Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
      <text>
        <body>
          <chap id="N2136B">
            <p id="N21AB5" type="main">
              <s id="N21ADA">
                <pb pagenum="280" xlink:href="026/01/314.jpg"/>
              motus circularis ratione eiuſdem radij, vel mobilis explicari per ſpatia
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              magis, vel minùs communicantia; </s>
              <s id="N21AE5">at verò velocitatem motus recti per
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              inſtantia maiora, & minora: </s>
              <s id="N21AEB">Sed hæc fusè in Metaphyſica explicabimus; </s>
              <s id="N21AEF">
                <lb/>
              neque hîc contendimus dari vel puncta, vel inſtantia; </s>
              <s id="N21AF4">ſed tantùm poſito
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              quod dentur, ita ſolui poſſe argumentum illud, quod vulgò ducitur ex
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              motu circulari, quo reuerâ puncta Mathematica non tamen phyſica pro­
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              fligantur: </s>
              <s id="N21AFE">ſimiliter ſolues argumentum illud vix triobolare, quo dicuntur
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              eſſe tot puncta in minore circulo, quot in maiore, eo quod iidem radij
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              vtrumque ſecent, quia ſi duo radij ad duo puncta immediata maioris
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              terminentur, penetrantur inadæquatè in ſectione minoris circuli; ſed
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              de hoc aliàs. </s>
            </p>
            <p id="N21B0A" type="main">
              <s id="N21B0C">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              19.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N21B18" type="main">
              <s id="N21B1A">
                <emph type="italics"/>
              Motus circularis poteſt eſſe velocior, & tardior in infinitum
                <emph.end type="italics"/>
              ; </s>
              <s id="N21B23">quia quocun­
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              que dato radio poteſt dari maior, & minor; </s>
              <s id="N21B29">immò poteſt compenſari
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              motus; </s>
              <s id="N21B2F">ſit enim radius EC diuiſus bifariam in H; </s>
              <s id="N21B33">certè ſi moueatur
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              EC circa centrum E; </s>
              <s id="N21B39">C mouebitur duplo velociùs quàm H, quia arcus
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              CN eſt duplus HT; </s>
              <s id="N21B3F">ſi tamen ſit radius AH; </s>
              <s id="N21B43">certè ſi poteſt moueri
                <lb/>
              æquè velociter, ſi enim aſſumatur H
                <foreign lang="grc">μ</foreign>
              æqualis HT, & percurrat H
                <foreign lang="grc">μ</foreign>
                <lb/>
              eo tempore, quo alter radius EC percurrit CN, motus erit æqualis; </s>
              <s id="N21B52">quia
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              arcus CN & H
                <foreign lang="grc">μ</foreign>
              ſunt æquales, vt conſtat: </s>
              <s id="N21B5C">poteſt etiam vectis longio­
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              ris extremitas moueri motu æquali cum extremitate minoris; </s>
              <s id="N21B62">ſi enim
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              H extremitas HE percurrit H
                <foreign lang="grc">μ</foreign>
              , & aſſumatur vectis duplus EC, diuida­
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              tur H
                <foreign lang="grc">μ</foreign>
              bifariam in T ducaturque ETN; </s>
              <s id="N21B72">certè ſi C conficiat CN co­
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              dem tempore, vtraque extremitas C & H æquè velociter mouebitur; </s>
              <s id="N21B78">ſi
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              autem duplicetur adhuc longitudo radij, diuidatur HT bifariam in X,
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              ducaturque linea, atque ita deinceps; quæ omnia ſunt trita. </s>
            </p>
            <p id="N21B80" type="main">
              <s id="N21B82">Ex his habes principium motus tardioris, & velocioris in infinitum; </s>
              <s id="N21B86">ſi
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              enim punctum H ſemper æquali tempore conficiat arcum H
                <foreign lang="grc">μ</foreign>
              ; </s>
              <s id="N21B90">certè
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              punctum C conficiet arcum C
                <foreign lang="grc">β</foreign>
              duplum prioris; </s>
              <s id="N21B9A">quia EC eſt dupla
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              EH; </s>
              <s id="N21BA0">ſi verò accipiatur tripla, conficiet triplum, atque ita deinceps; </s>
              <s id="N21BA4">ſed
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              poteſt vectis eſſe longior, & longior in infinitum; </s>
              <s id="N21BAA">igitur motus velo­
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              cior, & velocior; </s>
              <s id="N21BB0">ſi verò punctum C conficiat tantùm arcum CN æqua­
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              lem H
                <foreign lang="grc">μ</foreign>
              ; haud dubiè punctum H mouebitur duplò tardiùs, & ſi acci­
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              piatur vectis duplus CE, cuius extremitas percurrat arcum æqualem
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              CN, punctum H mouebitur quadruplò tardiùs, atque ita deinceps. </s>
            </p>
            <p id="N21BBE" type="main">
              <s id="N21BC0">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              20.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N21BCC" type="main">
              <s id="N21BCE">
                <emph type="italics"/>
              Motus circularis non eſt naturaliter acceleratus.
                <emph.end type="italics"/>
              </s>
              <s id="N21BD5"> Probatur, quia in infi­
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              nitum intenderetur, quod eſſet abſurdum in natura; </s>
              <s id="N21BDB">caret enim termino: </s>
              <s id="N21BDF">
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              non eſt difficultas pro motu circulari violento quo v.g. vertitur rota in
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              circulo verticali, vel mixto, quo ſcilicet lapis ſphæricus ita deſcendit, vt
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              circa ſuum centrum etiam voluatur, vel indifferenti, quo recta vertitur
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              in circulo horizontali; </s>
              <s id="N21BEC">quia nullum eſt principium accelerationis iſto­
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              rum motuum; </s>
              <s id="N21BF2">igitur eſt tantùm difficultas pro naturali circulari, quo </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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