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

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        <div xml:id="echoid-div212" type="section" level="1" n="154">
          <pb o="45" file="527.01.045" n="45" rhead="*DE* S*TATIC Æ ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div214" type="section" level="1" n="155">
          <head xml:id="echoid-head167" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1377" xml:space="preserve">Quoniam rectæ F H, F K inter eaſdem ſunt parallelas angulusq́ue HFC,
              <lb/>
            ex conceſſo, æqualis eſt angulo K F D, etiam F H & </s>
            <s xml:id="echoid-s1378" xml:space="preserve">F K æquales ſunt; </s>
            <s xml:id="echoid-s1379" xml:space="preserve">un-
              <lb/>
            de conſequens eſt, ita eſſe M F ad F K: </s>
            <s xml:id="echoid-s1380" xml:space="preserve">quemadmodum eſt M F ad F H.
              <lb/>
            </s>
            <s xml:id="echoid-s1381" xml:space="preserve">Atqui quemadmodum eſt M F ad F H: </s>
            <s xml:id="echoid-s1382" xml:space="preserve">ita eſt L ad G: </s>
            <s xml:id="echoid-s1383" xml:space="preserve">ideoq́ue ut M F ad
              <lb/>
            F K: </s>
            <s xml:id="echoid-s1384" xml:space="preserve">ita L ad G. </s>
            <s xml:id="echoid-s1385" xml:space="preserve">I autĕ æquatur G extheſi. </s>
            <s xml:id="echoid-s1386" xml:space="preserve">itaque ut M Fad F K: </s>
            <s xml:id="echoid-s1387" xml:space="preserve">ita L ad I: </s>
            <s xml:id="echoid-s1388" xml:space="preserve">
              <lb/>
            quo poſito, etiam I columnamin eodem ſitu ſuſtinet. </s>
            <s xml:id="echoid-s1389" xml:space="preserve">per 20 propoſitionem. </s>
            <s xml:id="echoid-s1390" xml:space="preserve">
              <lb/>
            Conſimilis planè in quibuſvis aliis exemplis demonſtratio fuerit.</s>
            <s xml:id="echoid-s1391" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1392" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1393" xml:space="preserve">Æqualia pondera ſuſpenſa de ductariis lineis, quæ ex co-
              <lb/>
            dem axis puncto in contrarias partes ductæ æquales cum axe angulos faciunt:
              <lb/>
            </s>
            <s xml:id="echoid-s1394" xml:space="preserve">in columnam æqualem vim potentiamq́ue exercent; </s>
            <s xml:id="echoid-s1395" xml:space="preserve">quod nobis erat demon-
              <lb/>
            ſtrandum.</s>
            <s xml:id="echoid-s1396" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div215" type="section" level="1" n="156">
          <head xml:id="echoid-head168" xml:space="preserve">15 THEOREMA. 24 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1397" xml:space="preserve">Potentia ponderis, cujus ductaria linea axi perpendi-
              <lb/>
            cularis eſt, in columnam dati ſitus omnium eſt maxima.</s>
            <s xml:id="echoid-s1398" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1399" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1400" xml:space="preserve">AB columna, CD axis, E firmum, F mobile punctum eſto,
              <lb/>
            eique G pondus obliquè extollens affigatur in ſitu columnam conſervans,
              <lb/>
            ut linea extollens H F horizonti obliqua axi C D ſit recta. </s>
            <s xml:id="echoid-s1401" xml:space="preserve">eidemq́; </s>
            <s xml:id="echoid-s1402" xml:space="preserve">F pondus
              <lb/>
            I obliquè extollens, æquali cum G pondere, obliquâ linea K F affigatur.</s>
            <s xml:id="echoid-s1403" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1404" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1405" xml:space="preserve">Demonſtrandum eſt ponderis G in columnam majo-
              <lb/>
            rem eſſe potentiam, quam ponderis I, eamq́ue potentiam omnium eſſe maxi-
              <lb/>
            mam. </s>
            <s xml:id="echoid-s1406" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s1407" xml:space="preserve">A D punctum F pondus L rectè extollens ad-
              <lb/>
            figatur, quod columnam in ſitu ſuo retineat, cujus rectè extollens ſit F M.</s>
            <s xml:id="echoid-s1408" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div216" type="section" level="1" n="157">
          <head xml:id="echoid-head169" xml:space="preserve">DEMONSTRATIO.</head>
          <p style="it">
            <s xml:id="echoid-s1409" xml:space="preserve">A. </s>
            <s xml:id="echoid-s1410" xml:space="preserve">Quodcunque pondus extollens minorem rationem habet ad L, quam ſua linea
              <lb/>
            extollens ad F M, levius eſt quam ut columnam in ſuo ſitu detineat. </s>
            <s xml:id="echoid-s1411" xml:space="preserve">per
              <lb/>
            20 propoſit.</s>
            <s xml:id="echoid-s1412" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1413" xml:space="preserve">I. </s>
            <s xml:id="echoid-s1414" xml:space="preserve">Atqui I pondus extollens minorem rationem habet ad L, quam ſua linea K F
              <lb/>
            extollens ad F M.</s>
            <s xml:id="echoid-s1415" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1416" xml:space="preserve">I. </s>
            <s xml:id="echoid-s1417" xml:space="preserve">I pondus extollens igitur levius eſt, quam ut columnam in ſuo ſitu detineat.</s>
            <s xml:id="echoid-s1418" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1419" xml:space="preserve">Syllogiſmi aſſumptio ita approbatur. </s>
            <s xml:id="echoid-s1420" xml:space="preserve">Pondus G (quod columnam in ſuo
              <lb/>
            ſitu ſuſtinet) eam habet rationem ad L; </s>
            <s xml:id="echoid-s1421" xml:space="preserve">quam H F ad F M, atqui I æquatur
              <lb/>
            G, K F vero major eſt quam F H. </s>
            <s xml:id="echoid-s1422" xml:space="preserve">I igitur
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            minorem rationem habet, ad L: </s>
            <s xml:id="echoid-s1423" xml:space="preserve">quam K F
              <lb/>
            ad F M. </s>
            <s xml:id="echoid-s1424" xml:space="preserve">& </s>
            <s xml:id="echoid-s1425" xml:space="preserve">propter ea,
              <unsure/>
            ut paulo ante monui-
              <lb/>
            mus, I levius eſt, quàm ut columnam eo ſitu
              <lb/>
            ſuſtineat: </s>
            <s xml:id="echoid-s1426" xml:space="preserve">at G ſuſtinere poteſt, potentia igi-
              <lb/>
            t
              <unsure/>
            ur G major eſt, quam potentia I. </s>
            <s xml:id="echoid-s1427" xml:space="preserve">Poten-
              <lb/>
            @iam vero ponderis G majorem effe nõ poſſe
              <lb/>
            @n
              <unsure/>
            de cõſtat, quod ab F, ea quidem columnæ
              <lb/>
            parte, brevior linea quam F H ducinon poſ-
              <lb/>
            ſit, quandoquidem perpendicularis eſt.</s>
            <s xml:id="echoid-s1428" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1429" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1430" xml:space="preserve">Si igitur ductaria linea axi perpendicularis eſt, maximam
              <lb/>
            potentiam in columnam dati ſitus habet, quod demonſtrandum fuit.</s>
            <s xml:id="echoid-s1431" xml:space="preserve"/>
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