Bion, Nicolas, Traité de la construction et principaux usages des instruments de mathématique, 1723

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        <div xml:id="echoid-div232" type="section" level="1" n="95">
          <p>
            <s xml:id="echoid-s2020" xml:space="preserve">
              <pb o="61" file="075" n="75" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/>
            de 44 & </s>
            <s xml:id="echoid-s2021" xml:space="preserve">demi pour le côté du cube égal au parallelipipede propoſé,</s>
          </p>
        </div>
        <div xml:id="echoid-div233" type="section" level="1" n="96">
          <head xml:id="echoid-head157" xml:space="preserve">USAGE VIII.</head>
          <head xml:id="echoid-head158" style="it" xml:space="preserve">Conſtruire & diviſer une jauge, pour meſurer les tonneaux &
            <lb/>
          tous vaiſſeaux ſemblables propres à contenir des liqueurs.</head>
          <p>
            <s xml:id="echoid-s2022" xml:space="preserve">LA jauge dont je pretends parler ici eſt une regle de quelque
              <lb/>
            métal diviſée en certaines parties, qui marquent le nombre des
              <lb/>
            pintes contenuës dans le tonneau, l'ayant fait entrer par le bondon
              <lb/>
            juſqu'à ce que ſon extremité touche l'angle que fait le fonds avec
              <lb/>
            les douves dans la partie la plus éloignée du bondon, comme on
              <lb/>
              <note position="right" xlink:label="note-075-01" xlink:href="note-075-01a" xml:space="preserve">Fig. 13.</note>
            voit la ligne AC, ſituée en forme de diagonale.</s>
            <s xml:id="echoid-s2023" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2024" xml:space="preserve">Cette jauge étant ainſi poſée, la diviſion qui répond au milieu
              <lb/>
            de l'ouverture du bondon au-dedans du tonneau, marque le nom-
              <lb/>
            bre des pintes qu'il contient.</s>
            <s xml:id="echoid-s2025" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2026" xml:space="preserve">Mais il eſt à propos de rechanger la poſition de ladite verge, en
              <lb/>
            ſorte que ſon extremité C touche l'angle de l'autre fonds B, afin de
              <lb/>
            connoître ſi l'ouverture du bondon eſt juſtement au milieu, car s'il
              <lb/>
            ſe trouve quelque difference, il en faut prendre la moitié.</s>
            <s xml:id="echoid-s2027" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2028" xml:space="preserve">L'uſage de cette jauge eſt très-facile, puiſque ſans calcul on trou-
              <lb/>
            ve d'abord la capacité des tonneaux; </s>
            <s xml:id="echoid-s2029" xml:space="preserve">toute l'adreſſe conſiſte à la
              <lb/>
            bien divifer.</s>
            <s xml:id="echoid-s2030" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2031" xml:space="preserve">Pour cet effet on peut faire conſtruire un petit baril contenant un
              <lb/>
            ſeptier, c'eſt-à-dire huit pintes, lequel ſoit parfaitement ſemblable
              <lb/>
            aux tonneaux qui ſont en uſage dans le païs, car cette jauge ne peut
              <lb/>
            être juſte que dans des tonneaux ſemblables; </s>
            <s xml:id="echoid-s2032" xml:space="preserve">c'eſt-à-dire, qui ont les
              <lb/>
            diametres des fonds, & </s>
            <s xml:id="echoid-s2033" xml:space="preserve">celui à l'endroit du bondon avec la longueur
              <lb/>
            dans les mêmes proportions que celui qui a ſervi pour les diviſions.</s>
            <s xml:id="echoid-s2034" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2035" xml:space="preserve">Suppoſons, par exemple, que le diametre de chacun des fonds d'un
              <lb/>
            tonneau ſoit de vingt pouces, le diametre de la coupe à l'endroit du
              <lb/>
            bondon de vingt-deux pouces, & </s>
            <s xml:id="echoid-s2036" xml:space="preserve">ſa longueur interieure de trente
              <lb/>
            pouces, ce vaiſſeau contiendra vingt-ſept ſeptiers, meſure de Paris,
              <lb/>
            comme ſont les demi-queuës d'Orlcans; </s>
            <s xml:id="echoid-s2037" xml:space="preserve">& </s>
            <s xml:id="echoid-s2038" xml:space="preserve">ſa meſure diagonale qui
              <lb/>
            répond au milieu de l'ouverture du bondon ſera de vingt-cinq pou-
              <lb/>
            ces neuf lignes & </s>
            <s xml:id="echoid-s2039" xml:space="preserve">demie, comme il eſt aiſé de trouver par le calcul,
              <lb/>
              <note position="right" xlink:label="note-075-02" xlink:href="note-075-02a" xml:space="preserve">Fig. 13.</note>
            puiſque dans le triangle rectangle ADC, on connoît le côté CD
              <lb/>
            15 pouces, & </s>
            <s xml:id="echoid-s2040" xml:space="preserve">DA 21, & </s>
            <s xml:id="echoid-s2041" xml:space="preserve">qu'ajouûtant leurs quarrez, on aura par la
              <lb/>
            quarante-ſeptiéme Prop. </s>
            <s xml:id="echoid-s2042" xml:space="preserve">du premier livre d'Euclide le quarré de
              <lb/>
            la diagonale ou hypotenuſe AC, & </s>
            <s xml:id="echoid-s2043" xml:space="preserve">enſuite ſa racine.</s>
            <s xml:id="echoid-s2044" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2045" xml:space="preserve">Suivant les mêmes proportions un baril dont les dimenſions ſe-
              <lb/>
            roient le tiers des prccedentes, contiendroit un ſeptier ou huit
              <lb/>
            </s>
          </p>
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