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

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        <div xml:id="echoid-div513" type="section" level="1" n="368">
          <pb o="125" file="527.01.125" n="125" rhead="*DE* H*YDROSTATICES ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div515" type="section" level="1" n="369">
          <head xml:id="echoid-head386" xml:space="preserve">4 Exemplum.</head>
          <p>
            <s xml:id="echoid-s3635" xml:space="preserve">Quamvis tribus diagrammatis {γρ}αμμικῶς theorematis hujus veritatem evi-
              <lb/>
            cerimus atque iſta via rationes & </s>
            <s xml:id="echoid-s3636" xml:space="preserve">cauſæ plenius uberiuſque pateſcant, uberta-
              <lb/>
            tem tamen iſtam arithmetico calculo 4 hoc exemplo fœcundiorem efficere pla-
              <lb/>
            cuit. </s>
            <s xml:id="echoid-s3637" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3638" xml:space="preserve">Vaſis A B aqua pleni fundum A C D E quadratum hori-
              <lb/>
            zonti perpendiculare eſto, cujus ſupremum labrum A C pedalis longitudinis
              <lb/>
            ſit in ſummitate aquæ A C F G, ſitq́ue altitudo A E item pedalis; </s>
            <s xml:id="echoid-s3639" xml:space="preserve">reliqualon-
              <lb/>
            gitudo A B pro libitu exporrigatur.</s>
            <s xml:id="echoid-s3640" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3641" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3642" xml:space="preserve">Pondus aquæ fundo
              <lb/>
              <figure xlink:label="fig-527.01.125-01" xlink:href="fig-527.01.125-01a" number="175">
                <image file="527.01.125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.125-01"/>
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            A C D E annixum dimidię aqueæ columnæ,
              <lb/>
            baſe iſti fundo, altitudine perpendiculari A E
              <lb/>
            æquali æquari demonſtrator. </s>
            <s xml:id="echoid-s3643" xml:space="preserve">At cum columna
              <lb/>
            iſta hîc cubus ſit pedalis, demonſtrandum erit
              <lb/>
            fundo A C D E incumbere pondus cubici pe-
              <lb/>
            dis dimidium.</s>
            <s xml:id="echoid-s3644" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3645" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s3646" xml:space="preserve">Tres parallelę H I, K L, M N, contra A C æquali diſtan-
              <lb/>
            tia rectam A E quadripartitò dividant.</s>
            <s xml:id="echoid-s3647" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div517" type="section" level="1" n="370">
          <head xml:id="echoid-head387" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3648" xml:space="preserve">Manife
              <unsure/>
            ſtum eſt fundo A I plus inſidere quam o, nam ſi iſtiuſmodi fundum
              <lb/>
            horizonti effet parallelum nihil ſeu o ipſi inſideret, at nunc cùm infra conſiſtat
              <lb/>
            plus nihilo ſeu o ipſi incumbit: </s>
            <s xml:id="echoid-s3649" xml:space="preserve">Et tamen pondus illud citra {1/16} pedis eſt, cum
              <lb/>
            enim ad horizontem parallelum agitur per H I tantò urgetur pondere: </s>
            <s xml:id="echoid-s3650" xml:space="preserve">quare
              <lb/>
            cum in hâc theſi ſuperiori loco conſiſtat, minus ſuſtinet quam pedis cubici {1/16}.
              <lb/>
            </s>
            <s xml:id="echoid-s3651" xml:space="preserve">ſimili ratione efficitur in fundo H L plus inſidere quàm {1/16}, minusq́ue {2/16}: </s>
            <s xml:id="echoid-s3652" xml:space="preserve">item
              <lb/>
            fundo K N plus {2/16}, minus autem {3/16}: </s>
            <s xml:id="echoid-s3653" xml:space="preserve">denique fundo M D plus {3/16}, at mi-
              <lb/>
            nus {4/16}. </s>
            <s xml:id="echoid-s3654" xml:space="preserve">Addita igitur quatuor pondera (ſi o huc annumeres) in ſingulis termi-
              <lb/>
            nis priora & </s>
            <s xml:id="echoid-s3655" xml:space="preserve">minora, hoc eſt, o, {1/16}. </s>
            <s xml:id="echoid-s3656" xml:space="preserve">{2/16}. </s>
            <s xml:id="echoid-s3657" xml:space="preserve">{3/16}, danttotum {6/16}: </s>
            <s xml:id="echoid-s3658" xml:space="preserve">item quatuor poſte-
              <lb/>
            riora & </s>
            <s xml:id="echoid-s3659" xml:space="preserve">majora {1/16}, {2/16}, {3/16}, {4/16}, colligunt {10/16}. </s>
            <s xml:id="echoid-s3660" xml:space="preserve">Quamobrem fundo A C D E inſi-
              <lb/>
            detpondus quoddam majus quàm {6/16} pedis, at minus quàm {10/16}, interq́ue hos
              <lb/>
            terminos pes dimidius medius conſiſtit, quem fundo A C D E inſidere de-
              <lb/>
            monſtrare neceſſum eſt.</s>
            <s xml:id="echoid-s3661" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3662" xml:space="preserve">Cæterùm qua ratione tribus parallelis fundum quadrifariam diſſecuimus,
              <lb/>
            eadem omninò via in partes quotlibet optatas dirimetur. </s>
            <s xml:id="echoid-s3663" xml:space="preserve">ſit denarius ſegmen-
              <lb/>
            torum optatus numerus. </s>
            <s xml:id="echoid-s3664" xml:space="preserve">Iam ob cauſas ante expoſitas, decem priora in colla-
              <lb/>
            tione & </s>
            <s xml:id="echoid-s3665" xml:space="preserve">minora pondera quæſingulis inſident fundis, uto, {1/100}, {2/100}, {3/100}, {4/100},
              <lb/>
            {5/100}, {6/100}, {7/100}, {8/100}, {9/100}, collecta efficiunt ſummam {45/100}: </s>
            <s xml:id="echoid-s3666" xml:space="preserve">ſimiliter poſteriora & </s>
            <s xml:id="echoid-s3667" xml:space="preserve">
              <lb/>
            graviora ut {1/100}, {2/100}, {3/100}, {4/100}, {5/100}, {6/100}, {7/100}, {8/100}, {9/100}, {10/100}. </s>
            <s xml:id="echoid-s3668" xml:space="preserve">dant ſumman; </s>
            <s xml:id="echoid-s3669" xml:space="preserve">{55/100}.
              <lb/>
            </s>
            <s xml:id="echoid-s3670" xml:space="preserve">quamobrem fundo A C D E plus inſidet quàm {45/100} & </s>
            <s xml:id="echoid-s3671" xml:space="preserve">minus quàm {55/100}, qui
              <lb/>
            termini utrimque à dimidio pede, propter quem demonſtratio inſtituitur, ab-
              <lb/>
            ſunt pari intervallo. </s>
            <s xml:id="echoid-s3672" xml:space="preserve">Atqui quemadmodum hi proprius abſunt à pede dimidio
              <lb/>
            prioribus illis, nam {45/100} differentia ab {1/2} minor eſt quàm {6/16}; </s>
            <s xml:id="echoid-s3673" xml:space="preserve">& </s>
            <s xml:id="echoid-s3674" xml:space="preserve">{55/100}, minor item
              <lb/>
            differentia quam {10/16}: </s>
            <s xml:id="echoid-s3675" xml:space="preserve">ita in quo plura ſegmenta æqualia fundum A C D E par-
              <lb/>
            titus eris, continuò magis magisq́ue ad ipſum dimidium pedem accedes.</s>
            <s xml:id="echoid-s3676" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3677" xml:space="preserve">Quibus ritè intellectis, fingamus (ſi ſieri poſſit) fundo A C D E plus minusvé
              <lb/>
            {1/1000} pondere dimidii pedis inſidere: </s>
            <s xml:id="echoid-s3678" xml:space="preserve">veritatem igitur, fundo in 1000 partis lineis
              <lb/>
            parallelis ut ante diſtributo, ratione viaq́ue jam uſitata inquiramus. </s>
            <s xml:id="echoid-s3679" xml:space="preserve">Hîc propter
              <lb/>
            antecedentes cauſas mille ponduſcula priora mille particulis inſidentia erunt
              <lb/>
            O {1/1000000}, {2/1000000}, atque ita deinceps, ultimumq́; </s>
            <s xml:id="echoid-s3680" xml:space="preserve">{999/1000000}, horum omniũ ſumma </s>
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