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

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          <pb o="124" file="527.01.124" n="124" rhead="4 L*IBER* S*TATICÆ*"/>
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        <div xml:id="echoid-div510" type="section" level="1" n="367">
          <head xml:id="echoid-head384" xml:space="preserve">3 Exemplum.</head>
          <p>
            <s xml:id="echoid-s3602" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3603" xml:space="preserve">Fundum regulare A B ellipſis eſto, cujus ſupremum punctum
              <lb/>
            A ſit in aquæ ſuperficie ſumma, B in ima, A C perpendicularis à ſummo A in
              <lb/>
            planum horizonti parallelum per imum B.</s>
            <s xml:id="echoid-s3604" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3605" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3606" xml:space="preserve">Pondus aquæ fundo A B
              <lb/>
              <figure xlink:label="fig-527.01.124-01" xlink:href="fig-527.01.124-01a" number="173">
                <image file="527.01.124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.124-01"/>
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            incumbentis æquari dimidiæ columnæ, cu-
              <lb/>
            jus baſis A B, altitudo A C.</s>
            <s xml:id="echoid-s3607" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3608" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s3609" xml:space="preserve">Circumſcribito ellipſi
              <lb/>
            A B parallelogrammum quadrangulum
              <lb/>
            D E F G ut D E in aquæ ſummo tangat ejus
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            ſummum A, & </s>
            <s xml:id="echoid-s3610" xml:space="preserve">G F imum B; </s>
            <s xml:id="echoid-s3611" xml:space="preserve">ſitq́ue F I
              <lb/>
            perpendicularis in F G æqualis lateri F E, & </s>
            <s xml:id="echoid-s3612" xml:space="preserve">
              <lb/>
            horizonti parallela; </s>
            <s xml:id="echoid-s3613" xml:space="preserve">jam reliqua latera G H,
              <lb/>
            H I claudant parallelogrammum F G H I & </s>
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              <lb/>
            connecto E I, D H.</s>
            <s xml:id="echoid-s3615" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3616" xml:space="preserve">Conſtruito deinde alteram figuram non tan-
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            tum forma ſimilem, ſed etiam magnitudine & </s>
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              <lb/>
              <figure xlink:label="fig-527.01.124-02" xlink:href="fig-527.01.124-02a" number="174">
                <image file="527.01.124-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.124-02"/>
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            ponderitate ipſi æqualem, cujus latus F I hori-
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            zonti ad perpendiculum inſiſtat, ut in ſubjecto
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            diagrammate. </s>
            <s xml:id="echoid-s3618" xml:space="preserve">ſitq́ue corpus hoc ſolidum ſub-
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            nixum fundo D E F G.</s>
            <s xml:id="echoid-s3619" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div513" type="section" level="1" n="368">
          <head xml:id="echoid-head385" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3620" xml:space="preserve">Quanto preſſu ſolidum D E F G H I afficit
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            ſuam hedram D E F G, tanto quoq, afficitaqua
              <lb/>
            primæ ſiguræ ſuum fundum D E F G, quod
              <lb/>
            paulò ante nobis demonſtratum eſt, & </s>
            <s xml:id="echoid-s3621" xml:space="preserve">conſe-
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            quenter quantâ preſſione ellipſis A B ſecundæ
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            formæ afficitur, tantâ q
              <unsure/>
            uoque omninò inerit ellipſi A B primæ formæ: </s>
            <s xml:id="echoid-s3622" xml:space="preserve">Atqui
              <lb/>
            preſſio quam ellipſis ſecunda perpetitur, eſt ſemiſſis columnæ (ut jam mox de-
              <lb/>
            monſtraturi ſumus) cujus baſis ellipſis, altitudo æqualis rectę A C, nam per-
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            pendicularis à K in planum ellipſis A B demiſſa æqualis foret dictę A C; </s>
            <s xml:id="echoid-s3623" xml:space="preserve">qua-
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            re aquę in primam ellipſin A B impreſſio, æquatur dimidiæ columnæ cujus ba-
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            ſis ipſa ellipſis ſit, altitudo autem A C.</s>
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          <p>
            <s xml:id="echoid-s3625" xml:space="preserve">Pondus autem ſecundæ ſiguræ inſidens ellipſi A B, æquari dimidiæ colum-
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            næ, cujus baſis iſta ipſa ſit ellipſis, & </s>
            <s xml:id="echoid-s3626" xml:space="preserve">altitudo æqualis A C, hoc pacto arguo.
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            </s>
            <s xml:id="echoid-s3627" xml:space="preserve">Ducito B K æqualem & </s>
            <s xml:id="echoid-s3628" xml:space="preserve">parallelam rectæ F I, & </s>
            <s xml:id="echoid-s3629" xml:space="preserve">ípſam ita circum ellipſin A B
              <lb/>
            circumducito ut tamen perpetuò contra F I parallela ſit, eâque converſione in-
              <lb/>
            ter duas hedras oppoſitas figurabit columnam A B K L, quæ plano D E I H
              <lb/>
            per duo puncta A, K ſimili ſitu atque tranſverſim in parallelarum ellipſium am-
              <lb/>
            bitu ſibi mutuo reſpondentia incidetur: </s>
            <s xml:id="echoid-s3630" xml:space="preserve">ſed quęlibet columna cujus baſis eſt
              <lb/>
            planum regulare, ſectum plano per duo puncta in oppoſitis iſtis hedris tranſver-
              <lb/>
            ſim ὁμοταγῆ ab ipſo in duas æquas partes dirimitur: </s>
            <s xml:id="echoid-s3631" xml:space="preserve">Quare ſegmentum
              <note symbol="*" position="left" xlink:label="note-527.01.124-01" xlink:href="note-527.01.124-01a" xml:space="preserve">Similiter
                <lb/>
              fita.</note>
            lumnæ hujus infra planum D E I H, eſt ſemiſſis columnæ A B K L in ellipſi
              <lb/>
            A B tanquam baſe inſidentis. </s>
            <s xml:id="echoid-s3632" xml:space="preserve">Columnam autem A B K L æquari columnæ
              <lb/>
            baſis A B, altitudinis A C, hinc palam eſt quia ipſius altitudo altitudini A C
              <lb/>
            æqualis ſit. </s>
            <s xml:id="echoid-s3633" xml:space="preserve">Pondus itaque ſubnixum ellipſi A B ęquatur dimidiæ columnæ
              <lb/>
            cujus baſis ellipſis A B, altitudo æqualis rectæ A C.</s>
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