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-s6759" xml:space="preserve">
              <pb o="215" file="230" n="230" rhead="ASTRONOMIQUE. Liv. VI. Chap. I."/>
            la diviſion du bord ſe diviſe en 60 minutes, par le moyen d'onze
              <lb/>
            cercles concentriques, & </s>
            <s xml:id="echoid-s6760" xml:space="preserve">de 6 lignes droites tranſverſales, comme
              <lb/>
            la figure 6 le marque. </s>
            <s xml:id="echoid-s6761" xml:space="preserve">Les diſtances tranſverſales ſon égales entr'-
              <lb/>
              <note position="right" xlink:label="note-230-01" xlink:href="note-230-01a" xml:space="preserve">Fig. 6.</note>
            elles, mais celles des cercles ſont inégales. </s>
            <s xml:id="echoid-s6762" xml:space="preserve">Néanmoins cette iné-
              <lb/>
            galité n'eſt preſque pas ſenſible ſi nous ſuppoſons le raïon du quart
              <lb/>
            de cercle de 3 pieds, & </s>
            <s xml:id="echoid-s6763" xml:space="preserve">la diſtance entre les 2 cercles extérieurs, d'un
              <lb/>
            pouce. </s>
            <s xml:id="echoid-s6764" xml:space="preserve">Car ſi nous prenons l'arc AE du cercle extérieur de 10 m. </s>
            <s xml:id="echoid-s6765" xml:space="preserve">& </s>
            <s xml:id="echoid-s6766" xml:space="preserve">
              <lb/>
            que l'on tire au centre C du quart de cercle les raïons ADC, EBC,
              <lb/>
            leſquels rencontrent le cercle intérieur aux points D & </s>
            <s xml:id="echoid-s6767" xml:space="preserve">B, l'arc DB
              <lb/>
            ſera auſſi de 10 minutes: </s>
            <s xml:id="echoid-s6768" xml:space="preserve">(l'on ſuppoſe ici que la figure 6 eſt po-
              <lb/>
            ſée ſur le Limbe de l'inſtrument, figure 1.)</s>
            <s xml:id="echoid-s6769" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6770" xml:space="preserve">Mais ſi on tire les droites tranſverſales AB, LE, leſquelles s'entre-
              <lb/>
            coupent au point F, je dis que F eſt le point milieu de la diviſion par
              <lb/>
            lequel doit paſſer le cercle du milieu, car il y a même raiſon de l'arc
              <lb/>
            AE, à l'arc BD, que l'on peut confiderer comme lignes droites, que
              <lb/>
            de AF à FB. </s>
            <s xml:id="echoid-s6771" xml:space="preserve">Or le raïon qui partant du centre C diviſe en 2 par-
              <lb/>
            ties égales l'angle au centre, compris par les raïons CDA, CBE,
              <lb/>
            rencontrera la tranſverſale AB au même point F: </s>
            <s xml:id="echoid-s6772" xml:space="preserve">car il eſt évident
              <lb/>
            que CA eſt à CB, comme les diviſions de la baſe AB du triangle
              <lb/>
            rectiligne ACB; </s>
            <s xml:id="echoid-s6773" xml:space="preserve">mais comme CA eſt à C B, ainſi AE eſt à D B,
              <lb/>
            c'eſt pourquoi AE eſt à DB, comme les diviſions de la baſe AB,
              <lb/>
            faites par le raïon qui diviſe en 2 l'angle ACB, & </s>
            <s xml:id="echoid-s6774" xml:space="preserve">par couſequent
              <lb/>
            le point F ci-devant trouvé dans la droite tranſverſale AB, ſera le
              <lb/>
            poins milieu de la diviſion.</s>
            <s xml:id="echoid-s6775" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6776" xml:space="preserve">Or nous avons ſuppoſé que AC eſt à CB, comme 36 pouces ſont
              <lb/>
            a 34; </s>
            <s xml:id="echoid-s6777" xml:space="preserve">donc AB eſt à AF, comme 71 à 36. </s>
            <s xml:id="echoid-s6778" xml:space="preserve">C'eſt pourquoi ſi la lar-
              <lb/>
            geur d'un pouce ou de 12 lignes, qui eſt la meſure ſuppoſée de AB,
              <lb/>
            eſt diviſée en 71 parties égales, la partie AF en aura 36, laquelle ſe-
              <lb/>
            ra plus grande d'un demi ou d'environ un douziéme de ligne, que
              <lb/>
            la moitié de AB, qui n'eſt que 35 & </s>
            <s xml:id="echoid-s6779" xml:space="preserve">demi. </s>
            <s xml:id="echoid-s6780" xml:space="preserve">Cette difference n'eſt
              <lb/>
            d'aucune conſequence, & </s>
            <s xml:id="echoid-s6781" xml:space="preserve">peut ſans aucune erreur ſenſible, ſe ne-
              <lb/>
            gliger dans la diviſion du milieu, & </s>
            <s xml:id="echoid-s6782" xml:space="preserve">à plus forte raiſon dans les
              <lb/>
            autres, où elle eſt moindre.</s>
            <s xml:id="echoid-s6783" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6784" xml:space="preserve">On peut, au lieu de faire les tranſverſales en ligne droites, les
              <lb/>
            faire en portion d'un cercle qui paſſeroit par le centre de l'Inſtru-
              <lb/>
            ment, & </s>
            <s xml:id="echoid-s6785" xml:space="preserve">par le le premier point & </s>
            <s xml:id="echoid-s6786" xml:space="preserve">le dernier de la même tranſver-
              <lb/>
            fale; </s>
            <s xml:id="echoid-s6787" xml:space="preserve">alors il n'y auroit qu'à diviſer cette portion de circonference
              <lb/>
            circulaire en 10 parties égales, & </s>
            <s xml:id="echoid-s6788" xml:space="preserve">l'on auroit les points exacts par
              <lb/>
            où doivent paſſer les onze cercles concentriques.</s>
            <s xml:id="echoid-s6789" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6790" xml:space="preserve">Il eſt facile de calculer le raïon de ce cercle, & </s>
            <s xml:id="echoid-s6791" xml:space="preserve">de donner cette fi-
              <lb/>
            </s>
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