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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            <pb o="58" file="0166" n="169" rhead="LA SCIENCE DES INGENIEURS,"/>
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          <div xml:id="echoid-div239" type="section" level="2" n="64">
            <head xml:id="echoid-head187" xml:space="preserve">PROPOSITION SECONDE</head>
            <head xml:id="echoid-head188" xml:space="preserve">
              <emph style="sc">Proble’me</emph>
            .</head>
            <p style="it">
              <s xml:id="echoid-s3293" xml:space="preserve">Trouver l’épaiſſeur qu’il faut donner aux piés-droits des
                <lb/>
              Voûtes Elliptiques ou ſurbaiſſées.</s>
              <s xml:id="echoid-s3294" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3295" xml:space="preserve">54. </s>
              <s xml:id="echoid-s3296" xml:space="preserve">Pouravoirune parfaite intelligence de ce Probléme, je con-
                <lb/>
              ſeille à ceux qui ne ſe ſont point apliqués au Chapitre précédent,
                <lb/>
              de lire avec attention l’Article 30. </s>
              <s xml:id="echoid-s3297" xml:space="preserve">où il eſt parlé de la maniere de
                <lb/>
              tracer une Ellipſe, ce qui leur ſuffira pour me ſuivre.</s>
              <s xml:id="echoid-s3298" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3299" xml:space="preserve">Ayant une Voûte Elliptique comme dans la figure 8. </s>
              <s xml:id="echoid-s3300" xml:space="preserve">dont on
                <lb/>
              connoît les demi axes BH & </s>
              <s xml:id="echoid-s3301" xml:space="preserve">HD, on commencera par diviſer le
                <lb/>
                <note position="left" xlink:label="note-0166-01" xlink:href="note-0166-01a" xml:space="preserve">
                  <emph style="sc">Planch</emph>
                .
                  <lb/>
                5.</note>
              quart d’Ellipſe BD en deux également au point L, duquel on abaiſ-
                <lb/>
                <note position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">
                  <emph style="sc">Fig</emph>
                . 8.</note>
              ſera ſur DH & </s>
              <s xml:id="echoid-s3302" xml:space="preserve">HB les perpendiculaires LK & </s>
              <s xml:id="echoid-s3303" xml:space="preserve">LV, dont on cher-
                <lb/>
              chera la valeur avec le ſecours de l’échelle; </s>
              <s xml:id="echoid-s3304" xml:space="preserve">& </s>
              <s xml:id="echoid-s3305" xml:space="preserve">ſupoſant que BH
                <lb/>
              ſoit de 12 pieds, & </s>
              <s xml:id="echoid-s3306" xml:space="preserve">HD de 8, on trouvera que LK ou VH eſt de 7
                <lb/>
              pieds 6 pouces, & </s>
              <s xml:id="echoid-s3307" xml:space="preserve">LV ou KH de 6 pieds 3 pouces; </s>
              <s xml:id="echoid-s3308" xml:space="preserve">& </s>
              <s xml:id="echoid-s3309" xml:space="preserve">faiſant la
                <lb/>
              hauteur BS du pié-droit de 15 pieds, comme à l’ordinaire, il faut
                <lb/>
              pour en avoir l’épaiſſeur ſe propoſer cinq opérations.</s>
              <s xml:id="echoid-s3310" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3311" xml:space="preserve">Pour la premiere, il faut dire, comme le quarré de DH (de 64
                <lb/>
              pieds) eſt au quarré de BH (de 144,) ainſi la ligne KH (de 6 pieds
                <lb/>
              3 pouces) eſt à la ligne KA, qu’on trouvera de 14 pieds 9 lignes,
                <lb/>
              qui eſt le premier terme dont nous avons beſoin.</s>
              <s xml:id="echoid-s3312" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3313" xml:space="preserve">Pour la ſeconde opération, il faut chercher la ſuperficie des
                <lb/>
              deux Ellipſes, dont la premiere auroit pour demi axe BH & </s>
              <s xml:id="echoid-s3314" xml:space="preserve">HD,
                <lb/>
              (de 12 pieds & </s>
              <s xml:id="echoid-s3315" xml:space="preserve">de 8,) & </s>
              <s xml:id="echoid-s3316" xml:space="preserve">la ſeconde pour demi axe HE & </s>
              <s xml:id="echoid-s3317" xml:space="preserve">HG,
                <lb/>
              (de 15 & </s>
              <s xml:id="echoid-s3318" xml:space="preserve">de 4, parce qu’on ſupoſe que la Voûte a encore 3 pieds
                <lb/>
              d’épaiſſeur,) on retranchera la petite Ellipſe de la grande, & </s>
              <s xml:id="echoid-s3319" xml:space="preserve">on
                <lb/>
              prendra le quart de la difference (que l’on trouvera de 54 pieds)
                <lb/>
              qu’il faut diviſer par la hauteur du pié-droit, le quotient ſera 3 pieds
                <lb/>
              2 pouces 4 lignes, pour le ſecond terme.</s>
              <s xml:id="echoid-s3320" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3321" xml:space="preserve">Pour la troiſiéme opération, il faut ajoûter la ligne LV (qu’on
                <lb/>
              a trouvée de 6 pieds 3 pouces) à la hauteur du pié-droit, (pour
                <lb/>
              avoir 21 pieds 3 pouces) qu’il faut multiplier par le premier terme
                <lb/>
              (14 pieds 9 pouces) & </s>
              <s xml:id="echoid-s3322" xml:space="preserve">diviſer le produit par la valeur de LK) qui
                <lb/>
              eſt de 7 pieds 6 pouces,) le quotient ſera d’environ 41 pieds 10
                <lb/>
              pouces pour le troiſiéme terme.</s>
              <s xml:id="echoid-s3323" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s3324" xml:space="preserve">A l’égard de la quatriéme, il faut ajoûter le ſecond terme au </s>
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