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

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        <div xml:id="echoid-div163" type="section" level="1" n="127">
          <p>
            <s xml:id="echoid-s964" xml:space="preserve">
              <pb o="33" file="527.01.033" n="33" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
            funt. </s>
            <s xml:id="echoid-s965" xml:space="preserve">Verum quæcunque binæ proportiones quaternûm terminorum, ſecun-
              <lb/>
            dos quartosq́ue terminos equales habent, reliquos æquè rationales, id eſt pro-
              <lb/>
            portionales habebunt. </s>
            <s xml:id="echoid-s966" xml:space="preserve">Vt T R igitur ad T V: </s>
            <s xml:id="echoid-s967" xml:space="preserve">ita 11 ad Δ. </s>
            <s xml:id="echoid-s968" xml:space="preserve">Atqui pondus 11
              <lb/>
            æquatur columnæ ponderi, quod puncto V, ſuper puncto Æ quieſcit;
              <lb/>
            </s>
            <s xml:id="echoid-s969" xml:space="preserve">pondusq́ue Δ ponderi, quod R puncto quieſcit ſuper OE. </s>
            <s xml:id="echoid-s970" xml:space="preserve">Ideoq́ue ut T R
              <lb/>
            ad T V: </s>
            <s xml:id="echoid-s971" xml:space="preserve">ita pondus puncto Æ innitens, ad pondus OE innixum.</s>
            <s xml:id="echoid-s972" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s973" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s974" xml:space="preserve">Columnâigitur duobus punctis axis quieſcente, &</s>
            <s xml:id="echoid-s975" xml:space="preserve">c.</s>
            <s xml:id="echoid-s976" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div166" type="section" level="1" n="128">
          <head xml:id="echoid-head137" xml:space="preserve">C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s977" xml:space="preserve">Si puncta, in quibus columna quieſcit, in perpendicularibus ſint per R & </s>
            <s xml:id="echoid-s978" xml:space="preserve">
              <lb/>
            V ductis, pondera quæ antea ſuper quieſcent@bus punctis erant, etiam nunc
              <lb/>
            eſſe poſſunt. </s>
            <s xml:id="echoid-s979" xml:space="preserve">Per puncta R & </s>
            <s xml:id="echoid-s980" xml:space="preserve">V perpendiculares, exempli cauſa, ducantur,
              <lb/>
            in iiſque puncta ut Y, & </s>
            <s xml:id="echoid-s981" xml:space="preserve">λ ſignentur. </s>
            <s xml:id="echoid-s982" xml:space="preserve">Si columna in Y & </s>
            <s xml:id="echoid-s983" xml:space="preserve">λ quieſcit, in
              <lb/>
            Y 2 ℔, in λ 4 ℔ quieſcere manifeſtũ eſt, unde theorematis veritas manifeſta eſt.</s>
            <s xml:id="echoid-s984" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div167" type="section" level="1" n="129">
          <head xml:id="echoid-head138" xml:space="preserve">10 THEOREMA. 18 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s985" xml:space="preserve">Columna duobus in punctis quieſcĕte:</s>
            <s xml:id="echoid-s986" xml:space="preserve">erit ut ſegmen-
              <lb/>
            tum axis inter gravitatis centrum & </s>
            <s xml:id="echoid-s987" xml:space="preserve">perpendicularem per
              <lb/>
            punctum ſiniſtrum, ad eju ſdem ſegmentum inter gravi-
              <lb/>
            tatis centrum & </s>
            <s xml:id="echoid-s988" xml:space="preserve">perpĕdicularem per punctum dextrum:
              <lb/>
            </s>
            <s xml:id="echoid-s989" xml:space="preserve">ita ſuſtentatum pondus columnæ dextro puncto, ad pon-
              <lb/>
            dus quod ſuſtinetur ſiniſtro.</s>
            <s xml:id="echoid-s990" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s991" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s992" xml:space="preserve">A B C D columna eſto,
              <lb/>
              <figure xlink:label="fig-527.01.033-01" xlink:href="fig-527.01.033-01a" number="52">
                <image file="527.01.033-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.033-01"/>
              </figure>
            ejusq́ue axis E F gravitatis centrum G,
              <lb/>
            puncta quibus columna ſuſtinetur H, I, quà
              <lb/>
            perpendiculares K L, M N ductæ axem
              <lb/>
            in O, P ſecant. </s>
            <s xml:id="echoid-s993" xml:space="preserve">Dico quemadmodũ G O ad
              <lb/>
            G P: </s>
            <s xml:id="echoid-s994" xml:space="preserve">ita pondus puncto I ſuſtentatum, ad
              <lb/>
            pondus reliquum quod H ſuſtinet: </s>
            <s xml:id="echoid-s995" xml:space="preserve">cujus
              <lb/>
            demonſtratio ex conſectario 17 propoſit.
              <lb/>
            </s>
            <s xml:id="echoid-s996" xml:space="preserve">manifeſta eſt. </s>
            <s xml:id="echoid-s997" xml:space="preserve">Verumenimverò, ut paulo
              <lb/>
            fuſius de neceſſaria hujus veritateagatur, ſi
              <lb/>
            Hloco O eſſe fingamus, ratio põderis pun-
              <lb/>
              <figure xlink:label="fig-527.01.033-02" xlink:href="fig-527.01.033-02a" number="53">
                <image file="527.01.033-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.033-02"/>
              </figure>
            cto H ſuſtentati ad pondus P ſuſtentatum
              <lb/>
            erit, quæ eſt G P ad G O, per 17 propoſit.
              <lb/>
            </s>
            <s xml:id="echoid-s998" xml:space="preserve">Puncto H ſixo, columnam in dato ſitu
              <lb/>
            deſcĕdere ponamus intervallo ab H uſque
              <lb/>
            in O, pondus H puncto ſuſtentatũ per 3 po-
              <lb/>
            ſtulatum, idem manèt. </s>
            <s xml:id="echoid-s999" xml:space="preserve">Cõſimiliter pondus
              <lb/>
            quod in puncto P quieſcit, etiam puncto I
              <lb/>
            quieſcere oſtĕdetur, ut igitur G O ad G P: </s>
            <s xml:id="echoid-s1000" xml:space="preserve">
              <lb/>
            ita põdus quod I ſuſtinet ad pondus quod
              <lb/>
            ſuſtinetur in H. </s>
            <s xml:id="echoid-s1001" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1002" xml:space="preserve">Quieſcente igitur columnâ in duobus
              <lb/>
            punctis, &</s>
            <s xml:id="echoid-s1003" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1004" xml:space="preserve"/>
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