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

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          <p>
            <s xml:id="echoid-s2101" xml:space="preserve">
              <pb o="46" file="0088" n="94" rhead="PHYSICES ELEMENTA"/>
            poteſt. </s>
            <s xml:id="echoid-s2102" xml:space="preserve">In Cochleis attritus admodum eſt ſenſibilis, & </s>
            <s xml:id="echoid-s2103" xml:space="preserve">et-
              <lb/>
              <note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">211.</note>
            iam magni uſus; </s>
            <s xml:id="echoid-s2104" xml:space="preserve">nam eo machina in ſitu ſuo ſervatur, & </s>
            <s xml:id="echoid-s2105" xml:space="preserve">
              <lb/>
            actione corporum, quæ comprimuntur, aut gravitate pon-
              <lb/>
            derum quæ elevantur, ceſſante actione potentiæ, motu con-
              <lb/>
            trario non agitatur, & </s>
            <s xml:id="echoid-s2106" xml:space="preserve">ad priſtinum ſitum non redit.</s>
            <s xml:id="echoid-s2107" xml:space="preserve"/>
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        <div xml:id="echoid-div343" type="section" level="1" n="117">
          <head xml:id="echoid-head169" xml:space="preserve">SCHOLIUM I.</head>
          <head xml:id="echoid-head170" xml:space="preserve">De ligno findendo.</head>
          <p>
            <s xml:id="echoid-s2108" xml:space="preserve">Detur lignum, cujus partes jam ſeparatæ efficiant angulum EFL; </s>
            <s xml:id="echoid-s2109" xml:space="preserve">ſit hoc
              <lb/>
              <note position="left" xlink:label="note-0088-02" xlink:href="note-0088-02a" xml:space="preserve">212.</note>
            ulterius findendum ope cunei ACB, cujus baſis eſt AB, & </s>
            <s xml:id="echoid-s2110" xml:space="preserve">cujus alti-
              <lb/>
              <note position="left" xlink:label="note-0088-03" xlink:href="note-0088-03a" xml:space="preserve">TAB. VIII.
                <lb/>
              fig. 6.</note>
            tudinem menſurat CD.</s>
            <s xml:id="echoid-s2111" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2112" xml:space="preserve">Ubi partes, ut ſuperius monuimus, quantumvis parum ſeparantur, omnis
              <lb/>
            tollitur reſiſtentia; </s>
            <s xml:id="echoid-s2113" xml:space="preserve">antequam autem ſeparentur partes in F, puncta E, L,
              <lb/>
            paululum moveri debent, id eſt augendus eſt angulus E F L; </s>
            <s xml:id="echoid-s2114" xml:space="preserve">de-
              <lb/>
            terminaada ideò eſt vis, qua angulus hic augeri poteſt.</s>
            <s xml:id="echoid-s2115" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2116" xml:space="preserve">Ponamus angulum auctum, ut ſit e F l; </s>
            <s xml:id="echoid-s2117" xml:space="preserve">cuneus intravit, & </s>
            <s xml:id="echoid-s2118" xml:space="preserve">datur in a c b;
              <lb/>
            </s>
            <s xml:id="echoid-s2119" xml:space="preserve">partes ligni E, L, translatæ fuere per E e, L l, ſed quæ minus ab F diſtant
              <lb/>
            per minus ſpatium moventur, lineæque EF, LF, motibus ſuis deſeribunt
              <lb/>
            areas triangulorum æqualium inter ſe F E, l FL.</s>
            <s xml:id="echoid-s2120" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2121" xml:space="preserve">Ductis e f & </s>
            <s xml:id="echoid-s2122" xml:space="preserve">f F, parallelis EF & </s>
            <s xml:id="echoid-s2123" xml:space="preserve">e E, formetur parallelogrammum e E F f;
              <lb/>
            </s>
            <s xml:id="echoid-s2124" xml:space="preserve">ſunt æqualia triangula e F E & </s>
            <s xml:id="echoid-s2125" xml:space="preserve">f e F ; </s>
            <s xml:id="echoid-s2126" xml:space="preserve">& </s>
            <s xml:id="echoid-s2127" xml:space="preserve">parallelogrammum valet ambo
              <note symbol="*" position="left" xlink:label="note-0088-04" xlink:href="note-0088-04a" xml:space="preserve">34. El. 1.</note>
            angula e F E & </s>
            <s xml:id="echoid-s2128" xml:space="preserve">L F l conjuncta: </s>
            <s xml:id="echoid-s2129" xml:space="preserve">ideò translationes memoratæ linearum
              <lb/>
            ambarum EF, LF, conjunctæ, valent translationem ſolius lineæ E F per ſpa-
              <lb/>
            tium E e aut F f: </s>
            <s xml:id="echoid-s2130" xml:space="preserve">quæ lineola ergo diſtantiam repræſentat, qua partes ligni à
              <lb/>
            ſe invicem ſeparantur, cum autem de hac ſeparatione hìc agatur, eſt hæci-
              <lb/>
            pſa lineola ſpatium, ab obſtaculo quod ſuperandum eſt, percurſum, dum
              <lb/>
            ſpatium, quod percurrit potentia, eſt C c, ſpatium nempe per quod cuneus
              <lb/>
            fuit tranſlatum.</s>
            <s xml:id="echoid-s2131" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2132" xml:space="preserve">Vis ergo, qua cuneus intruditur, eſt ad ligni reſiſtentiam, quando æquè pol-
              <lb/>
            lent, ut e E ad C c. </s>
            <s xml:id="echoid-s2133" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">112.</note>
          <p>
            <s xml:id="echoid-s2134" xml:space="preserve">Ducatur C g ipſi E e parallela, erunt hæ lineæ æquales , quia motu
              <note symbol="*" position="left" xlink:label="note-0088-06" xlink:href="note-0088-06a" xml:space="preserve">34. El. 1.</note>
            latus cunei AG fuit tranſlatum;</s>
            <s xml:id="echoid-s2135" xml:space="preserve">ratio memorata eſt ergo quæ datur inter g C&</s>
            <s xml:id="echoid-s2136" xml:space="preserve">Cc.</s>
            <s xml:id="echoid-s2137" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2138" xml:space="preserve">Lineola E e, ideò etiam g C, perpendicularis eſt ad F E;</s>
            <s xml:id="echoid-s2139" xml:space="preserve">eſt enim E e arcus cir-
              <lb/>
            culi, adeo exiguus ut pro rectâ lineâ haberi poſſit; </s>
            <s xml:id="echoid-s2140" xml:space="preserve">cujus circuli radius eſt
              <lb/>
            F E.</s>
            <s xml:id="echoid-s2141" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2142" xml:space="preserve">Per punctum baseos medium D linea ducatur DH, ad latus AC cunei per-
              <lb/>
              <note position="left" xlink:label="note-0088-07" xlink:href="note-0088-07a" xml:space="preserve">213.</note>
            veniens in H & </s>
            <s xml:id="echoid-s2143" xml:space="preserve">cum FE latere ligni ſeparato, continuato, angulum efficiens re-
              <lb/>
            ctum; </s>
            <s xml:id="echoid-s2144" xml:space="preserve">quare ipſi Cg parallela eſt.</s>
            <s xml:id="echoid-s2145" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2146" xml:space="preserve">Propter latera c C, CD, in eadem linea, & </s>
            <s xml:id="echoid-s2147" xml:space="preserve">reliqua parallela, ſunt ſimilia
              <lb/>
            triangula C gc, DHC; </s>
            <s xml:id="echoid-s2148" xml:space="preserve">idcirco DH ſe babet ad DC, id eſt altitudinem cu-
              <lb/>
            nei, ut g C ad C c, id eſt, ut vis qua cuneus intruditur ad ligni reſiſtentiam, quan-
              <lb/>
            do neutra alteram vincere poteſt, auctâ paulum potentiâ ſeparantur ligni par-
              <lb/>
            tes.</s>
            <s xml:id="echoid-s2149" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2150" xml:space="preserve">Quando ligni partes non ſeparantur, niſi quo uſque cuneus intruditur, lineæ AC
              <lb/>
              <note position="left" xlink:label="note-0088-08" xlink:href="note-0088-08a" xml:space="preserve">214.</note>
            & </s>
            <s xml:id="echoid-s2151" xml:space="preserve">EF con veniunt, & </s>
            <s xml:id="echoid-s2152" xml:space="preserve">angulus DHC eſt rectus, ideoque ſimilia ſunt </s>
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