Bélidor, Bernard Forest de, La science des ingenieurs dans la conduite des travaux de fortification et d' architecture civile

Table of Notes

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              <s xml:id="echoid-s2742" xml:space="preserve">
                <pb o="33" file="0141" n="144" rhead="LIVRE II. DE LA MECANIQUE DES VOUTES."/>
              l’Ellipſe. </s>
              <s xml:id="echoid-s2743" xml:space="preserve">Par exemple, ſi on avoit quelque raiſon pour abaiſſer du
                <lb/>
              point H, pris ſur la courbe la perpendiculaire HI, à l’axe AB,
                <lb/>
              on pourra avec l’échelle trouver la valeur de la coupée DI, & </s>
              <s xml:id="echoid-s2744" xml:space="preserve">de
                <lb/>
              l’ordonnée IH, en pieds pouces & </s>
              <s xml:id="echoid-s2745" xml:space="preserve">lignes auſſi exactement qu’on
                <lb/>
              peut le déſirer dans la Pratique. </s>
              <s xml:id="echoid-s2746" xml:space="preserve">Nous allons faire uſage de tout
                <lb/>
              ceci.</s>
              <s xml:id="echoid-s2747" xml:space="preserve"/>
            </p>
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          <div xml:id="echoid-div193" type="section" level="2" n="34">
            <head xml:id="echoid-head147" xml:space="preserve">PROPOSITION PREMIERE.</head>
            <head xml:id="echoid-head148" xml:space="preserve">
              <emph style="sc">Proble’me</emph>
            .</head>
            <head xml:id="echoid-head149" style="it" xml:space="preserve">Trouver l’épaiſſeur qu’il faut donner aux piés-droits d’une
              <lb/>
            voûte Elliptique.</head>
            <p>
              <s xml:id="echoid-s2748" xml:space="preserve">31. </s>
              <s xml:id="echoid-s2749" xml:space="preserve">Comme la pouſſée d’une Voûte ſe fait toujours ſelon les di-
                <lb/>
                <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">
                  <emph style="sc">Fig</emph>
                . 8.</note>
              rections des tangentes menées à la courbe qu’elle forme, il faut com-
                <lb/>
              mencer par diviſer le quart d’Ellipſe BD, en deux également au
                <lb/>
              point L, pour mener à ce point la tangente LO, & </s>
              <s xml:id="echoid-s2750" xml:space="preserve">ſur l’extrêmité
                <lb/>
              L, lá perpendiculaire LA, qui étant prolongée juſqu’en F, parta-
                <lb/>
              gera comme à l’ordinaire la demi Voûte en deux parties à peu-près
                <lb/>
              égales; </s>
              <s xml:id="echoid-s2751" xml:space="preserve">alors la ligne FA, pourra être regardée comme le plan in-
                <lb/>
              cliné ſur lequel agit le vouſſoir FGDL, & </s>
              <s xml:id="echoid-s2752" xml:space="preserve">la ligne OL, comme la
                <lb/>
              direction de la puiſſance qui ſeroit en équilibre avec l’action du
                <lb/>
              même vouſſoir: </s>
              <s xml:id="echoid-s2753" xml:space="preserve">on ſera peut-être ſurpris que cette direction ne ſoit
                <lb/>
              pas perpendiculaire ſur le milieu du joint FL, comme dans lespro-
                <lb/>
              blémes précédents; </s>
              <s xml:id="echoid-s2754" xml:space="preserve">mais comme il falloit neceſſairement qu’elleré-
                <lb/>
              pondit au point L, pour avoir les lignes LK, LV, KA, nous avons
                <lb/>
              été obligé d’en uſer ainſi afin d’agir avec plus de préciſion, mais
                <lb/>
              nous y aurons égard dans l’application; </s>
              <s xml:id="echoid-s2755" xml:space="preserve">ainſi ſupoſant les autres li-
                <lb/>
              gnes tirées comme ci-devant, nous nommerons LK, a; </s>
              <s xml:id="echoid-s2756" xml:space="preserve">KA, b;
                <lb/>
              </s>
              <s xml:id="echoid-s2757" xml:space="preserve">LA, c; </s>
              <s xml:id="echoid-s2758" xml:space="preserve">BV, d; </s>
              <s xml:id="echoid-s2759" xml:space="preserve">BS, f; </s>
              <s xml:id="echoid-s2760" xml:space="preserve">MP, g; </s>
              <s xml:id="echoid-s2761" xml:space="preserve">ZB, y; </s>
              <s xml:id="echoid-s2762" xml:space="preserve">& </s>
              <s xml:id="echoid-s2763" xml:space="preserve">le vouſſoir CG, ou CE,
                <lb/>
              nn.</s>
              <s xml:id="echoid-s2764" xml:space="preserve"/>
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              <s xml:id="echoid-s2765" xml:space="preserve">Cela poſé, je conſidere que les triangles LKA & </s>
              <s xml:id="echoid-s2766" xml:space="preserve">LMN, étant
                <lb/>
              ſemblables donnent AK (b), LK (a):</s>
              <s xml:id="echoid-s2767" xml:space="preserve">: LM (y+d), MN({ay+ad/b})
                <lb/>
              par conſequent NP ſera {gb-ad-ay/b}, & </s>
              <s xml:id="echoid-s2768" xml:space="preserve">commelestriangles LKA
                <lb/>
              & </s>
              <s xml:id="echoid-s2769" xml:space="preserve">NOP, ſont encore ſemblables on aura auſſi LA(c), AK (b):</s>
              <s xml:id="echoid-s2770" xml:space="preserve">: NP
                <lb/>
              ({gb-ad-ay/b}), PO ({gb-ad-ay/c}) qui donne l’expreſſion du </s>
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