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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          <pb o="99" file="0103" n="103" rhead="Von verbeß. Fernröhren."/>
          <p>
            <s xml:id="echoid-s1147" xml:space="preserve">{1/a} = {1/a′} - m′ a ({1/a′
              <emph style="super">2</emph>
            } - {1/q′
              <emph style="super">2</emph>
            })</s>
          </p>
          <p>
            <s xml:id="echoid-s1148" xml:space="preserve">{1/b} = {1/b′} - m′ a ({1/b′
              <emph style="super">2</emph>
            } - {1/q′
              <emph style="super">2</emph>
            })</s>
          </p>
          <p>
            <s xml:id="echoid-s1149" xml:space="preserve">{1/f} = {1/a} + {1/b}</s>
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          <p>
            <s xml:id="echoid-s1150" xml:space="preserve">m - 1 = {f/u} - {m′ a f/q′
              <emph style="super">2</emph>
            } = ({1/u} - {m′ a/q′
              <emph style="super">2</emph>
            }): </s>
            <s xml:id="echoid-s1151" xml:space="preserve">{1/f}. </s>
            <s xml:id="echoid-s1152" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1153" xml:space="preserve">136. </s>
            <s xml:id="echoid-s1154" xml:space="preserve">Die Werthe u′ und u″ laſſen ſich
              <lb/>
            ſehr füglich, und genau nach der oben (114)
              <lb/>
            beſchriebenen Methode finden, zu welcher die
              <lb/>
            ganze Vorrichtung in einer kleinen Oeffnung
              <lb/>
            des Fenſterladens, einem darüber geſpannten
              <lb/>
            Haare, und einem Stücke weiſen Papiers be-
              <lb/>
            ſteht. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">Auf eben die Art erhält man die dio-
              <lb/>
            ptriſche Brennweite u, für welche nämlich ſo
              <lb/>
            wohl der Abſtand des Glaſes von der Oeffnung,
              <lb/>
            als die Weite des Bildes, da man das Haar
              <lb/>
            deutlich ausnimmt, von dem Glaſe abzumeſſen
              <lb/>
            iſt: </s>
            <s xml:id="echoid-s1156" xml:space="preserve">man multiplicirt dieſe beyden Längen mit-
              <lb/>
            einander, und das Product durch ihre Summe
              <lb/>
            dividirt, giebt die Brennweite des Glaſes für
              <lb/>
            Parallelſtraalen.</s>
            <s xml:id="echoid-s1157" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1158" xml:space="preserve">137. </s>
            <s xml:id="echoid-s1159" xml:space="preserve">Dieſes weiſet ſich aus der Formel
              <lb/>
            (55): </s>
            <s xml:id="echoid-s1160" xml:space="preserve">ſetzen wir, daß die Brennweite für
              <lb/>
            Straalen, die aus einem Punkte ansfahren,
              <lb/>
            und unendlich nahe bey der Achſe einfallen,
              <lb/>
            z ſey, ſo wird z = r - {r
              <emph style="super">2</emph>
            m a/q
              <emph style="super">2</emph>
            }, mithin
              <lb/>
              <note symbol="*" position="foot" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">Sieh den 6 Art. des Anh.</note>
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