nullum de iis theorema inſtituimus. </s>
            <s xml:id="echoid-s4031" xml:space="preserve">Quare initio ducto à fundis in clinatis, ita or dimur.</s>
            <s xml:id="echoid-s4032" xml:space="preserve"/>
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        <div xml:id="echoid-div582" type="section" level="1" n="421">
          <head xml:id="echoid-head438" xml:space="preserve">12 THEOREMA. 18 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s4033" xml:space="preserve">Si parallelogrammiad horizonrem inclina ti recta ſupre-
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            mum ejus latus, in ſumma aquæ ſuperficie conſiſtens, & </s>
            <s xml:id="echoid-s4034" xml:space="preserve">
              <lb/>
            imum ſibi oppoſitum biſecet, hæc à preſſus gravitatis cen-
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            tro ita tribuitur ut pars ſumma reliquæ ſit dupla.</s>
            <s xml:id="echoid-s4035" xml:space="preserve"/>
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        <div xml:id="echoid-div583" type="section" level="1" n="422">
          <head xml:id="echoid-head439" style="it" xml:space="preserve">1 Exemplum.</head>
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            <s xml:id="echoid-s4036" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s4037" xml:space="preserve">* Exponatur aqua A B, fundumq́ue ACDE figura parallelo-
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            gramma ad horizontem annuens, cujus ſuperũ
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                <image file="527.01.136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.136-01"/>
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            latus A C ſit in aquæ ſuperficie ſumma, tumq́;
              <lb/>
            </s>
            <s xml:id="echoid-s4038" xml:space="preserve">ſuperum inferumq́ue latus A C, E D, biſecen-
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            tur in F & </s>
            <s xml:id="echoid-s4039" xml:space="preserve">G, quæ jungat F G in puncto H ita
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            diviſa ut ſegmentum F H reliqui H G ſit du-
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            plum.</s>
            <s xml:id="echoid-s4040" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4041" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s4042" xml:space="preserve">* H preſſus quo fundum affi-
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            citur gravitatis eſſe centrum demonſtrator.</s>
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          <figure number="196">
            <image file="527.01.136-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.136-02"/>
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            <s xml:id="echoid-s4044" xml:space="preserve">P*RAEPARATIO.</s>
            <s xml:id="echoid-s4045" xml:space="preserve">* Acta CI ſubtendat an-
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            gulum C D I æquicrurum; </s>
            <s xml:id="echoid-s4046" xml:space="preserve">ut priſi
              <unsure/>
            ma A C I D E
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            ſit dimidia columna, cujus baſis A C D E, alti-
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            tudo perpendicularis ab A uſque ad planum per
              <lb/>
            E D horizonti parallelum.</s>
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          <p>
            <s xml:id="echoid-s4048" xml:space="preserve">Figurato item alterum corpus K L M N O P
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            ſimile priori A C I D E, planumque K L M N
              <lb/>
            plano A C E, & </s>
            <s xml:id="echoid-s4049" xml:space="preserve">M O horizonti perpendi-
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            cularis lateri D I homologa ſunto, itemq́ue Q R
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            ipſi F G: </s>
            <s xml:id="echoid-s4050" xml:space="preserve">hinc ab S medio lateris O P agantur S Q, S R, atque trianguli Q S R
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            gravitatis centrum T, unde V X horizonti perpendieularis ſit.</s>
            <s xml:id="echoid-s4051" xml:space="preserve"/>
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        <div xml:id="echoid-div585" type="section" level="1" n="423">
          <head xml:id="echoid-head440" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s4052" xml:space="preserve">Iam per 11 propof. </s>
            <s xml:id="echoid-s4053" xml:space="preserve">qua to preſſu corpus K L M N O P afficit fundum
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            K L M N, tanto afficit aqua A B fundum A C D E; </s>
            <s xml:id="echoid-s4054" xml:space="preserve">quare preſſuum gravita-
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            tis centra in fundis K L M N, A C D E ſimili erunt ſitu. </s>
            <s xml:id="echoid-s4055" xml:space="preserve">Cæterùm T quod </s>
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