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

Table of figures

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[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
[121] Fig. 6.F E K G A D I H B C
[122] Fig. 7.A D E B
[123] Fig. 8.A B
[124] Fig. 9.A D E F C B
[125] Fig. 10.C A B
[126] Fig. 11.C A B
[127] Fig. 12.C A B
[128] Fig. 13.F D E
[129] Fig. 14.C A B
[130] Fig. 15.G H I
[131] Fig. 16.F D E
[132] Fig. 17.D E C F F A B
[133] Fig. 18.D E A B
[134] Fig. 19.C A E B D
[135] Fig. 1.C A 1 2 3 4 5 B D
[136] Fig. 2.D F B A C H G E
[137] Fig. 3.D E G F A B C
[138] Fig. 4.D A C B
[139] Fig. 5.E K G A C D B F I H
[140] Fig. 6.D A E G F B C
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        <div xml:id="echoid-div158" type="section" level="1" n="46">
          <p>
            <s xml:id="echoid-s1256" xml:space="preserve">
              <pb o="28" file="042" n="42" rhead="USAGES DES PREM. INSTRUM. Liv. I. Chap. III."/>
            quera ſur la circonference la ſeptiéme partie du cercle; </s>
            <s xml:id="echoid-s1257" xml:space="preserve">après quoy
              <lb/>
            il ſera facile d'achever l'eptagone.</s>
            <s xml:id="echoid-s1258" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1259" xml:space="preserve">Il y a des rapporteurs, ſur leſquels ſont gravez des nombres qui
              <lb/>
            marquent les polygones reguliers, pour épargner la peine de faire
              <lb/>
            les diviſions. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">Le nombre cinq qui ſignifie le pentagone, eſt marqué
              <lb/>
            vis-à-vis 72 degrez de la circonference, le nombre ſix qui ſignifie
              <lb/>
            l'exagone eſt marqué vis-à-vis 60 degrez; </s>
            <s xml:id="echoid-s1261" xml:space="preserve">le nombre ſept qui ſignifie
              <lb/>
            l'eptagone, eſt marqué vis-à-vis les 51 degrez & </s>
            <s xml:id="echoid-s1262" xml:space="preserve">demi, &</s>
            <s xml:id="echoid-s1263" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1264" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div160" type="section" level="1" n="47">
          <head xml:id="echoid-head81" xml:space="preserve">USAGE IV.</head>
          <head xml:id="echoid-head82" style="it" xml:space="preserve">Pour décrire ſur une ligne donneé tout polygone regulier.</head>
          <p>
            <s xml:id="echoid-s1265" xml:space="preserve">SOit la ligne donnée CD, ſur laquelle on veut décrire un pen-
              <lb/>
              <note position="left" xlink:label="note-042-01" xlink:href="note-042-01a" xml:space="preserve">Fig. 16.</note>
            tagone.</s>
            <s xml:id="echoid-s1266" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1267" xml:space="preserve">Nous avons enſeigné dans l'uſage precedent le moyen de con-
              <lb/>
            noitre les angles de tous les polygones reguliers; </s>
            <s xml:id="echoid-s1268" xml:space="preserve">& </s>
            <s xml:id="echoid-s1269" xml:space="preserve">comme celui
              <lb/>
            que font les deux côtez du pentagone eſt de 108 degrez, ſa moitié
              <lb/>
            54 ſera le demi angle du pentagone, & </s>
            <s xml:id="echoid-s1270" xml:space="preserve">ſervira à le décrire en la
              <lb/>
            maniere ſuivante.</s>
            <s xml:id="echoid-s1271" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1272" xml:space="preserve">Poſez le diametre du rapporteur ſur la ligne CD, & </s>
            <s xml:id="echoid-s1273" xml:space="preserve">ſon centre à
              <lb/>
              <note position="left" xlink:label="note-042-02" xlink:href="note-042-02a" xml:space="preserve">Fig. 16.</note>
            l'extremité D. </s>
            <s xml:id="echoid-s1274" xml:space="preserve">Marquez un point vis-à-vis les 54 degrez de ſa cir-
              <lb/>
            conference, & </s>
            <s xml:id="echoid-s1275" xml:space="preserve">tirez la ligne DF faiſant un angle de 54 degrezavec la
              <lb/>
            ligne CD. </s>
            <s xml:id="echoid-s1276" xml:space="preserve">Tranſportez le centre du rapporteur à l'autre extremi-
              <lb/>
            té C, pour y faire pareillement un angle de 54 degrez, en tirant
              <lb/>
            la ligne CF; </s>
            <s xml:id="echoid-s1277" xml:space="preserve">le point F où ces deux lignes ſe rencontrent, ſera le
              <lb/>
            centre d'un cercle que vous tracerez en ouvrant le compas de la
              <lb/>
            grandeur CF. </s>
            <s xml:id="echoid-s1278" xml:space="preserve">Prenez enſuite la grandeur de la ligne donnée CD,
              <lb/>
            pour diviſer en cinq la circonference du cercle, & </s>
            <s xml:id="echoid-s1279" xml:space="preserve">tirant cinq
              <lb/>
            lignes, le pentagone ſera décrit.</s>
            <s xml:id="echoid-s1280" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1281" xml:space="preserve">Si l'on propoſe de décrire un octogone ſur une ligne donnée,
              <lb/>
            ayant reconnu que ſon angle de poligone eſt de 135 degrez, pre-
              <lb/>
            nez-en la moitié, 67 degrez & </s>
            <s xml:id="echoid-s1282" xml:space="preserve">demi, & </s>
            <s xml:id="echoid-s1283" xml:space="preserve">faites un angle de pareil
              <lb/>
            nombre de degrez à chaque extremité de la ligne donnée, pour y
              <lb/>
            faire un triangle Iſocele, dont le ſommet ſera le centre d'une cir-
              <lb/>
            conference, que vous diviſerez en huit, en y appliquant huit fois
              <lb/>
            la ligne donnée, & </s>
            <s xml:id="echoid-s1284" xml:space="preserve">l'octogone ſera formé.</s>
            <s xml:id="echoid-s1285" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1286" xml:space="preserve">On peut faire, avec les inſtrumens dont nous venons de parler,
              <lb/>
            quantité d'autres operations, ſuivant les differens ſujets; </s>
            <s xml:id="echoid-s1287" xml:space="preserve">mais on
              <lb/>
            s'eſt contenté d'y rapporter les plus utiles, & </s>
            <s xml:id="echoid-s1288" xml:space="preserve">les plus ordinaires.</s>
            <s xml:id="echoid-s1289" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div163" type="section" level="1" n="48">
          <head xml:id="echoid-head83" style="it" xml:space="preserve">Fin du premier Livre.</head>
        </div>
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