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

Table of Notes

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        <div xml:id="echoid-div631" type="section" level="1" n="321">
          <pb o="313" file="329" n="329" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/>
          <p>
            <s xml:id="echoid-s10175" xml:space="preserve">Il y a quelques-uns de ces Cadrans où les vives arrêtes des pier-
              <lb/>
            res ſervent d'axes, & </s>
            <s xml:id="echoid-s10176" xml:space="preserve">doivent être taillées de maniere qu'elles ten-
              <lb/>
            dent toutes au Pole & </s>
            <s xml:id="echoid-s10177" xml:space="preserve">ſoient paralleles à l'axe du Monde.</s>
            <s xml:id="echoid-s10178" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div634" type="section" level="1" n="322">
          <head xml:id="echoid-head455" style="it" xml:space="preserve">Conſtruction des Cadrans par le calcul des Angles.</head>
          <p>
            <s xml:id="echoid-s10179" xml:space="preserve">CEtte méthode eſt d'un grand ſecours pour verifier toutes les
              <lb/>
            operations de la Gnomonique où l'on a beſoin de beaucoup
              <lb/>
            d'exactitude, principalement quand on eſt obligé de faire un petit
              <lb/>
            modele pour tracer un grand Cadran, car une erreur preſque inſen-
              <lb/>
            ſible dans le modele devient très-conſiderable dans les longues li-
              <lb/>
            gnes qu'il faut tracer ſur un Plan de grande étenduë.</s>
            <s xml:id="echoid-s10180" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10181" xml:space="preserve">En la conſtruction des Cadrans reguliers, comme par exemple, de
              <lb/>
              <note position="right" xlink:label="note-329-01" xlink:href="note-329-01a" xml:space="preserve">XXII,
                <lb/>
              planche.
                <lb/>
              Fig. 4.</note>
            l'horiſontal, fig. </s>
            <s xml:id="echoid-s10182" xml:space="preserve">4, planche 22, les diviſions de la ligne équinoxialé
              <lb/>
            LK ſont les tangentes des angles du quart de cercle MH, & </s>
            <s xml:id="echoid-s10183" xml:space="preserve">les li-
              <lb/>
            gnes ponctuées en ſont les ſecantes, c'eſt pourquoi on les peut mar-
              <lb/>
            quer avec une Echelle de parties égales ou un Compas de propor-
              <lb/>
            tion, en ſuppoſant, par exemple, le raïon HB de cent parties, la diſ-
              <lb/>
            tance HI, tangente de 15 deg. </s>
            <s xml:id="echoid-s10184" xml:space="preserve">ſera de 27 des mêmes parties; </s>
            <s xml:id="echoid-s10185" xml:space="preserve">H2,
              <lb/>
            tangente de 30 d. </s>
            <s xml:id="echoid-s10186" xml:space="preserve">ſera de 58; </s>
            <s xml:id="echoid-s10187" xml:space="preserve">H3, tangente de 45d. </s>
            <s xml:id="echoid-s10188" xml:space="preserve">égale au raïon
              <lb/>
            ſera de 100. </s>
            <s xml:id="echoid-s10189" xml:space="preserve">H4, tangente de 60 d. </s>
            <s xml:id="echoid-s10190" xml:space="preserve">ſera de 173; </s>
            <s xml:id="echoid-s10191" xml:space="preserve">& </s>
            <s xml:id="echoid-s10192" xml:space="preserve">H5, tangente
              <lb/>
            de 75 d. </s>
            <s xml:id="echoid-s10193" xml:space="preserve">eſt de 373. </s>
            <s xml:id="echoid-s10194" xml:space="preserve">Les diviſions de l'autre moitié de cette ligno
              <lb/>
            pour les heures avant midi ſont ſemblables.</s>
            <s xml:id="echoid-s10195" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10196" xml:space="preserve">On peut de même trouver ſur cette ligne les points des demi-
              <lb/>
            heures & </s>
            <s xml:id="echoid-s10197" xml:space="preserve">des quarts, en prenant les tangentes des arcs convenables,
              <lb/>
            qu'il ſera facile de trouver dans les Tables imprimées; </s>
            <s xml:id="echoid-s10198" xml:space="preserve">à quoi l'on
              <lb/>
            peut ajoûter quelques abregez tirez de la valeur des ſecantes; </s>
            <s xml:id="echoid-s10199" xml:space="preserve">com-
              <lb/>
            me par exemple, laligne B4, ſecante de 60 d. </s>
            <s xml:id="echoid-s10200" xml:space="preserve">étant double du raïon,
              <lb/>
            ſi vous poïtez le double de BH, de B en 4, vous aurez le point de 4
              <lb/>
            h. </s>
            <s xml:id="echoid-s10201" xml:space="preserve">ſur la ligne Equinoxiale. </s>
            <s xml:id="echoid-s10202" xml:space="preserve">Cette même ſecante portée de 4 en L,
              <lb/>
            donnera le point de 5; </s>
            <s xml:id="echoid-s10203" xml:space="preserve">& </s>
            <s xml:id="echoid-s10204" xml:space="preserve">ſi vous en faites autant de l'autre côté,
              <lb/>
            vous aurez le point d'onze heures.</s>
            <s xml:id="echoid-s10205" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10206" xml:space="preserve">A l'égard des demi-heures on peut les trouver par le moyen des
              <lb/>
            ſecantes des heures qui ſont en nombre impair; </s>
            <s xml:id="echoid-s10207" xml:space="preserve">par exemple, la ſe-
              <lb/>
            cante B3, portée ſur la ligne Equinoxiale au point 3, donnera d'un
              <lb/>
            côté 4 h. </s>
            <s xml:id="echoid-s10208" xml:space="preserve">& </s>
            <s xml:id="echoid-s10209" xml:space="preserve">demie, & </s>
            <s xml:id="echoid-s10210" xml:space="preserve">de l'autre 10 h. </s>
            <s xml:id="echoid-s10211" xml:space="preserve">& </s>
            <s xml:id="echoid-s10212" xml:space="preserve">demie. </s>
            <s xml:id="echoid-s10213" xml:space="preserve">La ſecante B 6,
              <lb/>
            donue 7 h. </s>
            <s xml:id="echoid-s10214" xml:space="preserve">& </s>
            <s xml:id="echoid-s10215" xml:space="preserve">demie & </s>
            <s xml:id="echoid-s10216" xml:space="preserve">une & </s>
            <s xml:id="echoid-s10217" xml:space="preserve">demie. </s>
            <s xml:id="echoid-s10218" xml:space="preserve">B11, donne 8 & </s>
            <s xml:id="echoid-s10219" xml:space="preserve">demie & </s>
            <s xml:id="echoid-s10220" xml:space="preserve">2
              <lb/>
            & </s>
            <s xml:id="echoid-s10221" xml:space="preserve">demie B1, donne 3 & </s>
            <s xml:id="echoid-s10222" xml:space="preserve">demie & </s>
            <s xml:id="echoid-s10223" xml:space="preserve">9 & </s>
            <s xml:id="echoid-s10224" xml:space="preserve">demie. </s>
            <s xml:id="echoid-s10225" xml:space="preserve">B7, donne 6 & </s>
            <s xml:id="echoid-s10226" xml:space="preserve">de-
              <lb/>
            mie & </s>
            <s xml:id="echoid-s10227" xml:space="preserve">12 & </s>
            <s xml:id="echoid-s10228" xml:space="preserve">demie. </s>
            <s xml:id="echoid-s10229" xml:space="preserve">Enfin B5, donne 11 & </s>
            <s xml:id="echoid-s10230" xml:space="preserve">demi & </s>
            <s xml:id="echoid-s10231" xml:space="preserve">5 & </s>
            <s xml:id="echoid-s10232" xml:space="preserve">demie.</s>
            <s xml:id="echoid-s10233" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10234" xml:space="preserve">La diviſion de cette ligne ſert à faire exactement les Cadrans ho-
              <lb/>
            riſontaux, verticaux, & </s>
            <s xml:id="echoid-s10235" xml:space="preserve">principalement les Cadrans reguliers ſans
              <lb/>
            </s>
          </p>
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