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

Table of figures

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[91] 22
[92] 22
[93] 22
[94] 23
[95] 23
[96] A
[97] A
[98] A
[99] BDemy Pied du Roy 1 2 3 4 5 6
[100] C
[101] DDemy Pied du Polm Rhin Echelle 10 20 30 40 50 60
[102] EN. Bion A Paris. B E C G D F A O 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10
[103] Fig. 1.D H F A B C G E
[104] Fig. 2.G H E D F A C B
[105] Fig. 3.F E H D G C B
[106] Fig. 4.F D C B
[107] Fig. 5.D P C A B
[108] Fig. 6.C A D G E B
[109] Fig. 7.C A 2 1 B D
[110] Fig. 8.A D G C F E B
[111] Fig. 9.F C A B
[112] Fig. 9.E F G
[113] Fig. 10.C D A B
[114] Fig. 11.C D A B
[115] Fig. 12.C D A B
[116] Fig. 1.C A B D
[117] Fig. 2.C A B a b
[118] Fig. 3.10 9 8 7 6 5 4 3 2 1 10. 20. 30. 40. 50. 60. 70. 80. D E F G H C Y Z A B
[119] Fig. 4.10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 90 100 5 5 5 5 5 200. 300. 400. 500. 600. 700. 800. 900. 1000. B F C A E D
[120] Fig. 5.C 4 3 2 1 A D B
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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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