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

Table of Notes

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            <s xml:id="echoid-s4682" xml:space="preserve">
              <pb o="144" file="158" n="158" rhead="CONSTRUCTION ET USAGES DU QUART, &c."/>
            ble de le faire ſans conſuſion, & </s>
            <s xml:id="echoid-s4683" xml:space="preserve">de telle ſorte que les diviſions & </s>
            <s xml:id="echoid-s4684" xml:space="preserve">
              <lb/>
            ſubdiviſions des degrez puiſſent être juſtes & </s>
            <s xml:id="echoid-s4685" xml:space="preserve">bien diſtinctement
              <lb/>
            marquées ſur le bord de l'inſtrument.</s>
            <s xml:id="echoid-s4686" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4687" xml:space="preserve">Pour cet eſſet on décrit premierement deux circonferences ſur
              <lb/>
            le bord du quart de cercle, l'une intérieure, & </s>
            <s xml:id="echoid-s4688" xml:space="preserve">l'autre extérieure,
              <lb/>
            éloignées l'une de l'autre d'environ 8'ou 6 lignes, & </s>
            <s xml:id="echoid-s4689" xml:space="preserve">après les avoir
              <lb/>
            diviſées en degrez, on tire des lignes tranſverſales entre ces deux
              <lb/>
            circonferences du premier degré au ſecond, du ſecond au troiſié-
              <lb/>
            me, & </s>
            <s xml:id="echoid-s4690" xml:space="preserve">ainſi de ſuite, juſqu'au dernier.</s>
            <s xml:id="echoid-s4691" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4692" xml:space="preserve">Enſuite dequoi, ſi l'on veut ſubdiviſer chaque degré de 10 en 10
              <lb/>
            minutes, on décrit du centre de l'inſtrument 5 autres circonferen-
              <lb/>
            ces concentriques qui coupent toutes les tranſverſales; </s>
            <s xml:id="echoid-s4693" xml:space="preserve">mais ſi l'on
              <lb/>
            vouloit ſubdiviſer chaque degré de 5 en 5 minutes, il faudroit dé-
              <lb/>
            crire onze circonferences concentriques entre les deux extremitez.</s>
            <s xml:id="echoid-s4694" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4695" xml:space="preserve">Les diſtances entre ces circonferences ne doivent pas être tout-à-
              <lb/>
            fait égales, à cauſe que l'étenduë d'un degré priſe dans la largeur
              <lb/>
            du bord forme une eſpece de trapeze plus large vers la circonferen-
              <lb/>
            ce extérieure, & </s>
            <s xml:id="echoid-s4696" xml:space="preserve">plus étroite vers l intérieure, ce qui fait que la cir-
              <lb/>
            conference moyenne qui diviſe chaque degré en deux parties égales
              <lb/>
            doit être un peu plus près de la circonference intérieure que de l'ex-
              <lb/>
            térieure, & </s>
            <s xml:id="echoid-s4697" xml:space="preserve">les autres à proportion.</s>
            <s xml:id="echoid-s4698" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4699" xml:space="preserve">Pour faire exactement ces ſubdiviſions les tranſverſales doivent
              <lb/>
              <note position="left" xlink:label="note-158-01" xlink:href="note-158-01a" xml:space="preserve">I.XIII.
                <lb/>
              Planche.
                <lb/>
              Fig. H.</note>
            être des lignes courbes comme BCD, que l'on décrit en faiſant
              <lb/>
            paſſer une portion de circonference par le centre du quart de cercle
              <lb/>
            B, par le commencement du I
              <emph style="sub">r</emph>
            degré marqué D, ſur le bord en la cir-
              <lb/>
            conference intérieure, & </s>
            <s xml:id="echoid-s4700" xml:space="preserve">par la fin du même degré C, en la circon-
              <lb/>
            ference extérieure; </s>
            <s xml:id="echoid-s4701" xml:space="preserve">ce qui eſt facile à executer par l'uſage 18, du I
              <emph style="sub">r</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s4702" xml:space="preserve">Liv. </s>
            <s xml:id="echoid-s4703" xml:space="preserve">qui enſeigne à ſaire paſſer la circonference d'un cercle par trois
              <lb/>
            point donnez, & </s>
            <s xml:id="echoid-s4704" xml:space="preserve">par ce moyen on trouvera le point F pour centre
              <lb/>
            de la tranſverſale courbe qui paſſe par le premier degré.</s>
            <s xml:id="echoid-s4705" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4706" xml:space="preserve">On diviſe enſuite une de ces lignes courbes tranſverſales en parties
              <lb/>
            égales, & </s>
            <s xml:id="echoid-s4707" xml:space="preserve">du centre de l'inſtrument on trace autant de circonferen-
              <lb/>
            ces concentriques qu'il en faut pour ſnbdiviſer chaque degré en au-
              <lb/>
            tant de parties égales qu'il eſt poſſible de le faire ſans confuſion.</s>
            <s xml:id="echoid-s4708" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4709" xml:space="preserve">La raiſon de cette operation eſt que la tranſverſale courbe étant
              <lb/>
            diviſée en parties égales, ſi du centre de l'inſtrument vous menez
              <lb/>
            par tous les points de diviſion de cet arc des lignes droites, vous
              <lb/>
            aurez audit centre autant d'angles égaux entr'eux, puiſqu'ils ſeront
              <lb/>
            tous dans la circonference d'un même cercle, & </s>
            <s xml:id="echoid-s4710" xml:space="preserve">qu'ils s'appuïeront
              <lb/>
            tous ſur des arcs égaux; </s>
            <s xml:id="echoid-s4711" xml:space="preserve">& </s>
            <s xml:id="echoid-s4712" xml:space="preserve">les côtez de ces angles étant continuez,
              <lb/>
            </s>
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