Bošković, Ruđer Josip, Abhandlung von den verbesserten dioptrischen Fernröhren aus den Sammlungen des Instituts zu Bologna sammt einem Anhange des Uebersetzers

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    <echo version="1.0RC">
      <text xml:lang="de" type="free">
        <div xml:id="echoid-div7" type="section" level="1" n="5">
          <pb o="25" file="0029" n="29" rhead="Von verbeß. Fernröhren."/>
          <p>
            <s xml:id="echoid-s251" xml:space="preserve">Setze man nun in dieſem Ausdrucke des
              <lb/>
            zweyten Theils nach {k
              <emph style="super">2</emph>
            /m p} hinzu + {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            p} -
              <lb/>
            {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            p}, ſo wird er q
              <emph style="super">2</emph>
            ({k
              <emph style="super">2</emph>
            /m p} + {k
              <emph style="super">2</emph>
            /m p} - {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            p}
              <lb/>
            - {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            a} + {k
              <emph style="super">3</emph>
            /m
              <emph style="super">3</emph>
            }) {1/2}e
              <emph style="super">2</emph>
            .</s>
            <s xml:id="echoid-s252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s253" xml:space="preserve">Weil aber - {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            a} + {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            p} = {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            }
              <lb/>
            (- {1/a} + {1/p}) (das iſt, wegen k = {1/a}
              <lb/>
            - {1/p}) = {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            } x - k = - {k
              <emph style="super">3</emph>
            /m
              <emph style="super">2</emph>
            }; </s>
            <s xml:id="echoid-s254" xml:space="preserve">kann
              <lb/>
            man auch ſchreiben q
              <emph style="super">2</emph>
            ({k
              <emph style="super">2</emph>
            /m p} - {k
              <emph style="super">3</emph>
            /m
              <emph style="super">2</emph>
            } - {k
              <emph style="super">2</emph>
            /m
              <emph style="super">2</emph>
            p}
              <lb/>
            + {k
              <emph style="super">3</emph>
            /m
              <emph style="super">3</emph>
            }) {1/2}e
              <emph style="super">2</emph>
            = q
              <emph style="super">2</emph>
            (- {m - 1/m
              <emph style="super">3</emph>
            } x (k
              <emph style="super">3</emph>
            -
              <lb/>
            {m k
              <emph style="super">2</emph>
            /p}) {1/2}e
              <emph style="super">2</emph>
            = - q
              <emph style="super">2</emph>
            x {m - 1/m
              <emph style="super">3</emph>
            } (k
              <emph style="super">3</emph>
            -
              <lb/>
            {m k
              <emph style="super">2</emph>
            /p}) {1/2}e
              <emph style="super">2</emph>
            . </s>
            <s xml:id="echoid-s255" xml:space="preserve">Auf dieſe Weiſe hat man x =
              <lb/>
            q - q
              <emph style="super">2</emph>
            x {m - 1/m
              <emph style="super">3</emph>
            } (k
              <emph style="super">3</emph>
            - {m k
              <emph style="super">2</emph>
            /p}) {1/2}e
              <emph style="super">2</emph>
            . </s>
            <s xml:id="echoid-s256" xml:space="preserve">Setzet
              <lb/>
            man φ = {m - 1/m
              <emph style="super">3</emph>
            } (k
              <emph style="super">3</emph>
            - {m k
              <emph style="super">2</emph>
            /p}) {1/2}e
              <emph style="super">2</emph>
            , ſo
              <lb/>
            wird endlich x = q - q
              <emph style="super">2</emph>
            φ.</s>
            <s xml:id="echoid-s257" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s258" xml:space="preserve">32. </s>
            <s xml:id="echoid-s259" xml:space="preserve">III Anmerkung. </s>
            <s xml:id="echoid-s260" xml:space="preserve">Dieſe Formel kommt
              <lb/>
            in allem mit des Herrn Clairaut ſeiner, die
              <lb/>
            man zu Ende der zweyten Aufgabe ſeiner Ab-
              <lb/>
            bandlung vom Jahre 1756 findet, überein, </s>
          </p>
        </div>
      </text>
    </echo>
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