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

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        <div xml:id="echoid-div661" type="section" level="1" n="471">
          <p>
            <s xml:id="echoid-s4825" xml:space="preserve">
              <pb o="167" file="527.01.167" n="167" rhead="*DE* S*PARTOSTATICA.*"/>
            diſtendatur concludes. </s>
            <s xml:id="echoid-s4826" xml:space="preserve">ac pari ratione quo pondere reliquæ C D, C E diſti-
              <lb/>
            neantur cognoſces.</s>
            <s xml:id="echoid-s4827" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4828" xml:space="preserve">Præterea ſi hæ retinaculorum lineæ in alias inſuper lineas diducantur, pon-
              <lb/>
            dus quo ipſarum unaquæque diſtenditur, conſimiliter 9 conſectario conclu-
              <lb/>
            detur.</s>
            <s xml:id="echoid-s4829" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div663" type="section" level="1" n="472">
          <head xml:id="echoid-head500" xml:space="preserve">11 C*ONSECTARIUM.*</head>
          <p>
            <s xml:id="echoid-s4830" xml:space="preserve">Si quatuor lineæ adidem punctum cohæreſcant, cujuſmodi antecedenti cõ-
              <lb/>
            ſectario tres, propoſitio hæc unam certamq́ue determinationem non habet.
              <lb/>
            </s>
            <s xml:id="echoid-s4831" xml:space="preserve">Sic A, B, C, D tanquam ſuprema linearum, è quibus pondus dependet,
              <lb/>
            puncta intelligantor. </s>
            <s xml:id="echoid-s4832" xml:space="preserve">lam pendula ejus diameter vel incidet in rectam A D, vel
              <lb/>
            extra ipſam intra trian gulum A D B, vel intra A D C (fieri enim non poteſt ut in
              <lb/>
            ambitu quadranguli A B C D cadat, nedum extra) ſi incidat in A D, conſtat
              <lb/>
            rectas ad B & </s>
            <s xml:id="echoid-s4833" xml:space="preserve">C pertingentes, potentiam quâ iſtæ ſub A & </s>
            <s xml:id="echoid-s4834" xml:space="preserve">D diſtenduntur
              <lb/>
            quiddam allevare; </s>
            <s xml:id="echoid-s4835" xml:space="preserve">ſed cùm triangulũ dua-
              <lb/>
            rum iſtarum linearum quæ ſub A, B, con-
              <lb/>
              <figure xlink:label="fig-527.01.167-01" xlink:href="fig-527.01.167-01a" number="227">
                <image file="527.01.167-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.167-01"/>
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            ſiſtunt & </s>
            <s xml:id="echoid-s4836" xml:space="preserve">tertiæ A D, nullam admittat mu-
              <lb/>
            tationem varietatemvé, diverſę & </s>
            <s xml:id="echoid-s4837" xml:space="preserve">multipli-
              <lb/>
            ces potĕtiæ, ad C & </s>
            <s xml:id="echoid-s4838" xml:space="preserve">B adjungi poſſunt quę
              <lb/>
            linearũ ſub A, D diſtenſionem immutent,
              <lb/>
            manente tamen eâdĕ datæ formæ diſpoſi-
              <lb/>
            tione, adeò ut certa ſingularũ partium de-
              <lb/>
            terminatio nulla hic inveniri poſſit Cumautem pendula gravitatis diameter in
              <lb/>
            E intra triangulum A D B cadet, tum quarta C à mutatione ſitus ponderum
              <lb/>
            quæ ad A, B, C pertinent planè erit immunis. </s>
            <s xml:id="echoid-s4839" xml:space="preserve">ex quibus efficitur propoſitio-
              <lb/>
            nem hujuſmodinullam partium ratam determinationem admittere.</s>
            <s xml:id="echoid-s4840" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4841" xml:space="preserve">Advertendum autem inſuper, cùm quatuor lineæ certam aliquam determi-
              <lb/>
            nationem reſpuant, multò firmioriratione complurium linearum concluſio-
              <lb/>
            nem incertam eſſe. </s>
            <s xml:id="echoid-s4842" xml:space="preserve">Similiq́ue ratione, cum 9 conſectario demonſtratum ſit,
              <lb/>
            tres lineas in eodem plano nullam certam cõcluſionem habere, etiam quatuor,
              <lb/>
            aliasq́ue plures longè minùs determinatione aliqua certa circumſcribi.</s>
            <s xml:id="echoid-s4843" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div665" type="section" level="1" n="473">
          <head xml:id="echoid-head501" xml:space="preserve">NOTATO</head>
          <p>
            <s xml:id="echoid-s4844" xml:space="preserve">Corpus etiam modo ab 11 conſectario diverſo è tribus lineis depĕdere poſſe,
              <lb/>
            cùm ſcilicet tribus diſtantibus locis ipſæ corpori affigentur, ut continuatæ ta-
              <lb/>
            men in eodem puncto non concurrant; </s>
            <s xml:id="echoid-s4845" xml:space="preserve">quod per 25 propoſ. </s>
            <s xml:id="echoid-s4846" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4847" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4848" xml:space="preserve">ſide duabus
              <lb/>
            tantum lineis ſuſpendantur neceſſariò cõtingit. </s>
            <s xml:id="echoid-s4849" xml:space="preserve">Sed quâ viâ inveniatur pondus
              <lb/>
            iſtarum unicuique debitum, nondum etiam, dum hæctypis excuderentur, aſſe-
              <lb/>
            cutus eram: </s>
            <s xml:id="echoid-s4850" xml:space="preserve">ſi quid vel à meipſo, vel ab alio quopiam hoc problema juvabi-
              <lb/>
            tur, id temporis proceſſu fiet palam.</s>
            <s xml:id="echoid-s4851" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div666" type="section" level="1" n="474">
          <head xml:id="echoid-head502" xml:space="preserve">12 C*ONSECTARIUM.*</head>
          <p>
            <s xml:id="echoid-s4852" xml:space="preserve">Ponderis igitur ab unâlineâ ſuſpenſi, ex qua deinde duæ treſvé aliæ in partes
              <lb/>
            diverſas diſtractæ exiſtant, ratio hujuſmodi fuit; </s>
            <s xml:id="echoid-s4853" xml:space="preserve">unde affectiones Staticæ dua-
              <lb/>
            rum triumvé itidem linearum, eidem ponderi affixarum & </s>
            <s xml:id="echoid-s4854" xml:space="preserve">ſurſum tendentium,
              <lb/>
            inq́ue idem pendulæ gravitatis diametri punctum incurrentium, in procinctu
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s4855" xml:space="preserve">enimverò A B pondus eſto, de duabus lineis D C, E C ſuſpenſum, inq́
              <lb/>
            C puncto concurrunto, pendulaq́ue diameter F C. </s>
            <s xml:id="echoid-s4856" xml:space="preserve">quantum igitur </s>
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