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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          <p>
            <s xml:id="echoid-s299" xml:space="preserve">
              <pb o="29" file="0033" n="33" rhead="Von verbeß. Fernröhren."/>
            {l
              <emph style="super">2</emph>
            /m q}) {1/2}e
              <emph style="super">2</emph>
            = - {m - 1/m} (m
              <emph style="super">3</emph>
            l
              <emph style="super">3</emph>
            - {m
              <emph style="super">2</emph>
            l
              <emph style="super">2</emph>
            /q}) {1/2}e
              <emph style="super">3</emph>
              <lb/>
            fü 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>
            ; </s>
            <s xml:id="echoid-s300" xml:space="preserve">und
              <lb/>
            man bekäme alſogleich B I = r - r
              <emph style="super">2</emph>
            π.</s>
            <s xml:id="echoid-s301" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s302" xml:space="preserve">40. </s>
            <s xml:id="echoid-s303" xml:space="preserve">Weil aber BH nicht mit q, ſondern mit
              <lb/>
            q - q
              <emph style="super">2</emph>
            φ - a gleich iſt, muß auch der Werth
              <lb/>
            des B I von r - r
              <emph style="super">2</emph>
            π unterſchieden ſeyn. </s>
            <s xml:id="echoid-s304" xml:space="preserve">Der
              <lb/>
            Urſprung dieſes Unterſchieds iſt zweytach: </s>
            <s xml:id="echoid-s305" xml:space="preserve">erſt-
              <lb/>
            lich weil man in dem Werthe des {1/b} - {1/q}
              <lb/>
            für q hätte den ganzen Ausdruck q - q
              <emph style="super">2</emph>
            φ - a
              <lb/>
            ſetzen ſollen, gleich wie auch in dem Theile {l
              <emph style="super">2</emph>
            /q}
              <lb/>
            des Werths vom π: </s>
            <s xml:id="echoid-s306" xml:space="preserve">zweytens weil bey dem Ab-
              <lb/>
            wachſen q
              <emph style="super">2</emph>
            φ + a der Länge B H, die man
              <lb/>
            für q hat angenommen, auch der Werth des
              <lb/>
            B I vermindert wird, gemäß jenem, was wir
              <lb/>
            oben (35) geſagt haben.</s>
            <s xml:id="echoid-s307" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s308" xml:space="preserve">41. </s>
            <s xml:id="echoid-s309" xml:space="preserve">Was das erſte betrifft, kann hieraus
              <lb/>
            kein merklicher Unterfchied entſtehen, weil der
              <lb/>
            Werth des π wegen ſeines Coefficientens e
              <emph style="super">2</emph>
            ſehr
              <lb/>
            klein ſeyn muß, und mithin im Anſehen ſeiner
              <lb/>
            Größe eine ſehr kleine Veränderung leidet,
              <lb/>
            wenn man q anſtatt einer ihm faſt gleichen
              <lb/>
            Größe annimmt.</s>
            <s xml:id="echoid-s310" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s311" xml:space="preserve">Was aber den Unterſchied, der aus der
              <lb/>
            zweyten Urſache herkommet, anbelanget, kann
              <lb/>
            man ſelben alſo erſetzen, daß man vermöge (35)
              <lb/>
            von dem gefundenen Werthe des B I den Ueber-
              <lb/>
            ſchuß des B H mit {m X B I
              <emph style="super">2</emph>
            /B H
              <emph style="super">2</emph>
            }, das iſt, mit {m r
              <emph style="super">2</emph>
            /q
              <emph style="super">2</emph>
            </s>
          </p>
        </div>
      </text>
    </echo>
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