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

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              <pb o="193" file="0273" n="298" rhead="MATHEMATICA. LIB. I. CAP. XXIX."/>
            f g, noteturque diviſio in lamina de ad quam extremitas
              <lb/>
            g laminæ f g deſcendit. </s>
            <s xml:id="echoid-s7563" xml:space="preserve">Mutetur pondus P, & </s>
            <s xml:id="echoid-s7564" xml:space="preserve">ſit quatuor
              <lb/>
            librarum, duplicandum etiam eſt pondus, quo chorda infle-
              <lb/>
            ctitur, ut deſcendat g ad eandem diviſionem, & </s>
            <s xml:id="echoid-s7565" xml:space="preserve">pondus hoc
              <lb/>
            eſt duarum unciarum; </s>
            <s xml:id="echoid-s7566" xml:space="preserve">tres unciæ ad eandem inflexionem
              <lb/>
            requiruntur, quando pondus P eſt ſex librarum.</s>
            <s xml:id="echoid-s7567" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7568" xml:space="preserve">Ex hoc Experimento ſequitur, pondus, quo certa quan-
              <lb/>
              <note position="right" xlink:label="note-0273-01" xlink:href="note-0273-01a" xml:space="preserve">675.</note>
            titate producitur fibra, in variis gradibus tenſionis fibræ,
              <lb/>
            eandem cum tenſione rationem ſequi: </s>
            <s xml:id="echoid-s7569" xml:space="preserve">ſi dentur ex. </s>
            <s xml:id="echoid-s7570" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s7571" xml:space="preserve">tres
              <lb/>
            fibræ ejuſdem generis, longitudinis, & </s>
            <s xml:id="echoid-s7572" xml:space="preserve">craſſitiei, quarum
              <lb/>
            tenſiones ſunt ut 1. </s>
            <s xml:id="echoid-s7573" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7574" xml:space="preserve">& </s>
            <s xml:id="echoid-s7575" xml:space="preserve">3.</s>
            <s xml:id="echoid-s7576" xml:space="preserve">; pondera quæcunque in eadem
              <lb/>
            proportione æqualiter producunt illas fibras.</s>
            <s xml:id="echoid-s7577" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7578" xml:space="preserve">Ejuſdem fibræ productiones minimæ ſunt inter ſe quam
              <lb/>
              <note position="right" xlink:label="note-0273-02" xlink:href="note-0273-02a" xml:space="preserve">676.</note>
            proxime ut vires quibus fibræ producuntur. </s>
            <s xml:id="echoid-s7579" xml:space="preserve">Detur ex.
              <lb/>
            </s>
            <s xml:id="echoid-s7580" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s7581" xml:space="preserve">fibra tenſa pondere centum unciarum, ſi ſeparatim
              <lb/>
            producatur viribus unius unciæ, duarum unciarum, & </s>
            <s xml:id="echoid-s7582" xml:space="preserve">tri-
              <lb/>
            um unciarum, productiones erunt quam proxime ut unum,
              <lb/>
            duo, & </s>
            <s xml:id="echoid-s7583" xml:space="preserve">tria , id eſt, unaquæque uncia ſuperaddita
              <note symbol="*" position="right" xlink:label="note-0273-03" xlink:href="note-0273-03a" xml:space="preserve">673.</note>
            æqualiter producit fibram: </s>
            <s xml:id="echoid-s7584" xml:space="preserve">nam tenſiones ponderibus 100.
              <lb/>
            </s>
            <s xml:id="echoid-s7585" xml:space="preserve">101. </s>
            <s xml:id="echoid-s7586" xml:space="preserve">& </s>
            <s xml:id="echoid-s7587" xml:space="preserve">102. </s>
            <s xml:id="echoid-s7588" xml:space="preserve">unciarum, quibus in ſingulis caſibus, quando
              <lb/>
            uncia ſuperadditur, tenditur fibra, parum inter ſe diffe-
              <lb/>
            runt.</s>
            <s xml:id="echoid-s7589" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7590" xml:space="preserve">Hæc fibrarum proprietas ad inflexionem ipſarum appli-
              <lb/>
              <note position="right" xlink:label="note-0273-04" xlink:href="note-0273-04a" xml:space="preserve">677.</note>
            cari poteſt, & </s>
            <s xml:id="echoid-s7591" xml:space="preserve">magni uſus eſt. </s>
            <s xml:id="echoid-s7592" xml:space="preserve">Inflectatur chorda AB, ita ut
              <lb/>
              <note position="right" xlink:label="note-0273-05" xlink:href="note-0273-05a" xml:space="preserve">
                <emph style="sc">TA. XXVI.</emph>
                <lb/>
              fig. 3.</note>
            ſitus A c B, A c B, & </s>
            <s xml:id="echoid-s7593" xml:space="preserve">ACB acquirat, ita tamen ut in maxima
              <lb/>
            inflexione ſagitta non ſit quartæ partis unius pollicis, po-
              <lb/>
            ſitâ chordæ longitudine duorum pedum cum ſemiſſe; </s>
            <s xml:id="echoid-s7594" xml:space="preserve">in
              <lb/>
            iſtis caſibus productiones chordæ ſunt admodum parvæ, er-
              <lb/>
            go in ratione virium, a quibus oriuntur , & </s>
            <s xml:id="echoid-s7595" xml:space="preserve">iſtas vires
              <note symbol="*" position="right" xlink:label="note-0273-06" xlink:href="note-0273-06a" xml:space="preserve">676.</note>
            ſignant; </s>
            <s xml:id="echoid-s7596" xml:space="preserve">denotet c D vim qua chorda non inflexa tenditur,
              <lb/>
            & </s>
            <s xml:id="echoid-s7597" xml:space="preserve">centro B deſcribatur circulus Dd; </s>
            <s xml:id="echoid-s7598" xml:space="preserve">lineæ dc, dc, dC, quæ
              <lb/>
            ſingulæ ſuperant lineam cD, quantitate, qua in ſingulis inflexio-
              <lb/>
            nibus fibra fuit producta, exprimunt vires integras, quibus in
              <lb/>
            ſingulis caſibus fibra tenditur. </s>
            <s xml:id="echoid-s7599" xml:space="preserve">Sed hic arcus D d vix eſt unius
              <lb/>
            gradus, & </s>
            <s xml:id="echoid-s7600" xml:space="preserve">D ſemper a puncto c ſatis diſtat, quare D d pro linea
              <lb/>
            recta ipſic C parallela haberi poteſt, & </s>
            <s xml:id="echoid-s7601" xml:space="preserve">lineæ cd, cd, C </s>
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