Fabri, Honoré, Tractatus physicus de motu locali, 1646
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N270EE">
            <p id="N29AB0" type="main">
              <s id="N29AF0">
                <pb pagenum="426" xlink:href="026/01/460.jpg"/>
              qualiter CI; </s>
              <s id="N29AF9">ſitque D centrum grauitatis trianguli BCI; </s>
              <s id="N29AFD">ſit E centrum
                <lb/>
              grauitatis ſectoris BCHI, ſitque vt ſectio FCHI, ad triangulum BEI,
                <lb/>
              ita DE ad EG, vel vt ſectio ad ſectorem, ita DE ad DG; G eſt centrum
                <lb/>
              grauitatis ſectionis, per p.7. </s>
            </p>
            <p id="N29B07" type="main">
              <s id="N29B09">His poſitis voluatur ſector AKHM, circa axem CB, perinde ſe ha­
                <lb/>
              bet circumactus, atque ſi ſingulis partibus incumberent rectæ, quæ eſſent
                <lb/>
              vt motus earumdem pretium, vt conſtat ex dictis; </s>
              <s id="N29B11">igitur ſit ſector AEF
                <lb/>
              D, æqualis priori, perinde ſe habet, atque ſolidum AEFDCB, quod
                <lb/>
              ſcilicet conſtat ex pyramide AEDCB, & ſegmento cylindri EFDCB; </s>
              <s id="N29B19">
                <lb/>
              pyramidis centrum grauitatis ſit I, ita vt IG ſit 1/4 GA, ſit M centrum
                <lb/>
              grauitatis ſegmenti ſolidi, ſeu potiùs ſit terminus perpendicularis deor­
                <lb/>
              ſum, quæ ducatur per centrum grauitatis eiuſdem ſolidi; </s>
              <s id="N29B22">diuidatur IM
                <lb/>
              in N, ita vt IN ſit ad NM, vt ſegmentum cylindri GEFDCB, ad
                <lb/>
              pyramidem AEDCB; certè N eſt centrum grauitatis ſolidi AEFDCHB,
                <lb/>
              per p.7. igitur N eſt centrum percuſſionis ſectoris circumacti. </s>
            </p>
            <p id="N29B2C" type="main">
              <s id="N29B2E">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              14.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N29B3A" type="main">
              <s id="N29B3C">
                <emph type="italics"/>
              Si
                <emph.end type="italics"/>
                <emph type="italics"/>
              ſector AKHM voluatur circa Tangentem NHL, determinari
                <lb/>
              poteſt centrum percuſſionis eodem modo
                <emph.end type="italics"/>
              ; </s>
              <s id="N29B4D">nam aſſumi poteſt cuneus, vt ſuprà,
                <lb/>
              cuius baſis ſit ſegmentum cylindri; </s>
              <s id="N29B53">tùm pyramis cum eadem baſi; </s>
              <s id="N29B57">tùm in­
                <lb/>
              ueniri centrum grauitatis vtriuſque; </s>
              <s id="N29B5D">tùm detracta pyramide ex cuneo,
                <lb/>
              haberi reſiduum ſolidum, cuius centrum grauitatis inuenietur, iuxta prę­
                <lb/>
              dictam praxim; quippe hoc erit centrum percuſſionis quæſitum. </s>
            </p>
            <p id="N29B65" type="main">
              <s id="N29B67">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              15.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N29B73" type="main">
              <s id="N29B75">
                <emph type="italics"/>
              Si voluatur
                <emph.end type="italics"/>
                <emph type="italics"/>
              triangulum FBH circa FM, in quam cadit HF perpen­
                <lb/>
              diculariter: </s>
              <s id="N29B83">ſi aſſumatur NH
                <emph.end type="italics"/>
              1/4
                <emph type="italics"/>
              FI, ducaturque NP parallela HB, ſe­
                <lb/>
              cans FC in O, dico punctum O eſſe centrum percuſſionis
                <emph.end type="italics"/>
              ; quod eodem modo
                <lb/>
              probatur quo ſuprà Th.11. </s>
            </p>
            <p id="N29B95" type="main">
              <s id="N29B97">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              16.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N29BA3" type="main">
              <s id="N29BA5">
                <emph type="italics"/>
              Si voluatur quodlibet triangulum circa angulum rectum, determinari pe­
                <lb/>
              test centrum percuſſionis
                <emph.end type="italics"/>
              ; </s>
              <s id="N29BB0">ſit enim triangulum ABC; </s>
              <s id="N29BB4">ducatur quælibet
                <lb/>
              linea Tangens angulum, v.g. DBE, circa quam voluatur triangulum, du­
                <lb/>
              cantur AE, CD perpendiculares AD; </s>
              <s id="N29BBE">aliæ duæ ipſis æquales AFCG,
                <lb/>
              perpendicularis in AC; </s>
              <s id="N29BC4">tùm FG connectantur; </s>
              <s id="N29BC8">eleueturque Trapezus
                <lb/>
              AG, donec AF, CG incubent perpendiculariter plano ABC; </s>
              <s id="N29BCE">denique
                <lb/>
              à B ducantur rectæ ad omnia puncta Trapezi erecti, habebitur pyramis,
                <lb/>
              cuius centrum grauitatis, dabit centrum percuſſionis quæſitum, per Th.
                <lb/>
              11. quod vt fiat, inueniatur centrum grauitatis Trapezi AG, modo di­
                <lb/>
              cto, ducta ſcilicet FC, aſſumptoque I centro grauitatis trianguli FGC
                <lb/>
              & L centro grauitatis trianguli FAC; </s>
              <s id="N29BDD">ſi enim ducatur LI, ſitque LI
                <lb/>
              ad LP, vt Trapezium AG, ad triangulum FGC; </s>
              <s id="N29BE3">certè P eſt centrum
                <lb/>
              grauitatis Trapezij per p.7. tùm ex P erecto ducatur recta ad B, hæc erit
                <lb/>
              axis pyramidis; </s>
              <s id="N29BEB">porrò ſi ducatur perpendicularis PO; </s>
              <s id="N29BEF">tùm BO habebi-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum