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

Table of Notes

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          <pb o="59" file="527.01.059" n="59" rhead="DE INVENIENDO GRAVITATIS CENTRO."/>
          <p>
            <s xml:id="echoid-s1774" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">Ab angulo B, trianguli A B C recta ducatur in D, medium
              <lb/>
            punctum oppoſiti lateris, conſimiliter & </s>
            <s xml:id="echoid-s1776" xml:space="preserve">à C recta in E punctum medium la-
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            teris A B, ſecans B D in F, gravitatis centro trianguli A B C.</s>
            <s xml:id="echoid-s1777" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1778" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">C F ad F E duplum eſſe demonſtrandum eſt.</s>
            <s xml:id="echoid-s1780" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div270" type="section" level="1" n="193">
          <head xml:id="echoid-head206" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1781" xml:space="preserve"> Subductâ ratione E B 1 ad B A 2, de
              <figure xlink:label="fig-527.01.059-01" xlink:href="fig-527.01.059-01a" number="95">
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              <note symbol="*" position="right" xlink:label="note-527.01.059-01" xlink:href="note-527.01.059-01a" xml:space="preserve"> Per inver-
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              ſionĕ cap. 12.
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              Almag. Pto-
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              lem.</note>
            D C 1 ad D A 1 (id eſt ratione {1/2} de ratione {1/1})
              <lb/>
            C F ad FE reliqua eſt. </s>
            <s xml:id="echoid-s1782" xml:space="preserve">Atqui ratione {1/2} ſubductâ
              <lb/>
            de ratione {1/1} relinquitur ratio {2/1}. </s>
            <s xml:id="echoid-s1783" xml:space="preserve">C Figitur ad F E
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            eſt, ut 2 ad 1. </s>
            <s xml:id="echoid-s1784" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1785" xml:space="preserve">Gravitatis igitur
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            centrum in triangulo ita ſecat rectam ab angulo in
              <lb/>
            medium oppoſiti lateris, ut ſegmentũ inter ipſum
              <lb/>
            & </s>
            <s xml:id="echoid-s1786" xml:space="preserve">angulum ad reliquum duplum ſit, quod fuit demonſtrandum.</s>
            <s xml:id="echoid-s1787" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div272" type="section" level="1" n="194">
          <head xml:id="echoid-head207" xml:space="preserve">4 THEOREMA. 5 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1788" xml:space="preserve">Trianguli duorum laterum unumquoq; </s>
            <s xml:id="echoid-s1789" xml:space="preserve">in tria æqua-
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            lia ſegmenta partito: </s>
            <s xml:id="echoid-s1790" xml:space="preserve">recta per ſectionum puncta tertio la-
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            teri proxima, pergravitatis centrum eſt ducta.</s>
            <s xml:id="echoid-s1791" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1792" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1793" xml:space="preserve">A B C trianguli duo latera A B & </s>
            <s xml:id="echoid-s1794" xml:space="preserve">A C utrumq; </s>
            <s xml:id="echoid-s1795" xml:space="preserve">in tria æqua-
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            lia ſegmenta ſecta ſunto, illud punctis D, E, iſtud vero F, G. </s>
            <s xml:id="echoid-s1796" xml:space="preserve">perq́ue E, G, ter-
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            tio lateri B C proxima, recta E G ſit ducta.</s>
            <s xml:id="echoid-s1797" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1798" xml:space="preserve">Q*VÆSITVM*. </s>
            <s xml:id="echoid-s1799" xml:space="preserve">E G per trianguli A B C gravitatis centrum eſſe, demon-
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            ſtrandum eſt. </s>
            <s xml:id="echoid-s1800" xml:space="preserve">P*ARASCEVE*. </s>
            <s xml:id="echoid-s1801" xml:space="preserve">Ab A in medium B C recta A H ducatur,
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            ſecans E G in I.</s>
            <s xml:id="echoid-s1802" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div273" type="section" level="1" n="195">
          <head xml:id="echoid-head208" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1803" xml:space="preserve"> Quandoquidem ratio A E ad E B, eſt ratio A G ad G C recta E G
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                <image file="527.01.059-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.059-02"/>
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              <note symbol="*" position="right" xlink:label="note-527.01.059-02" xlink:href="note-527.01.059-02a" xml:space="preserve">1. prop. 62
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              lib. Eucl.</note>
            rectam B C parallela erit, item E I ad B H. </s>
            <s xml:id="echoid-s1804" xml:space="preserve">Quemadmo-
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            dum igitur A E ad E B: </s>
            <s xml:id="echoid-s1805" xml:space="preserve">ita A I ad I H, atqui A E ad E B
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            ex conceſſo, eſt dupla; </s>
            <s xml:id="echoid-s1806" xml:space="preserve">dupla igitur erit & </s>
            <s xml:id="echoid-s1807" xml:space="preserve">A I ad H I. </s>
            <s xml:id="echoid-s1808" xml:space="preserve">Quia
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            vero A I dupla eſt ad I H, I gravitatis centrum eſt triangu-
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            li A BC per 4 propoſit. </s>
            <s xml:id="echoid-s1809" xml:space="preserve">E G igitur per gravitatis centrum
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            eſt ducta. </s>
            <s xml:id="echoid-s1810" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1811" xml:space="preserve">Trianguli igitur duorum la-
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            terum unoquoque in tria æqualia ſegmenta partito: </s>
            <s xml:id="echoid-s1812" xml:space="preserve">recta
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            perſectionum puncta tertio lateri proxima, per gravitatis
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            centrum eſt ducta.</s>
            <s xml:id="echoid-s1813" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div275" type="section" level="1" n="196">
          <head xml:id="echoid-head209" xml:space="preserve">2 PROBLEMA. 6 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1814" xml:space="preserve">Dato plano rectilineo; </s>
            <s xml:id="echoid-s1815" xml:space="preserve">gravitatis centrum invenire.</s>
            <s xml:id="echoid-s1816" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div276" type="section" level="1" n="197">
          <head xml:id="echoid-head210" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1817" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1818" xml:space="preserve">A B C D inordinatum quadrangulum eſto.</s>
            <s xml:id="echoid-s1819" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1820" xml:space="preserve">Q*VÆSITVM*. </s>
            <s xml:id="echoid-s1821" xml:space="preserve">Gravitatis centrum inveniendum nobis eſt.</s>
            <s xml:id="echoid-s1822" xml:space="preserve"/>
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