Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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              <pb o="7" file="0037" n="37" rhead="MATHEMATICA, LIB. I. CAP. IV."/>
            ut nullus ſit in eo porus cujus diameter minimam datam ſu-
              <lb/>
            peret lineam. </s>
            <s xml:id="echoid-s606" xml:space="preserve">Quod ut demonſtremus, ſpatium implendum,
              <lb/>
            diviſum concipimus in cellulas cubicas, quarum latera æqua-
              <lb/>
            lia aut minora ſint minimâ lineâ datâ: </s>
            <s xml:id="echoid-s607" xml:space="preserve">numerus cellularum
              <lb/>
            finitus erit, & </s>
            <s xml:id="echoid-s608" xml:space="preserve">in tot partes arenula data dividi poterit, quot
              <lb/>
            cellulæ dantur; </s>
            <s xml:id="echoid-s609" xml:space="preserve">ita ut in ſingulis cellulis particulam unam
              <lb/>
            poſitam concipere poſſimus: </s>
            <s xml:id="echoid-s610" xml:space="preserve">concipiendum ulterius ex ſin-
              <lb/>
            gulis hiſce particulis minimis globum cavum formari. </s>
            <s xml:id="echoid-s611" xml:space="preserve">Pro-
              <lb/>
            pter materiæ diviſibilitatem poteſt globus cavus ſemper au-
              <lb/>
            geri minuendo materiæ craſſitiem, cum autem in ſingulis
              <lb/>
            cellulis globus talis detur, poterunt ſinguli augeri, donec
              <lb/>
            vicini ſeſe mutuo tangant, ut omnes ſimul ſpatium impleant.</s>
            <s xml:id="echoid-s612" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s613" xml:space="preserve">Objectiones præcipuæ, contra diviſibilitatem materiæ in
              <lb/>
              <note position="right" xlink:label="note-0037-01" xlink:href="note-0037-01a" xml:space="preserve">24.</note>
            infinitum, ſunt, infinitum finito contineri non poſſe; </s>
            <s xml:id="echoid-s614" xml:space="preserve">ex di-
              <lb/>
            viſibilitate in infinitum ſequi, omnia corpora eſſe æqualia,
              <lb/>
            aut infinitum alio infinito majus dari.</s>
            <s xml:id="echoid-s615" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s616" xml:space="preserve">Sed hiſce reſponſio facilis eſt, infinito non tribuendæ ſunt
              <lb/>
            proprietates quantitatis finitæ & </s>
            <s xml:id="echoid-s617" xml:space="preserve">determinatæ. </s>
            <s xml:id="echoid-s618" xml:space="preserve">Partes infinite
              <lb/>
            parvas, numero infinito, in quantitate finita darinon poſle, quis
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            unquam probavit; </s>
            <s xml:id="echoid-s619" xml:space="preserve">ut & </s>
            <s xml:id="echoid-s620" xml:space="preserve">omnia infinita eſſe æqualia? </s>
            <s xml:id="echoid-s621" xml:space="preserve">Con-
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            trarium in Scholio ſequenti demonſtratur.</s>
            <s xml:id="echoid-s622" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s623" xml:space="preserve">Si, examinatâ poſſibili materia diviſibilitate, partium ſub-
              <lb/>
              <note position="right" xlink:label="note-0037-02" xlink:href="note-0037-02a" xml:space="preserve">25.</note>
            tilitatem in corporibus ad examen revocemus, hanc captum
              <lb/>
            noſtrum in immenſumſuperare conſtabit; </s>
            <s xml:id="echoid-s624" xml:space="preserve">innumeraque in re-
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            rum natura dantur exempla talium particularum a ſe invicem
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            ſeparatarum.</s>
            <s xml:id="echoid-s625" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s626" xml:space="preserve">Boileus hæc variis probat argumentis.</s>
            <s xml:id="echoid-s627" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s628" xml:space="preserve">Loquitur de filo ſerico trecentis ulnis Anglicanis longo & </s>
            <s xml:id="echoid-s629" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0037-03" xlink:href="note-0037-03a" xml:space="preserve">26.</note>
            ponderis duorum granorum cum ſemiſſe.</s>
            <s xml:id="echoid-s630" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s631" xml:space="preserve">Folia auri menſuravit, & </s>
            <s xml:id="echoid-s632" xml:space="preserve">ponderavit, & </s>
            <s xml:id="echoid-s633" xml:space="preserve">reperit quinqua-
              <lb/>
              <note position="right" xlink:label="note-0037-04" xlink:href="note-0037-04a" xml:space="preserve">27.</note>
            ginta pollices quadratos unicum tantum ponderare granum;
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            </s>
            <s xml:id="echoid-s634" xml:space="preserve">ſi unius pollicis longitudo dividatur in ducentas partes, omnes
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            oculo diſtingui poterunt, dantur ergo in pollice quadrato
              <lb/>
            partes viſibiles quadraginta millia, & </s>
            <s xml:id="echoid-s635" xml:space="preserve">in uno auri grano par-
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            tium numerus eſt duarum millionum, quas partes viſibiles
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            adhuc poſſe dividi nemo negabit.</s>
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