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-div417" type="section" level="1" n="192">
          <pb o="152" file="166" n="166" rhead="CONSTRUCTION ET USAGES DU QUART, &c."/>
        </div>
        <div xml:id="echoid-div418" type="section" level="1" n="193">
          <head xml:id="echoid-head292" xml:space="preserve">USAGE III.</head>
          <head xml:id="echoid-head293" style="it" xml:space="preserve">Connoitre avec le Treillis une hauteur inacceſſible.</head>
          <p>
            <s xml:id="echoid-s4963" xml:space="preserve">POur cet effet il faut faire deux ſtations & </s>
            <s xml:id="echoid-s4964" xml:space="preserve">meſurer la diſtance
              <lb/>
            entre les deux ſtations, mais il y a trois cas à obſerver.</s>
            <s xml:id="echoid-s4965" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div419" type="section" level="1" n="194">
          <head xml:id="echoid-head294" xml:space="preserve">PREMIER CAS.</head>
          <head xml:id="echoid-head295" style="it" xml:space="preserve">Où le côté d'ombre droite eſt coupé toutes les
            <emph style="bf">2</emph>
          fois par le fil du plomb.</head>
          <p>
            <s xml:id="echoid-s4966" xml:space="preserve">SUppoſons, par exemple, qu'à la premiere obſervation le fil coupe
              <lb/>
            le côté d'ombre droite au point marqué 30, & </s>
            <s xml:id="echoid-s4967" xml:space="preserve">que s'étant recu-
              <lb/>
            lé de 20 toiſes en place bien de niveau, au premier point, ce fil
              <lb/>
            coupe le même côté d'ombre droite au point 70; </s>
            <s xml:id="echoid-s4968" xml:space="preserve">marquez la poſi-
              <lb/>
            tion du filen ces deux ſtations, en traçant ſur le treillis une ligne de
              <lb/>
            craïon depuis le centre juſqu'audit point 30, & </s>
            <s xml:id="echoid-s4969" xml:space="preserve">une autre juſqu'au
              <lb/>
            point marqué 70; </s>
            <s xml:id="echoid-s4970" xml:space="preserve">cherchez entre ces deux lignes une portion de
              <lb/>
            parallele qui ſoit d'autant de parties que la dîſtance meſurée con-
              <lb/>
            tient de toiſes, c'eſt-à-dire 20 en cet exemple, ladite parallele étant
              <lb/>
            continuée, conviendra au nombre 50, compté depuis le centre;
              <lb/>
            </s>
            <s xml:id="echoid-s4971" xml:space="preserve">c'eſt pourquoi la hauteur de la Tour obſervée ſera de 50 toiſes; </s>
            <s xml:id="echoid-s4972" xml:space="preserve">on
              <lb/>
            connoîtra auſſi par le même moyen que la diſtance du pied de la
              <lb/>
            Tour juſqu'à la premiere ſtation qui n'avoit pû être meſurée, eſt de
              <lb/>
            15 toiſes; </s>
            <s xml:id="echoid-s4973" xml:space="preserve">parce qu'il y a 15 parties compriſes ſur la parallele entre
              <lb/>
            le nombre 50 & </s>
            <s xml:id="echoid-s4974" xml:space="preserve">la ligne de craïon de la premiere ſtation.</s>
            <s xml:id="echoid-s4975" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4976" xml:space="preserve">Au lieu de tirer des lignes de craïon on pourroit ſe ſervir de 2 fils
              <lb/>
            téndus depuis le centre, dont celui où eſt attaché le plomb en ſeroit
              <emph style="sc">I</emph>
            .</s>
            <s xml:id="echoid-s4977" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div420" type="section" level="1" n="195">
          <head xml:id="echoid-head296" xml:space="preserve">SECOND CAS.</head>
          <head xml:id="echoid-head297" style="it" xml:space="preserve">Où le côté d'ombre verſe eſt coupé toutes les deux fois par le fil.</head>
          <p>
            <s xml:id="echoid-s4978" xml:space="preserve">SUppoſons qu'en la premiere ſtation le fil du plomb coupe le côtê
              <lb/>
            d'ombre verſe au point marqué 80; </s>
            <s xml:id="echoid-s4979" xml:space="preserve">& </s>
            <s xml:id="echoid-s4980" xml:space="preserve">que s'étant reculé en pla-
              <lb/>
            ce unie, de 15 toiſes, le fil coupe le même côté d'ombre verſe au point
              <lb/>
            50; </s>
            <s xml:id="echoid-s4981" xml:space="preserve">marquez ſur le treillis les 2 differentes poſitions du fil par 2 li-
              <lb/>
            gnes de craion ou autrement, & </s>
            <s xml:id="echoid-s4982" xml:space="preserve">cherchez entre ces deux lignes une
              <lb/>
            portion de parallele qui contienne autant de parties que la diſtance
              <lb/>
            meſurée contient de toiſes, comme en cet exemple 15 parties à cauſe
              <lb/>
            des 15 toiſes de diſtance ſuppoſée entre les 2 ſtations; </s>
            <s xml:id="echoid-s4983" xml:space="preserve">à ces 15 parties
              <lb/>
            ajoûtez-en 25, qui ſont la continuation de la même parallele juſ-
              <lb/>
            qu'au côté du quarré qui aboutit au centre, ce qui fait en tout 40
              <lb/>
            parties, c'eſt pourquoi la diſtance de la Tour juſqu'au point de la ſe-
              <lb/>
            conde ſtation eſt de 40 toiſes; </s>
            <s xml:id="echoid-s4984" xml:space="preserve">& </s>
            <s xml:id="echoid-s4985" xml:space="preserve">pour avoir ſa hauteur, cherchez
              <lb/>
            </s>
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