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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            <p>
              <s xml:id="echoid-s3233" xml:space="preserve">
                <pb o="56" file="0164" n="167" rhead="LA SCIENCE DES INGENIEURS."/>
              prendre le quart de leur difference, (& </s>
              <s xml:id="echoid-s3234" xml:space="preserve">l’on aura 64 pieds quarrés)
                <lb/>
              qu’il faut diviſer par la hauteur du pié-droit; </s>
              <s xml:id="echoid-s3235" xml:space="preserve">(c’eſt-à-dire par 15) & </s>
              <s xml:id="echoid-s3236" xml:space="preserve">
                <lb/>
              le quotient donnera 4 pieds 3 pouces 4 lignes, que nous nomme-
                <lb/>
              rons premier terme.</s>
              <s xml:id="echoid-s3237" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3238" xml:space="preserve">Pour la ſeconde, il faut ajoûter au raïon AC la moitié de l’épaiſ-
                <lb/>
              ſeur de la Voûte, pour avoir la ligne AL de (13 pieds & </s>
              <s xml:id="echoid-s3239" xml:space="preserve">demi)
                <lb/>
              qu’il faut quarrer & </s>
              <s xml:id="echoid-s3240" xml:space="preserve">prendre la moitié du produit (c’eſt-à-dire 91
                <lb/>
              pieds 1 pouce 6 lignes) & </s>
              <s xml:id="echoid-s3241" xml:space="preserve">en extraire la racine quarrée (qu’on trou-
                <lb/>
              vera de 9 pieds 10 pouces) qu’on ajoûtera à la hauteur du pié-droit,
                <lb/>
              & </s>
              <s xml:id="echoid-s3242" xml:space="preserve">l’on aura 24 pieds 10 pouces que nous nommerons deuxiéme
                <lb/>
              terme.</s>
              <s xml:id="echoid-s3243" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3244" xml:space="preserve">Pour la troiſiéme, il faut ajoûter enſemble le premier & </s>
              <s xml:id="echoid-s3245" xml:space="preserve">le ſecond
                <lb/>
              termes, (c’eſt-à-dire 4 pieds 3 pouces 4 lignes, & </s>
              <s xml:id="echoid-s3246" xml:space="preserve">24 pieds 10 pouces,
                <lb/>
              pour avoir 29 pieds 1 pouce 4 lignes,) qu’on multipliera par le
                <lb/>
              premier (4 pieds 3 pouces 4 lignes) & </s>
              <s xml:id="echoid-s3247" xml:space="preserve">le produit donnera 124
                <lb/>
              pieds 6 pouces 4 lignes, pour la valeur du troiſiéme terme.</s>
              <s xml:id="echoid-s3248" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3249" xml:space="preserve">Enfin, pour la quatriéme opération, il faut extraire la racine quar-
                <lb/>
              rée du 3 terme, (j’entends de 124 pieds 6 pouces 4 lignes) qui
                <lb/>
              eſt à peu-près 11 pieds 1 pouce 8 lignes) & </s>
              <s xml:id="echoid-s3250" xml:space="preserve">en ſouſtraire la valeur
                <lb/>
              du premier, (c’eſt-à-dire 4 pieds 3 pouces 4 lignes,) la difference,
                <lb/>
              qui eſt 6 pieds 10 pouces 4 lignes, ſera l’épaiſſeur qu’il faut donner
                <lb/>
              aux piés-droits.</s>
              <s xml:id="echoid-s3251" xml:space="preserve"/>
            </p>
          </div>
          <div xml:id="echoid-div234" type="section" level="2" n="61">
            <head xml:id="echoid-head184" style="it" xml:space="preserve">Second Exemple.</head>
            <p>
              <s xml:id="echoid-s3252" xml:space="preserve">51. </s>
              <s xml:id="echoid-s3253" xml:space="preserve">Si l’on avoit une Voûte en plain ceintre, dont l’extrados,
                <lb/>
                <note position="left" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve">
                  <emph style="sc">Planch</emph>
                .
                  <lb/>
                4.</note>
              au lieu d’être circulaire, fut terminée par deux plans GH & </s>
              <s xml:id="echoid-s3254" xml:space="preserve">GI,
                <lb/>
                <note position="left" xlink:label="note-0164-02" xlink:href="note-0164-02a" xml:space="preserve">
                  <emph style="sc">Fig</emph>
                . 10.</note>
              comme dans la figure 10. </s>
              <s xml:id="echoid-s3255" xml:space="preserve">l’on trouvera l’épaiſſeur de ſes piés-droits
                <lb/>
              en faiſant encore quatre opérations ſemblables aux précédentes,
                <lb/>
              puiſqu’il n’y aura que la premiere qui ſera un peu differente à cauſe
                <lb/>
              que la Voûte n’eſt pas la même que cy-devant.</s>
              <s xml:id="echoid-s3256" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3257" xml:space="preserve">Supoſant le raïon AB de 12 pieds, la hauteur BS des piés-droits
                <lb/>
              de 15, l’épaiſſeur FC de 3 dans le milieu des reins, & </s>
              <s xml:id="echoid-s3258" xml:space="preserve">que l’angle
                <lb/>
              HGI ſoit droit, on aura le quarré AFGW, dont le côté AF ſera de
                <lb/>
              de 15 pieds.</s>
              <s xml:id="echoid-s3259" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3260" xml:space="preserve">Cela poſé, pour la premiere opération il faut chercher la ſuper-
                <lb/>
              ſicie du quarré GF AW, & </s>
              <s xml:id="echoid-s3261" xml:space="preserve">en retrancher le quart de cercle CA,
                <lb/>
              &</s>
              <s xml:id="echoid-s3262" xml:space="preserve">c. </s>
              <s xml:id="echoid-s3263" xml:space="preserve">diviſer la difference (qui ſera 112 pieds) par la hauteur BS des
                <lb/>
              piés-droits, (c’eſt-à-dire par 15 pieds) & </s>
              <s xml:id="echoid-s3264" xml:space="preserve">le quotient donnera 7
                <lb/>
              pieds 5 pouces 7 lignes, pour la valeur du premier terme.</s>
              <s xml:id="echoid-s3265" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3266" xml:space="preserve">La ſeconde opération ſe fera en ajoûtant la moitié de l’épaiſ-
                <lb/>
              ſeur de la Voûte FC au raïon AB pour avoir la ligne LA (de 13 </s>
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