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

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        <div xml:id="echoid-div251" type="section" level="1" n="178">
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        <div xml:id="echoid-div252" type="section" level="1" n="179">
          <head xml:id="echoid-head192" xml:space="preserve">DE INVENIENDO
            <lb/>
          GRAVITATIS CENTRO
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          IN PLANIS, PARS PRIOR.</head>
          <p>
            <s xml:id="echoid-s1641" xml:space="preserve">SI planis vel minimum pondusineſſet, illudq́ue ratio-
              <lb/>
            nem adipſorum magnitudinem habere cõcederetur,
              <lb/>
            de planorum ponderibus, ponderũ centris, diametris, & </s>
            <s xml:id="echoid-s1642" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s1643" xml:space="preserve">accuratè præcipi poſſet. </s>
            <s xml:id="echoid-s1644" xml:space="preserve">Quia vero nullum pondus plano
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            ineſt, neque gravitas igitur, neque gravitatis centrum, aut
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            diameter, propriè & </s>
            <s xml:id="echoid-s1645" xml:space="preserve">ſecundum naturam conſiderata. </s>
            <s xml:id="echoid-s1646" xml:space="preserve">Mo-
              <lb/>
            dificatè igitur, & </s>
            <s xml:id="echoid-s1647" xml:space="preserve">quidem metaphoricè, intelligenda ſint,
              <lb/>
            quaſiex theſi gravitas planis, pro ipſorum magnitudine,
              <lb/>
            ineſſet. </s>
            <s xml:id="echoid-s1648" xml:space="preserve">Falſum enim conceditur, ut verum inde adstruatur.</s>
            <s xml:id="echoid-s1649" xml:space="preserve"/>
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        <div xml:id="echoid-div253" type="section" level="1" n="180">
          <head xml:id="echoid-head193" xml:space="preserve">1 THEOREMA. 1 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1650" xml:space="preserve">In omni plano figuræ centrum, gravitatis quoque cen-
              <lb/>
            trum eſt.</s>
            <s xml:id="echoid-s1651" xml:space="preserve"/>
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        <div xml:id="echoid-div254" type="section" level="1" n="181">
          <head xml:id="echoid-head194" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1652" xml:space="preserve">DATVM. </s>
            <s xml:id="echoid-s1653" xml:space="preserve">ABC triangulum æquilaterum eſto, & </s>
            <s xml:id="echoid-s1654" xml:space="preserve">figuræ centrum D.</s>
            <s xml:id="echoid-s1655" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1656" xml:space="preserve">QVAESITVM. </s>
            <s xml:id="echoid-s1657" xml:space="preserve">Idem D gravitatis quoque centrum eſſe trianguli A B C
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            demonſtrandum eſt. </s>
            <s xml:id="echoid-s1658" xml:space="preserve">PRAEPARATIO. </s>
            <s xml:id="echoid-s1659" xml:space="preserve">Ab angulo A recta A E in me-
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            dium latus B C, conſimiliter ab angulo C recta C F in medium latus A B
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            ducatur.</s>
            <s xml:id="echoid-s1660" xml:space="preserve"/>
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        <div xml:id="echoid-div255" type="section" level="1" n="182">
          <head xml:id="echoid-head195" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s1661" xml:space="preserve">Triangulo A B C lineâ A E ſuſpenſo, ſegmentum A E C
              <lb/>
            ſegmento A E B æquilibre erit, ſunt enim æqualia, ſimilia,
              <lb/>
            & </s>
            <s xml:id="echoid-s1662" xml:space="preserve">ſimiliter ſita: </s>
            <s xml:id="echoid-s1663" xml:space="preserve">quapropter A E gravitatis diameter eſt trian-
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            guli A B C. </s>
            <s xml:id="echoid-s1664" xml:space="preserve">Eademq́ue de causâ F C quoque ejuſdem trian-
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            guli gravitatis diameter fuerit. </s>
            <s xml:id="echoid-s1665" xml:space="preserve">Atqui iſtæ in figuræ centro
              <lb/>
            D ſeſe interſecant, quarum quæque gravitatis centrum in ſe
              <lb/>
            habet, illud ipſum igitur D fuerit.</s>
            <s xml:id="echoid-s1666" xml:space="preserve"/>
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          <head xml:id="echoid-head196" xml:space="preserve">2 Exemplum.</head>
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            <s xml:id="echoid-s1667" xml:space="preserve">A B C D Quadrangulum parallelogrammum eſto, & </s>
            <s xml:id="echoid-s1668" xml:space="preserve">figuræ centrum E.</s>
            <s xml:id="echoid-s1669" xml:space="preserve"/>
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            <s xml:id="echoid-s1670" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">E etiam gravitatis centrum eſſe demonſtrandum eſt.</s>
            <s xml:id="echoid-s1672" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1673" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s1674" xml:space="preserve">Rectæ F G & </s>
            <s xml:id="echoid-s1675" xml:space="preserve">HI inter laterum A D & </s>
            <s xml:id="echoid-s1676" xml:space="preserve">B C, item
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            A B & </s>
            <s xml:id="echoid-s1677" xml:space="preserve">D C puncta media ducuntor.</s>
            <s xml:id="echoid-s1678" xml:space="preserve"/>
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