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

Table of Notes

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          <pb o="83" file="097" n="97" rhead="DE DIFFERENS COMPAS. Liv. III. Ch. I."/>
          <p>
            <s xml:id="echoid-s2685" xml:space="preserve">La mêmc ouverture du compas de proportion peut ſervir encore
              <lb/>
            à diviſer en 7, en 9, & </s>
            <s xml:id="echoid-s2686" xml:space="preserve">en 11 parties égales; </s>
            <s xml:id="echoid-s2687" xml:space="preserve">mais pour éviter les
              <lb/>
            fractions, il faudra changer ladite ouverture, pour diviſer en 6, en
              <lb/>
            8, en 10 & </s>
            <s xml:id="echoid-s2688" xml:space="preserve">en 12.</s>
            <s xml:id="echoid-s2689" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2690" xml:space="preserve">Avant que de changer ladite ouverture du compas de propor-
              <lb/>
            tion, prenez avec le compas commun quinze deſdites parties éga-
              <lb/>
            les, que vous porterez ſur la jambe du compas de reduction, & </s>
            <s xml:id="echoid-s2691" xml:space="preserve">y
              <lb/>
            marquerez le nombre 7, pour diviſer toute ligne donnée en ſept.</s>
            <s xml:id="echoid-s2692" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2693" xml:space="preserve">Prenez enſuite 12, pour marquer ſur ladite jambe le nombre 9.</s>
            <s xml:id="echoid-s2694" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2695" xml:space="preserve">Prenez enfin 10, pour marquer ſur ladite jambe le nombre 11, qui
              <lb/>
            ſervira pour diviſer en onze toute ligne donnée.</s>
            <s xml:id="echoid-s2696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2697" xml:space="preserve">Mais pour diviſer en ſix, prenez avec un compas commun la lon-
              <lb/>
            gueur exacte d'une des jambes du compas de reduction; </s>
            <s xml:id="echoid-s2698" xml:space="preserve">portez-la
              <lb/>
            ſur la ligne des parties égales du compas de proportion à l'ouver-
              <lb/>
            ture de 140; </s>
            <s xml:id="echoid-s2699" xml:space="preserve">& </s>
            <s xml:id="echoid-s2700" xml:space="preserve">ce compas reſtant ainſi ouvert, prenez l'ouverture
              <lb/>
            de 20, portez-la ſur la jambe du compas de reduction, pour y mar-
              <lb/>
            quer le nombre 6, qui ſervira pour diviſer toute ligne donnée en ſix
              <lb/>
            parties égales.</s>
            <s xml:id="echoid-s2701" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2702" xml:space="preserve">Ayant pris de même la longueur entiere d'une des jambes du
              <lb/>
            compas de reduction, portez-la ſur la ligne des parties égales du
              <lb/>
            compas de proportion à l'ouverture de 180, & </s>
            <s xml:id="echoid-s2703" xml:space="preserve">prenez en vingt, & </s>
            <s xml:id="echoid-s2704" xml:space="preserve">
              <lb/>
            avec cette ouverture marquez ſur la jambe du compas de reduction
              <lb/>
            le nombre 8, qui ſervira pour diviſer en huit toute ligne propoſée.</s>
            <s xml:id="echoid-s2705" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2706" xml:space="preserve">Portez de même toute la longueur du compas de reduction à
              <lb/>
            l'ouverture de 110, dont vous prendrez 10 pour marquer ſur la
              <lb/>
            jambe du compas de reduction le nombre 10 qui ſervira pour divi-
              <lb/>
            ſer en dix toute ligne donnée.</s>
            <s xml:id="echoid-s2707" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2708" xml:space="preserve">Portez enſin la longueur du compas de reduction à l'ouverture
              <lb/>
            de 130, dont vous prendrez 10 pour marquer ſur la jambe du
              <lb/>
            compas de reduction le nombre 12, qui ſervira pour diviſer toute
              <lb/>
            ligne donnée en douze.</s>
            <s xml:id="echoid-s2709" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2710" xml:space="preserve">L'uſage en eſt facile: </s>
            <s xml:id="echoid-s2711" xml:space="preserve">car ſi, par exemple, vous voulez diviſer une
              <lb/>
            ligne droite en trois parties égales, pouſſez la boëte, en ſorte que le
              <lb/>
            milieu de la vis ſe trouve juſtement ſur le point marqué 3, & </s>
            <s xml:id="echoid-s2712" xml:space="preserve">l'ayant
              <lb/>
            arrêté fixement ſur ce point, ouvrez le compas de reduction, enſor-
              <lb/>
            te que les deux pointes des plus longues parties des jambes convien-
              <lb/>
            nent exactement à la longueur de la ligne droite propoſée; </s>
            <s xml:id="echoid-s2713" xml:space="preserve">puis
              <lb/>
            ayant tourné le compas, ſans changer ſon ouverture, les deux plus
              <lb/>
            courtes parties deſdites jambes diviſeront en trois parties égales la
              <lb/>
            ligne droite propoſée; </s>
            <s xml:id="echoid-s2714" xml:space="preserve">& </s>
            <s xml:id="echoid-s2715" xml:space="preserve">ainſi des autres.</s>
            <s xml:id="echoid-s2716" xml:space="preserve"/>
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