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

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        <div xml:id="echoid-div51" type="section" level="1" n="28">
          <pb o="8" file="0038" n="38" rhead="PHYSICES ELEMENTA"/>
          <p>
            <s xml:id="echoid-s637" xml:space="preserve">Octo granis auri deaurari poteſt integra argenti uncia,
              <lb/>
              <note position="left" xlink:label="note-0038-01" xlink:href="note-0038-01a" xml:space="preserve">28.</note>
            quæ deinde porrigitur in filum longitudinis tredecim millium
              <lb/>
            pedum.</s>
            <s xml:id="echoid-s638" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s639" xml:space="preserve">In corporibus odoriferis majorem adhuc partium percipi-
              <lb/>
              <note position="left" xlink:label="note-0038-02" xlink:href="note-0038-02a" xml:space="preserve">29.</note>
            mus ſubtilitatem & </s>
            <s xml:id="echoid-s640" xml:space="preserve">quidem a ſe invicem ſeparatarum, plura
              <lb/>
            longo tempore fere nihil ſui ponderis amittunt & </s>
            <s xml:id="echoid-s641" xml:space="preserve">ſpatium
              <lb/>
            fatis magnum particulis odoriferis continuo implent, qui
              <lb/>
            computum de tali ſubtilitate inire voluerit in illarum nume-
              <lb/>
            ro quid portenti facile reperiet.</s>
            <s xml:id="echoid-s642" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s643" xml:space="preserve">Ope microſcopiorum objecta quæ viſum fugiunt magna
              <lb/>
              <note position="left" xlink:label="note-0038-03" xlink:href="note-0038-03a" xml:space="preserve">30.</note>
            videntur, dantur animalcula per optima microſcopia vix vi-
              <lb/>
            ſibilia, habent tamen partes omnes ad vitam neceſſarias, ſan-
              <lb/>
            guinem, & </s>
            <s xml:id="echoid-s644" xml:space="preserve">alia liquida: </s>
            <s xml:id="echoid-s645" xml:space="preserve">ſubtilitas partium illa componentium
              <lb/>
            quanta ſit quis non videt?</s>
            <s xml:id="echoid-s646" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div62" type="section" level="1" n="29">
          <head xml:id="echoid-head65" xml:space="preserve">SCHOLIUM.</head>
          <head xml:id="echoid-head66" style="it" xml:space="preserve">De Materiæ Diviſibilitate</head>
          <p>
            <s xml:id="echoid-s647" xml:space="preserve">In finitum vocant quidam illud, quo non datur majus, & </s>
            <s xml:id="echoid-s648" xml:space="preserve">negant materiam,
              <lb/>
            eſſe diviſibilem in infinitum, quod, hac Infiniti data definitione, libenter
              <lb/>
            concedimus. </s>
            <s xml:id="echoid-s649" xml:space="preserve">Corpus in talem numerum partium, qui ſit omuium maximus,
              <lb/>
            non poſſe dividi, nullumque diviſionis dari limitem, defendimus.</s>
            <s xml:id="echoid-s650" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div63" type="section" level="1" n="30">
          <head xml:id="echoid-head67" style="it" xml:space="preserve">Infinitum finito contineri.</head>
          <p>
            <s xml:id="echoid-s651" xml:space="preserve">Infinitum eſt quod finitum ſuperat; </s>
            <s xml:id="echoid-s652" xml:space="preserve">partes autem numero, omnem finitum nu-
              <lb/>
              <note position="left" xlink:label="note-0038-04" xlink:href="note-0038-04a" xml:space="preserve">31.</note>
            merum ſuperante, in quantitate finita contineri, ex conſideratione progreſſionis
              <lb/>
            geometricæ decreſcentis deducitur.</s>
            <s xml:id="echoid-s653" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s654" xml:space="preserve">Progreſſionem hanc Ex gr. </s>
            <s xml:id="echoid-s655" xml:space="preserve">{1/2}, {1/4}, {1/8}, {1/16} &</s>
            <s xml:id="echoid-s656" xml:space="preserve">c. </s>
            <s xml:id="echoid-s657" xml:space="preserve">in infinitum poſſe continuari,
              <lb/>
            nullumque dari continuationis limitem quis non videt? </s>
            <s xml:id="echoid-s658" xml:space="preserve">Omnium tamen ter-
              <lb/>
            minorum ſummam nunquam excedere unitatem; </s>
            <s xml:id="echoid-s659" xml:space="preserve">imo exacte unitati æquari
              <lb/>
            demonſtramus, ſi revera in infinitum continuatam concipiamus progreſſio-
              <lb/>
            nem.</s>
            <s xml:id="echoid-s660" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s661" xml:space="preserve">Sit linea AE unitas; </s>
            <s xml:id="echoid-s662" xml:space="preserve">hujus dimidium AB eſt primus terminus {1/2}; </s>
            <s xml:id="echoid-s663" xml:space="preserve">BC di-
              <lb/>
              <note position="left" xlink:label="note-0038-05" xlink:href="note-0038-05a" xml:space="preserve">TAB. I.
                <lb/>
              fig 1.</note>
            midium reliqui eſt terminus ſecundus {1/4}; </s>
            <s xml:id="echoid-s664" xml:space="preserve">tertius terminus erit CD {1/8}; </s>
            <s xml:id="echoid-s665" xml:space="preserve">dividen-
              <lb/>
            do DE in duas partes æquales habetur terminus ſequens; </s>
            <s xml:id="echoid-s666" xml:space="preserve">& </s>
            <s xml:id="echoid-s667" xml:space="preserve">eodem modo
              <lb/>
            in infinitum continuari poteſt ſeries, ſemperque defectus ſummæ termino-
              <lb/>
            rum ſeriei AB, BC, CD, &</s>
            <s xml:id="echoid-s668" xml:space="preserve">c. </s>
            <s xml:id="echoid-s669" xml:space="preserve">ab integra linea AE ultimo termino ipſius
              <lb/>
            ſeriei æqualis erit quantumvis hæc continuetur. </s>
            <s xml:id="echoid-s670" xml:space="preserve">Quamdiu autem numerus
              <lb/>
            terminorum eſt finitus denominator fractionis, ultimum terminum exprimen-
              <lb/>
            tis, eſt numerus finitus, & </s>
            <s xml:id="echoid-s671" xml:space="preserve">ultimus terminus eſt pars finita, qua ſumma ſeriei
              <lb/>
            ab integra unitate deficit.</s>
            <s xml:id="echoid-s672" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s673" xml:space="preserve">Sivero numerus terminorum lomnem finitum numerum ſuperet, denomi-
              <lb/>
            nator ultimi termini omnem numerum finitum ſuperabit, partemque lineæ
              <lb/>
            AE exprimet omni parte finita minorem, ideoque differentia ſumman </s>
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