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

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          <pb o="64" file="527.01.064" n="64" rhead="2 L*IBER* S*TATICÆ*"/>
        </div>
        <div xml:id="echoid-div304" type="section" level="1" n="218">
          <head xml:id="echoid-head231" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2009" xml:space="preserve">Continuator F E in G, ita ut ratio F E ad E G, ſit eadem rationi ſegmen-
              <lb/>
            ti B D C ad ſegmentum B D A; </s>
            <s xml:id="echoid-s2010" xml:space="preserve">ajo G reliqui ſegmenti B D C optatum eſſe
              <lb/>
            gravitatis centrum.</s>
            <s xml:id="echoid-s2011" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div305" type="section" level="1" n="219">
          <head xml:id="echoid-head232" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2012" xml:space="preserve">Cum F centrum ſit B D A, & </s>
            <s xml:id="echoid-s2013" xml:space="preserve">E totius A B C D, reliqui ſegmenti centrum
              <lb/>
            erit in F E infinitum continuata. </s>
            <s xml:id="echoid-s2014" xml:space="preserve">(Secus enim, ſi fieri poſsit, cadat extra in H,
              <lb/>
            totius igitur rectilinei gravitatis centrum conſiſteret
              <lb/>
            in recta F H, quod tamen theſi repugnat, nam ſta-
              <lb/>
              <figure xlink:label="fig-527.01.064-01" xlink:href="fig-527.01.064-01a" number="105">
                <image file="527.01.064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.064-01"/>
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            tuitur in E) quamobrem inquam cum ſit in ipſa F E
              <lb/>
            infinitum continuata autultra aut citra G, E verſum
              <lb/>
            cadet, ſi citra ceciderit ut in I ratio lõgioris radii E F,
              <lb/>
            ad breviorem E I, major fuerit, quam gravitatis pon-
              <lb/>
            deroſioris B C D ad leviorem B A D contra 1 pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s2015" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2016" xml:space="preserve">1 quamobrem citra G, E verſus non cadet: </s>
            <s xml:id="echoid-s2017" xml:space="preserve">neque ultra G quod ſi-
              <lb/>
            millima ratione evincetur. </s>
            <s xml:id="echoid-s2018" xml:space="preserve">Neceſſariò itaque in puncto G. </s>
            <s xml:id="echoid-s2019" xml:space="preserve">Quod demon-
              <lb/>
            ſtrari oportuit.</s>
            <s xml:id="echoid-s2020" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div307" type="section" level="1" n="220">
          <head xml:id="echoid-head233" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s2021" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2022" xml:space="preserve">Circuli A B C D ſemidiameter eſt E A, E centrum gravitatis,
              <lb/>
            circelli A F G H eidem inſcripti gravitatis centrum I, diameter A G.</s>
            <s xml:id="echoid-s2023" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2024" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2025" xml:space="preserve">Reliqui ſegmenti A B C D H G F gravitatis centrum in-
              <lb/>
            venire.</s>
            <s xml:id="echoid-s2026" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div308" type="section" level="1" n="221">
          <head xml:id="echoid-head234" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2027" xml:space="preserve">Continuator I E in K, ut I E ad continuationem E K habeat rationem
              <lb/>
            quam ſpatium A B C D H G F ad circulum A F G H; </s>
            <s xml:id="echoid-s2028" xml:space="preserve">ajo K eſſe optatum gra-
              <lb/>
            vitatis centrum, cujus demon-
              <lb/>
            ſtratio ſimillima ſuperiori. </s>
            <s xml:id="echoid-s2029" xml:space="preserve">Ve-
              <lb/>
              <figure xlink:label="fig-527.01.064-02" xlink:href="fig-527.01.064-02a" number="106">
                <image file="527.01.064-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.064-02"/>
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            rùm quô arbeli hujus ad reli-
              <lb/>
            quum circulum ratio ad rectas li-
              <lb/>
            neas revocetur, ſic ages; </s>
            <s xml:id="echoid-s2030" xml:space="preserve">Si inſcri-
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            ptæ C L diametro A G æqualis
              <lb/>
            terminum L cum reliquo dia-
              <lb/>
            metri termino C connectat adia-
              <lb/>
            metrum A L, & </s>
            <s xml:id="echoid-s2031" xml:space="preserve">rectis A L, L C
              <lb/>
            diametro & </s>
            <s xml:id="echoid-s2032" xml:space="preserve">inter ſe conterminis
              <lb/>
            tertia proportionalis ſit M, ratio
              <lb/>
            ſpatii ad circulum AFGH (cùm
              <lb/>
            A L C angulus in ſemicirculo ſit
              <lb/>
            rectus) erit eadem quæ primæ re-
              <lb/>
            ctæ A L ad tertiam M, & </s>
            <s xml:id="echoid-s2033" xml:space="preserve">circulus
              <lb/>
            diametri A L, ſpatio dicto æqua-
              <lb/>
            lis, nam A L ad M ratio eſt dupli-
              <lb/>
            cata A L ad L C, hoc eſtad A G.</s>
            <s xml:id="echoid-s2034" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2035" xml:space="preserve">Eadem planè ratio fuerit ſi plures circelli ex integro A B C D forent exem-
              <lb/>
            pti; </s>
            <s xml:id="echoid-s2036" xml:space="preserve">dicis gatia, deſit præterea circulus N O, cujus centrum erat P. </s>
            <s xml:id="echoid-s2037" xml:space="preserve">Continue-
              <lb/>
            tur P K centra connectens ad Q uſque ut P K ad K Q ſit quemadmodum re-
              <lb/>
            liquum ad circulum N O. </s>
            <s xml:id="echoid-s2038" xml:space="preserve">Quare erit optatum gravitatis centrum, atque </s>
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