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

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          <pb file="0025" n="25" rhead="MONITUM"/>
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        <div xml:id="echoid-div10" type="section" level="1" n="9">
          <head xml:id="echoid-head31" style="it" xml:space="preserve">De Demonſtrationibus quæ quantitates in-
            <lb/>
          finitè exiguas pro fundamento habent.</head>
          <p>
            <s xml:id="echoid-s375" xml:space="preserve">IN multis demonſtrationibus, in ſcholiis datis, quantitates conſi-
              <lb/>
            deramus infinite exiguas, & </s>
            <s xml:id="echoid-s376" xml:space="preserve">ita haſce proponimus, ut & </s>
            <s xml:id="echoid-s377" xml:space="preserve">a le-
              <lb/>
            ctoribus intelligi poſſint, quibus illa, quæ de talibus quantitatibus
              <lb/>
            a Geometris fuere explicata, ignota ſunt. </s>
            <s xml:id="echoid-s378" xml:space="preserve">Ne autem ipſis ſcrupulus
              <lb/>
            ullus circa demonſtrationes in mente hæreat, & </s>
            <s xml:id="echoid-s379" xml:space="preserve">ne ſibi de talibus de-
              <lb/>
            monſtrationibus non exactam forment ideam, monitum præmittere
              <lb/>
            non inutile credidi.</s>
            <s xml:id="echoid-s380" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s381" xml:space="preserve">Sit curva quæcunque ABC; </s>
            <s xml:id="echoid-s382" xml:space="preserve">quam in B tangit linea DE; </s>
            <s xml:id="echoid-s383" xml:space="preserve">ſint
              <lb/>
              <note position="right" xlink:label="note-0025-01" xlink:href="note-0025-01a" xml:space="preserve">TAB. XLVII
                <lb/>
              fig. 5.</note>
            rectæ duæ quæcunque FB, fG, parallelæ, junctæ lineâ Ff; </s>
            <s xml:id="echoid-s384" xml:space="preserve">qua-
              <lb/>
            rum fG curvam ſecat in b; </s>
            <s xml:id="echoid-s385" xml:space="preserve">ſit etiam Hb parallela Ff, ſecans tangen-
              <lb/>
            tem DE in g. </s>
            <s xml:id="echoid-s386" xml:space="preserve">Si nunc concipiamus, Ff minui, id eſt lineam, fG
              <lb/>
            motu parallelo ferri, dum etiam, per interſectionem hujus lineæ
              <lb/>
            cum curva, motu parallelo fertur gbH, clarum eſt rationes inter
              <lb/>
            gB, gH, HB, non mutari, donec, coincidentibus fG, FB li-
              <lb/>
            neolæ omnes ſimul evaneſcant.</s>
            <s xml:id="echoid-s387" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s388" xml:space="preserve">In codem lineæ fG motu, rationes inter bB, bH, HB, con-
              <lb/>
            tinuò mutantur, donec ubi evanuere nullæ rationes dentur; </s>
            <s xml:id="echoid-s389" xml:space="preserve">in ipſo
              <lb/>
            autem momento evaneſcentiæ dantur rationes ab omnibus, quæ in
              <lb/>
            præcedentibus momentis locum habuere diverſæ.</s>
            <s xml:id="echoid-s390" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s391" xml:space="preserve">Sic corpus quod cadit, & </s>
            <s xml:id="echoid-s392" xml:space="preserve">libere cadendo continuò celerius move-
              <lb/>
            tur, ubi ad punctum quodcunque pervenit, velocitatem habet majo-
              <lb/>
            rem omnibus velocitatibus quas antequam ibi perveniret habuit, mi-
              <lb/>
            norem autem omnibus illis, quas babebit poſtquam punctum præter-
              <lb/>
            greſſum erit, peculiariſque eſt velocitas qua ad punctum appellit, ab
              <lb/>
            omnibusaliis, quibus ad puncta alia quæcunque pervenit, diverſa. </s>
            <s xml:id="echoid-s393" xml:space="preserve">Eodem
              <lb/>
            modo non agitur hîc de rationibus, quas habent quantitates ante eva-
              <lb/>
            neſcentiam, aut poſtquam evanuere, ſed quas habent dum evaneſcunt.</s>
            <s xml:id="echoid-s394" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s395" xml:space="preserve">In ipſo autem hoc momento evaneſcentiæ, quia curva in puncto
              <lb/>
            contactus cum tangente conincidit, confunduntur puncta G, g, b, & </s>
            <s xml:id="echoid-s396" xml:space="preserve">
              <lb/>
            rationes inter bB, bH, HB, non differunt a rationibus gB, gH,
              <lb/>
            HB, aut GB, GI, IB.</s>
            <s xml:id="echoid-s397" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s398" xml:space="preserve">Ubi in demonſtrationibus Bb infinitè exiguam ponimus, hanc
              <lb/>
            pro recta habemus, & </s>
            <s xml:id="echoid-s399" xml:space="preserve">memoratam æqualitatem rationum, etiam
              <lb/>
            ponimus: </s>
            <s xml:id="echoid-s400" xml:space="preserve">Hæc tamen Mathematicè vera non ſunt, niſi in momen-
              <lb/>
            to evaneſcentiæ ubi ergo loquimur de quantitatibus infinitè </s>
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