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

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        <div xml:id="echoid-div94" type="section" level="1" n="61">
          <pb o="48" file="0074" n="76" rhead="LA SCIENCE DES INGENIEURS,"/>
        </div>
        <div xml:id="echoid-div95" type="section" level="1" n="62">
          <head xml:id="echoid-head76" xml:space="preserve">PROPOSITION TROISIE’ME.</head>
          <head xml:id="echoid-head77" xml:space="preserve">
            <emph style="sc">Proble’me</emph>
          </head>
          <p style="it">
            <s xml:id="echoid-s1228" xml:space="preserve">38. </s>
            <s xml:id="echoid-s1229" xml:space="preserve">Voulant augmenter l’épaiſſeur d’un revêtement qui
              <lb/>
            ſeroit en équilibre avec la pouſſée des Terres, on demande de
              <lb/>
            combien la réſiſtance de ce revêtement deviendra plus forte
              <lb/>
            qu’elle n’étoit par rapport à l’augmentation qu’on veut faire.</s>
            <s xml:id="echoid-s1230" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1231" xml:space="preserve">Pour réſoudre ce Probléme, nous ſupoſerons que a, exprime l’é-
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            paiſſeur au ſommet d’un revêtement quelconque, quand la réſiſtance
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            du Mur eſt égale à la pouſſée des Terres, & </s>
            <s xml:id="echoid-s1232" xml:space="preserve">que m, exprime la nouvel-
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            le épaiſſeur compoſée de la premiere & </s>
            <s xml:id="echoid-s1233" xml:space="preserve">de l’augmentation propo-
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            ſée; </s>
            <s xml:id="echoid-s1234" xml:space="preserve">cela poſé, ſi dans le premier membre de l’équation yy + 2dy
              <lb/>
            + {2dd/3} = 2bf, (où nous avons vû Art. </s>
            <s xml:id="echoid-s1235" xml:space="preserve">22. </s>
            <s xml:id="echoid-s1236" xml:space="preserve">que le poids étoit en
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            équilibre avec la puiſſance) l’on met a, au lieu de y, l’on aura
              <lb/>
            aa + 2da + {2dd/3} pour la réſiſtance dont le revêtement eſt capable
              <lb/>
            étant en équilibre avec la pouſſée des Terres; </s>
            <s xml:id="echoid-s1237" xml:space="preserve">& </s>
            <s xml:id="echoid-s1238" xml:space="preserve">mettant encore
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            m, à la place de y, dans la même équation, l’on aura mm + 2dm
              <lb/>
            + {2dd/3} pour la réſiſtance du revêtement après avoir augmenté
              <lb/>
            ſon épaiſſeur, par conſéquent le rapport que nous cherchons ſera
              <lb/>
            égal à {aa + 2da + {2dd/3}/mm + 2dm + {2dd/3}} qu’on connoîtra en mettant des nombres
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            à la place des Lettres.</s>
            <s xml:id="echoid-s1239" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div96" type="section" level="1" n="63">
          <head xml:id="echoid-head78" xml:space="preserve">APLICATION.</head>
          <p>
            <s xml:id="echoid-s1240" xml:space="preserve">Remarqués que le numerateur de la fraction précedente n’eſt au-
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            tre choſe que le quarré de a + d, c’eſt-à-dire le quarré de l’épaiſ-
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            ſeur de la baſe, du revêtement moins le tiers du quarré de la ligne
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            de talud, & </s>
            <s xml:id="echoid-s1241" xml:space="preserve">que le dénominateur eſt auſſi égal au quarré de la
              <lb/>
            baſe du revêtement, dont on a augmenté l’épaiſſeur, moins le tiers
              <lb/>
            du quarré de la même ligne de talud. </s>
            <s xml:id="echoid-s1242" xml:space="preserve">Or s’il s’agit d’un revêtement
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            de 30 pieds de hauteur, qui ſoûtienne un Rampart avec un Parapet,
              <lb/>
            ſelon la ſixiéme Colomne de la Table, l’épaiſſeur de ce revêtement </s>
          </p>
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