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

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            <s xml:id="echoid-s400" xml:space="preserve">
              <pb file="0026" n="26" rhead="MONITUM"/>
            intellige evaneſcentes, & </s>
            <s xml:id="echoid-s401" xml:space="preserve">demonſtrationes nulli Mathematicæ demon-
              <lb/>
            ſtrationi firmitate cedent.</s>
            <s xml:id="echoid-s402" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s403" xml:space="preserve">Clarum etiam eſt in momento evaneſcentiæ fb & </s>
            <s xml:id="echoid-s404" xml:space="preserve">FB confundi
              <lb/>
            reveraque æquales eſſe, ergo in demonſtratione quacunque in qua
              <lb/>
            portionem curvæ bB infinite exiguam ponimus, quia hanc evane-
              <lb/>
            ſcentem intelligimus, tuto lineas ut fb, & </s>
            <s xml:id="echoid-s405" xml:space="preserve">FB pro æqualibus habemus.</s>
            <s xml:id="echoid-s406" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s407" xml:space="preserve">Demonſtrationes hæ diſtingui debent a demonſtrationibus in qui-
              <lb/>
            bus error, licet inſenſibilis, datur, qualis eſt demonſtratio n. </s>
            <s xml:id="echoid-s408" xml:space="preserve">1222.
              <lb/>
            </s>
            <s xml:id="echoid-s409" xml:space="preserve">ex qua deducimus ſonum, ſive majorem ſive minorem, eâdem ſemper
              <lb/>
            velocitate per eundem aërem moveri; </s>
            <s xml:id="echoid-s410" xml:space="preserve">quod Mathematice verum non
              <lb/>
            eſt, ſed differentia velocitatum, quando datur, ita exigua eſt, ut
              <lb/>
            nulla arte percipi poſſit, quare differentiam in Phyſicis negligimus; </s>
            <s xml:id="echoid-s411" xml:space="preserve">
              <lb/>
            eodem modo ac in praxi geometriæ, ubi montis altitudinem conſi-
              <lb/>
            deramus, hanc non pro mutata habebimus, quamvis arenula adjecta
              <lb/>
            ſit. </s>
            <s xml:id="echoid-s412" xml:space="preserve">In talibus autem demonſtrationibus non agitur de quantitatibus
              <lb/>
            infinitè exiguis, ſed de quantitatibus finitis; </s>
            <s xml:id="echoid-s413" xml:space="preserve">numero enim finito
              <lb/>
            non modo exprimi poteſt ratio inter arenulæ diametrum & </s>
            <s xml:id="echoid-s414" xml:space="preserve">montis
              <lb/>
            altitudinem, ſed & </s>
            <s xml:id="echoid-s415" xml:space="preserve">inter illam diametrum & </s>
            <s xml:id="echoid-s416" xml:space="preserve">telluris diametrum, aut
              <lb/>
            ſi velis diſtantiam ſtellæ fixæ cujuſcunque a Tellure.</s>
            <s xml:id="echoid-s417" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s418" xml:space="preserve">In hiſce demonſtrationibus in quibus pro æqualibus habemus quan-
              <lb/>
            titates, quæ tali inſenſibili quantitate differunt, error in demonſtra-
              <lb/>
            tione ſenſibilis non erit, & </s>
            <s xml:id="echoid-s419" xml:space="preserve">ideò, ubi de rebus ipſis agitur, de qui-
              <lb/>
            bus ſenſibus dijudicamus, demonſtrationes hæ a Mathematicis jure
              <lb/>
            admittuntur; </s>
            <s xml:id="echoid-s420" xml:space="preserve">ex Matheſi pura removentur, quæ tamen admittit,
              <lb/>
            ut demonſtravimus, demonſtrationes quæ infinitè exiguas, aut eva-
              <lb/>
            neſcentes, quantitates pro fundamento habent.</s>
            <s xml:id="echoid-s421" xml:space="preserve"/>
          </p>
          <figure number="6">
            <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01"/>
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