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-s2389" xml:space="preserve">
                <pb o="19" file="0127" n="130" rhead="LIVRE II. DE LA MECANIQUE DES VOUTES."/>
              „de l’hipotenuſe NP; </s>
              <s xml:id="echoid-s2390" xml:space="preserve">pour avoir la pouſſée de la Voûte par raport
                <lb/>
              „au point d’apui P, ſans être obligé de faire aucune analogie; </s>
              <s xml:id="echoid-s2391" xml:space="preserve">c’eſt ce
                <lb/>
              que nous ſuivrons à l’avenir pour abreger les opérations; </s>
              <s xml:id="echoid-s2392" xml:space="preserve">mais „l’on
                <lb/>
              „fera attention que ceci n’a lieu que quand il eſt queſtion d’une
                <lb/>
              „Voûte en plein ceintre.</s>
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          <div xml:id="echoid-div164" type="section" level="2" n="15">
            <head xml:id="echoid-head125" xml:space="preserve">Remarque quatriéme.</head>
            <p>
              <s xml:id="echoid-s2394" xml:space="preserve">16. </s>
              <s xml:id="echoid-s2395" xml:space="preserve">L’on remarquera encore, que (ſi l’on vouloit conſtruire un
                <lb/>
                <note position="right" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">
                  <emph style="sc">Planch</emph>
                .
                  <lb/>
                3.
                  <lb/>
                  <emph style="sc">Fig</emph>
                . 2.</note>
              édifice où l’on ſeroit obligé de faire pluſieurs Voûtes les unes ſur
                <lb/>
              les autres ſoûtenuës par les mêmes piés-droits) il n’y auroit pas plus
                <lb/>
              de difficulté à trouver l’epaiſſeur de ſes piés-droits, que l’on n’en
                <lb/>
              a eu dans les cas précédens; </s>
              <s xml:id="echoid-s2396" xml:space="preserve">il arrivera ſeulement que les calculs
                <lb/>
              ſeront un peu plus compoſés, comme on en va juger.</s>
              <s xml:id="echoid-s2397" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s2398" xml:space="preserve">Si l’on conſidere le profil repréſenté par la Figure 2. </s>
              <s xml:id="echoid-s2399" xml:space="preserve">l’on verra
                <lb/>
              qu’on y ſupoſe deux étages: </s>
              <s xml:id="echoid-s2400" xml:space="preserve">le premier, qui eſt couvert par deux
                <lb/>
              Voûtes de même grandeur, pourra être pris ſi l’on veut pour un
                <lb/>
              ſoûterain, au-deſſus duquel eſt un magaſin qui compoſe le ſecond
                <lb/>
              étage; </s>
              <s xml:id="echoid-s2401" xml:space="preserve">& </s>
              <s xml:id="echoid-s2402" xml:space="preserve">comme ce magaſin eſt couvert par une Voûte qui eſt ſoûte-
                <lb/>
              nuë par les mêmes piés-droits que celle du ſoûterrain, la pouſſée des
                <lb/>
              deux Voûtes répondra au même point d’apui P; </s>
              <s xml:id="echoid-s2403" xml:space="preserve">par conſéquent ſi
                <lb/>
              on diviſe les quarts de cercles BD & </s>
              <s xml:id="echoid-s2404" xml:space="preserve">WQ en deux également, & </s>
              <s xml:id="echoid-s2405" xml:space="preserve">
                <lb/>
              qu’on éleve aux points L & </s>
              <s xml:id="echoid-s2406" xml:space="preserve">X, les perpendiculaires LO & </s>
              <s xml:id="echoid-s2407" xml:space="preserve">XE, elles
                <lb/>
              répréſenteront comme à l’ordinaire la direction des puiſſances qui
                <lb/>
              ſoûtiendroient en équilibre la pouſſée des vouſſoirs LG & </s>
              <s xml:id="echoid-s2408" xml:space="preserve">XQ; </s>
              <s xml:id="echoid-s2409" xml:space="preserve">par
                <lb/>
              conſéquent, ſi du point d’apui P l’on abaiſſe ſur ces directions les
                <lb/>
              perpendiculaires PO & </s>
              <s xml:id="echoid-s2410" xml:space="preserve">PE, l’on aura d’une part le triangle LKA ſem-
                <lb/>
              blable à PON, & </s>
              <s xml:id="echoid-s2411" xml:space="preserve">de l’autre le triangle XIS ſemblable à PEH; </s>
              <s xml:id="echoid-s2412" xml:space="preserve">or
                <lb/>
              pour avoir la pouſſée des deux vouſſoirs LG & </s>
              <s xml:id="echoid-s2413" xml:space="preserve">XQ, on n’aura qu’à
                <lb/>
              multiplier la ſuperficie du premier LG par l’hipotenuſe NP du trian-
                <lb/>
              gle rectangle PON, & </s>
              <s xml:id="echoid-s2414" xml:space="preserve">celle du ſecond XQ par l’hipotenuſe PH
                <lb/>
              du triangle PEH, & </s>
              <s xml:id="echoid-s2415" xml:space="preserve">ajoûter ces deux produits enſemble; </s>
              <s xml:id="echoid-s2416" xml:space="preserve">ainſinom-
                <lb/>
              mant LV ou MZ, a; </s>
              <s xml:id="echoid-s2417" xml:space="preserve">BV, c; </s>
              <s xml:id="echoid-s2418" xml:space="preserve">ZP, d; </s>
              <s xml:id="echoid-s2419" xml:space="preserve">MP ſera a + d; </s>
              <s xml:id="echoid-s2420" xml:space="preserve">& </s>
              <s xml:id="echoid-s2421" xml:space="preserve">ZB étant
                <lb/>
              toûjours y, ML ou MN ſera y + c; </s>
              <s xml:id="echoid-s2422" xml:space="preserve">par conſéquent NP ſera a + d
                <note symbol="*" position="right" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">Art. 15.</note>
              - c - y; </s>
              <s xml:id="echoid-s2423" xml:space="preserve">& </s>
              <s xml:id="echoid-s2424" xml:space="preserve">ſi l’on ſupoſe pour abreger a + d - c = f, NP ſera
                <lb/>
              f - y qui étant multiplié par nn ſuperficie du vouſſoir LG, l’on aura
                <lb/>
              nnf - nny pour le premier produit (c’eſt-à-dire) pour l’expreſſion
                <lb/>
              de la pouſſée de la Voûte ſuperieure, de même ſi on nomme Wr
                <lb/>
              b; </s>
              <s xml:id="echoid-s2425" xml:space="preserve">& </s>
              <s xml:id="echoid-s2426" xml:space="preserve">RP: </s>
              <s xml:id="echoid-s2427" xml:space="preserve">h; </s>
              <s xml:id="echoid-s2428" xml:space="preserve">RX ou RH ſera y + b, par conſéquent HP ſera h - b
                <lb/>
              - y, Et ſupoſant encore pour abreger h - b = p HP ſera p - y
                <lb/>
              qui étant multiplié par la ſuperficie du vouſſoir XQ que nous nom-
                <lb/>
              merons qq, l’on aura pqq - qqy pour le ſecond produit, ou ſi l’on </s>
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