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

List of thumbnails

< >
71
71 (71) 		72
72 (72)
73
73 (73) 		74
74 (74)
75
75 (75) 		76
76 (76)
77
77 (77) 		78
78
79
79 		80
80
< >
page |< < (76) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div360" type="section" level="1" n="257">
          <p>
            <s xml:id="echoid-s2505" xml:space="preserve">
              <pb o="76" file="527.01.076" n="76" rhead="2 L*IBER* S*TATICÆ*"/>
            dem ratione ſeſquitertia ſunt enim æquealti, ſimillima ratione BF cylindrus
              <lb/>
            rertii circumſcripti cujus centrum K erit du-
              <lb/>
              <figure xlink:label="fig-527.01.076-01" xlink:href="fig-527.01.076-01a" number="123">
                <image file="527.01.076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.076-01"/>
              </figure>
            plus, quarti verò cujus centrum I quadru-
              <lb/>
            plus. </s>
            <s xml:id="echoid-s2506" xml:space="preserve">poſito itaque imo cylindro 4 librarum,
              <lb/>
            ſecundus erit 3 ℔, tertius 2 ℔, ſummus de-
              <lb/>
            nique I ℔: </s>
            <s xml:id="echoid-s2507" xml:space="preserve">Pari ratione ſi imus inſcriptorum
              <lb/>
            ſit 3 librarum, ſecundus erit 2 ℔, ultimus ver
              <lb/>
            tici proximus I ℔. </s>
            <s xml:id="echoid-s2508" xml:space="preserve">Quæ cum ita ſint, & </s>
            <s xml:id="echoid-s2509" xml:space="preserve">cen-
              <lb/>
            tra cylindrorum, & </s>
            <s xml:id="echoid-s2510" xml:space="preserve">ipſorum ponderoſitas
              <lb/>
            nota, centrum gravitatis circumſcriptorum
              <lb/>
            cadet in L ut LE occupet {1/24} totius AD;
              <lb/>
            </s>
            <s xml:id="echoid-s2511" xml:space="preserve">Trium itidem inſcriptorum gravitatis centrum cadet in S, ut S E {1/24} totius A D
              <lb/>
            obtineat. </s>
            <s xml:id="echoid-s2512" xml:space="preserve">Quamobrem L & </s>
            <s xml:id="echoid-s2513" xml:space="preserve">S ab E rurſum æquidiſtant.</s>
            <s xml:id="echoid-s2514" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2515" xml:space="preserve">Verumenimvero ſi biſectio & </s>
            <s xml:id="echoid-s2516" xml:space="preserve">cylindrorum iſta ſiguratio continuentur, ut
              <lb/>
            octo datum conoïdale ambiantac ſeptem induant, diſtantia centrorum & </s>
            <s xml:id="echoid-s2517" xml:space="preserve">in-
              <lb/>
            ſcriptorum & </s>
            <s xml:id="echoid-s2518" xml:space="preserve">circumſcriptorum ſecabunt axem æquidiſtanter à puncto E, ab-
              <lb/>
            erunt enim {1/48} totius A D.</s>
            <s xml:id="echoid-s2519" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2520" xml:space="preserve">Denique ſi ſectio iſta viciſſim duplicetur ut ſedecim cylindri circumſcriban-
              <lb/>
            tur, & </s>
            <s xml:id="echoid-s2521" xml:space="preserve">quindecim intra includantur, nihilo ſecius centra gravitatis ſolidorum
              <lb/>
            inſcriptorum & </s>
            <s xml:id="echoid-s2522" xml:space="preserve">circumſcriptorum pari diſtantia ab E puncto utrimque diſta-
              <lb/>
            bant, videlicet {1/96} axis A D. </s>
            <s xml:id="echoid-s2523" xml:space="preserve">Atque adeò ſequens biſectio antecedentem di-
              <lb/>
            ſtantiam continuò bipartito ſecat, cujus conſecutionis veritatem & </s>
            <s xml:id="echoid-s2524" xml:space="preserve">neceſſita-
              <lb/>
            tem inductione continuatâ demonſtrarem, niſi brevitatis ſtudio ductus, cum
              <lb/>
            cuilibet in promptu ſit, iſtud omitterem.</s>
            <s xml:id="echoid-s2525" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2526" xml:space="preserve">Quamobrem E gravitatis centrum dati conoïdalis erit: </s>
            <s xml:id="echoid-s2527" xml:space="preserve">Enimverò ſi cen-
              <lb/>
            trum aliud ſumatur in ipſa E L aut E S tandem continua biſectione & </s>
            <s xml:id="echoid-s2528" xml:space="preserve">cylin-
              <lb/>
            drorum circumſcriptione & </s>
            <s xml:id="echoid-s2529" xml:space="preserve">inſcriptione eò devenitur ut centrum ſolidi ex cir-
              <lb/>
            cumſcriptis conflati deſcĕdat infra conoïdalis centrum; </s>
            <s xml:id="echoid-s2530" xml:space="preserve">vel inſcripti ſupra ejuſ-
              <lb/>
            dem conoïdalis centrũ adſcendat. </s>
            <s xml:id="echoid-s2531" xml:space="preserve">Quod impoſſibile per ſe clarum fuerit; </s>
            <s xml:id="echoid-s2532" xml:space="preserve">cum
              <lb/>
            enim ſolidum tale è cylindris circumſcriptis componi poſſit ut ejus à conoï-
              <lb/>
            dali differentia minor ſit quocunque ſolido, poſſit item tale ſolidum inſcribi,
              <lb/>
            utriuſque ab E puncto differentia tantulo utrimque intervallo aberit ut minus
              <lb/>
            nullum effingi poſſit. </s>
            <s xml:id="echoid-s2533" xml:space="preserve">Quamobrem eodem coïbunt in E. </s>
            <s xml:id="echoid-s2534" xml:space="preserve">Vnde efficitur E dati
              <lb/>
            conoïdalis gravitatis eſſe centrum.</s>
            <s xml:id="echoid-s2535" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2536" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2537" xml:space="preserve">Itaque conoïdalis gravitatis centrum invenimus. </s>
            <s xml:id="echoid-s2538" xml:space="preserve">Quod
              <lb/>
            feciſſe oportuit.</s>
            <s xml:id="echoid-s2539" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div363" type="section" level="1" n="258">
          <head xml:id="echoid-head272" xml:space="preserve">NOTA.</head>
          <p>
            <s xml:id="echoid-s2540" xml:space="preserve">Cum recta ab angulo trianguli ad medium oppoſitæ baſis educta per 4 pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s2541" xml:space="preserve">item ſecetur ratione dupla, conſequens eſt, ſimilem à centro æquidiſtan-
              <lb/>
            tiam iſtic ab inſcriptis & </s>
            <s xml:id="echoid-s2542" xml:space="preserve">circumſcriptis parallelogrammis argui, qualis hic in
              <lb/>
            cylindris adſcriptis demonſtrata eſt.</s>
            <s xml:id="echoid-s2543" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div364" type="section" level="1" n="259">
          <head xml:id="echoid-head273" xml:space="preserve">11 THE OREMA. 24 PROPOSITIO.</head>
          <head xml:id="echoid-head274" xml:space="preserve">Conoïdalis curtigravitatis centrum invenire.</head>
          <p>
            <s xml:id="echoid-s2544" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2545" xml:space="preserve">ABCD conoïdale curtum, baſis ima D C, ſumma A B, axis
              <lb/>
            verò EF. </s>
            <s xml:id="echoid-s2546" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2547" xml:space="preserve">Gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2548" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum