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

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          <p>
            <s xml:id="echoid-s1725" xml:space="preserve">
              <pb o="58" file="527.01.058" n="58" rhead="2 LIBER STATICÆ"/>
            & </s>
            <s xml:id="echoid-s1726" xml:space="preserve">I K R Q in N M, & </s>
            <s xml:id="echoid-s1727" xml:space="preserve">per conſequens idem centrum figuræ I K R H S F T
              <lb/>
            O E P G Q, è tribus parallelogrammis compoſitæ, erit in recta N D vel A D.
              <lb/>
            </s>
            <s xml:id="echoid-s1728" xml:space="preserve">Quemadmodum vero in dato triangulo tria quadrangula in-
              <lb/>
              <figure xlink:label="fig-527.01.058-01" xlink:href="fig-527.01.058-01a" number="93">
                <image file="527.01.058-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.058-01"/>
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            ſcripta ſunt, ita infinita inſcribi poſlunt, & </s>
            <s xml:id="echoid-s1729" xml:space="preserve">inſcriptæ figuræ
              <lb/>
            gravitatis centrum nihilo minus, ob cauſas jam commemo-
              <lb/>
            ratas, in A D rectâ erit. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">Verumenimvero quò plura quadran-
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            gula inſcribuntur, eo minor trianguli A B C ab inſcriptis
              <lb/>
            differentia fuerit. </s>
            <s xml:id="echoid-s1731" xml:space="preserve">Parallelis enim à latere A B per media ſe-
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            gmenta A N, N M, M L, L D. </s>
            <s xml:id="echoid-s1732" xml:space="preserve">ductis, differentia poſterio-
              <lb/>
            ris ſitus erit dimidium differentiæ prioris. </s>
            <s xml:id="echoid-s1733" xml:space="preserve">Quapropter infinita hujuſmodi
              <lb/>
            progreſſione, & </s>
            <s xml:id="echoid-s1734" xml:space="preserve">appropinquatione figura tandem invenietur, ut differentia in-
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            ter ipſam & </s>
            <s xml:id="echoid-s1735" xml:space="preserve">triangulum quovis plano, quantumvis minimo, minorſit. </s>
            <s xml:id="echoid-s1736" xml:space="preserve">Vnde
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            ſequitur, Si A D gravitatis diameter eſt, differentiã põderis ſegmenti A D C
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            à pondere ſegmenti A D B quovis plano, quantumvis minimo, minorem
              <lb/>
            eſſe. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">Quare ſic argumentor.</s>
            <s xml:id="echoid-s1738" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s1739" xml:space="preserve">A. </s>
            <s xml:id="echoid-s1740" xml:space="preserve">Inæqualibus ponderibus aliquod pondus inveniri poteſt, quod ipſorum diffe-
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            rentiâ ſit minus.</s>
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            <s xml:id="echoid-s1742" xml:space="preserve">O. </s>
            <s xml:id="echoid-s1743" xml:space="preserve">Atqui hiſce ponderibus A D C, A D B nullum pondus inveniri poteſt,
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            quod differentia ipſorum ſit minus.</s>
            <s xml:id="echoid-s1744" xml:space="preserve"/>
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            <s xml:id="echoid-s1745" xml:space="preserve">O. </s>
            <s xml:id="echoid-s1746" xml:space="preserve">Ponder a igitur A D C, A D B non differunt.</s>
            <s xml:id="echoid-s1747" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1748" xml:space="preserve">Ideoq́ue A D gravitatis diameter eſt, in eaq́ue propterea etiam gravitatis
              <lb/>
            centrum trianguli A B C. </s>
            <s xml:id="echoid-s1749" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1750" xml:space="preserve">Cujusq́ue trianguli gravitatis
              <lb/>
            centrum eſt in rectâ, ab angulo in medium oppoſiti lateris punctum ductâ,
              <lb/>
            quod demonſtrari oportuit.</s>
            <s xml:id="echoid-s1751" xml:space="preserve"/>
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        <div xml:id="echoid-div265" type="section" level="1" n="189">
          <head xml:id="echoid-head202" xml:space="preserve">1 PROBLEMA. 3 PROPOSITIO.</head>
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            <s xml:id="echoid-s1752" xml:space="preserve">Dato triangulo, gravitatis centrum invenire.</s>
            <s xml:id="echoid-s1753" xml:space="preserve"/>
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            <s xml:id="echoid-s1754" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">A B C triangulum eſto.</s>
            <s xml:id="echoid-s1756" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1757" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1758" xml:space="preserve">Centrum gravitatis inveniendum eſt.</s>
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          <head xml:id="echoid-head203" xml:space="preserve">PRAGMATIA.</head>
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            <s xml:id="echoid-s1760" xml:space="preserve">Ab A in medium B C recta A D ducatur, conſimiliter à C in medium
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            A B recta C E: </s>
            <s xml:id="echoid-s1761" xml:space="preserve">Gravitatis centrum F eſſe dico.</s>
            <s xml:id="echoid-s1762" xml:space="preserve"/>
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        <div xml:id="echoid-div267" type="section" level="1" n="191">
          <head xml:id="echoid-head204" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1763" xml:space="preserve">Gravitatis centrum trianguli A B C eſt in re-
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              <figure xlink:label="fig-527.01.058-02" xlink:href="fig-527.01.058-02a" number="94">
                <image file="527.01.058-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.058-02"/>
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            ctis A D & </s>
            <s xml:id="echoid-s1764" xml:space="preserve">C E per 2 propoſ. </s>
            <s xml:id="echoid-s1765" xml:space="preserve">quod demonſtran-
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            dum fuit.</s>
            <s xml:id="echoid-s1766" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1767" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1768" xml:space="preserve">Dato igitur triangulo, gravi-
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            tatis centrum invenimus, quod quærebatur.</s>
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          <head xml:id="echoid-head205" xml:space="preserve">3 THEOREMA. 4 PROPOSITIO.</head>
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            <s xml:id="echoid-s1770" xml:space="preserve">Centrum gravitatis cujusq́ue trianguli, rectam ab an-
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            gulo in oppoſitum latus medium ita ſecat: </s>
            <s xml:id="echoid-s1771" xml:space="preserve">ut ſegmentum
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            interipſum & </s>
            <s xml:id="echoid-s1772" xml:space="preserve">angulum, duplum ſit reliqui.</s>
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