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

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        <div xml:id="echoid-div121" type="section" level="1" n="97">
          <p>
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              <pb o="24" file="527.01.024" n="24" rhead="*I* L*IBER* S*TATICÆ*"/>
            adferetur: </s>
            <s xml:id="echoid-s707" xml:space="preserve">Eoq́uepoſito & </s>
            <s xml:id="echoid-s708" xml:space="preserve">conceſſo, H gravitatis centrum eſt corporis è co-
              <lb/>
            lumnâ, & </s>
            <s xml:id="echoid-s709" xml:space="preserve">duobus ponderibus I & </s>
            <s xml:id="echoid-s710" xml:space="preserve">K compoſiti, & </s>
            <s xml:id="echoid-s711" xml:space="preserve">ſuper eo centro quem de-
              <lb/>
            deris ſitum ſervabit per 4 definitionem, quod quovis in ſitu, in quo L M col-
              <lb/>
            locabitur, demonſtrari poterit.</s>
            <s xml:id="echoid-s712" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s713" xml:space="preserve">Denique I & </s>
            <s xml:id="echoid-s714" xml:space="preserve">K 1 ℔ pendentibus ſingulis, omnia inverti ita demonſtratur.
              <lb/>
            </s>
            <s xml:id="echoid-s715" xml:space="preserve">Perpendicularis per V, ut V Z, pendula gravitatis diameter eſt totius, eâ igi-
              <lb/>
            tur omiſsâ, totoq́ue è perpendiculari H Y, per H datum firmitudinis pun-
              <lb/>
            ctum, ſuſpenſo, ſegmentum A D I verſus ponderoſius erit illo, quod B C K
              <lb/>
            verſus eſt, ideoq́ue idem illud deorſum verget, donec H in pendulâ diame-
              <lb/>
            tro totius fuerit, & </s>
            <s xml:id="echoid-s716" xml:space="preserve">tametſi maximè L M (toto in H firmitudinis puncto mo-
              <lb/>
            to) ad horizontem N O parallela collocetur, iſtum tamen ſitum per 8 propo-
              <lb/>
            ſitionem non retinebit, ſed totum invertetur, quod nobis probandum fuit.</s>
            <s xml:id="echoid-s717" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s718" xml:space="preserve">C*ONCLVSIO.</s>
            <s xml:id="echoid-s719" xml:space="preserve">* Dato firmitudinis puncto notæ columnæ, &</s>
            <s xml:id="echoid-s720" xml:space="preserve">c.</s>
            <s xml:id="echoid-s721" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s722" xml:space="preserve">Satis ex antecedentibus liquet, quomodo in aliis procedendum operan-
              <lb/>
            dumq́ue ſit, ut in columnis quarum firmitudinis punctum extra G F lineam
              <lb/>
            eſt, ponderum puncta firmitudinis alio loco quam in C & </s>
            <s xml:id="echoid-s723" xml:space="preserve">D. </s>
            <s xml:id="echoid-s724" xml:space="preserve">Verumenim-
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            vero, quia cauſas qualitatum & </s>
            <s xml:id="echoid-s725" xml:space="preserve">affectionum libræ è fundamĕtis eruere & </s>
            <s xml:id="echoid-s726" xml:space="preserve">ape-
              <lb/>
            rire potiſſimum hic contendimus (qua de re in Statices exercitatione & </s>
            <s xml:id="echoid-s727" xml:space="preserve">praxi
              <lb/>
            fuſius dicetur) nulla admodum irregularium formarum exempla damus.</s>
            <s xml:id="echoid-s728" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div122" type="section" level="1" n="98">
          <head xml:id="echoid-head107" xml:space="preserve">6 PROBLEMA. 11 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s729" xml:space="preserve">Datis, notâ columnâ, notisq́; </s>
            <s xml:id="echoid-s730" xml:space="preserve">ponderibus inde ſuſpen-
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            ſis: </s>
            <s xml:id="echoid-s731" xml:space="preserve">invenire ſirmitudinis punctum, in quo quemlibet
              <lb/>
            datum ſitum ſervabit.</s>
            <s xml:id="echoid-s732" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div123" type="section" level="1" n="99">
          <head xml:id="echoid-head108" xml:space="preserve">1 NOTA.</head>
          <p style="it">
            <s xml:id="echoid-s733" xml:space="preserve">Si duorum æqualium ponderum, ut A, B, firmitudinis
              <lb/>
            puncta in columnæ axe ſint à centro E æquidi stantia, ut in
              <lb/>
              <figure xlink:label="fig-527.01.024-01" xlink:href="fig-527.01.024-01a" number="35">
                <image file="527.01.024-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.024-01"/>
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            istâ figurâ; </s>
            <s xml:id="echoid-s734" xml:space="preserve">dubium non eſt, quin E per ſecundam demen-
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            ſtrationis partem 10 propoſitionis, quæſitum ſit punctum.
              <lb/>
            </s>
            <s xml:id="echoid-s735" xml:space="preserve">Sed exemplum irregularis formæ esto.</s>
            <s xml:id="echoid-s736" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div125" type="section" level="1" n="100">
          <head xml:id="echoid-head109" xml:space="preserve">2 NOTA.</head>
          <p style="it">
            <s xml:id="echoid-s737" xml:space="preserve">Firmitudinis punctis ut C, D, duorum ponderum, item
              <lb/>
            anſæ ut E, in unâ rectâ lineâ conſtitutis, ut paulo ſupra, e{q́ue}
              <lb/>
            C, D ponderibus æquipondiis ſuſpenſis contingentis, ſive
              <lb/>
            cujuſlibet magnitudinis, E perpetuò firmitudinis punctum manere manifestum eſt, in
              <lb/>
            quo quemcunque dederis ſitum ſervabunt: </s>
            <s xml:id="echoid-s738" xml:space="preserve">& </s>
            <s xml:id="echoid-s739" xml:space="preserve">tribus istis punctis C, E, D in eadem
              <lb/>
            recta conſtitutis, C vero & </s>
            <s xml:id="echoid-s740" xml:space="preserve">D non æqualiter ab E diſtantibus, & </s>
            <s xml:id="echoid-s741" xml:space="preserve">deillis ſuſpenſis
              <lb/>
            ponderibus ad radios proportionalibus, E firmitudinis punctum nihilo minus manere
              <lb/>
            certum eſt, in quo datum ſitum ſervabunt.</s>
            <s xml:id="echoid-s742" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s743" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s744" xml:space="preserve">* A B C D columna 10 ℔ pendeat, cujus centrum gravitatis E,
              <lb/>
            pondera inde ſuſpenſa F 1 ℔, H 4 ℔ pendeant, firmitudinis punctum illius
              <lb/>
            G, hujus autem H.</s>
            <s xml:id="echoid-s745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s746" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s747" xml:space="preserve">* Inveniendum nobis firmitudinis punctum, in quo quem-
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            vis datum ſitum ſervant.</s>
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