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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nie bey ihrem Anfange I einer Parabel des drit-
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ten Grades unendlich nahe kommt, in welcher
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ſich E I zu E B, wie 3 zu 2 verhalten muß, wie
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man auch ganz leicht aus dem Werthe E B =
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{r y/c} findet, wenn man für y ſeine gleichgültige
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Größe 2 r δ e
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ſetzet: </
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">denn man erhält 2 r
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δ e
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im Falle, daß E I, oder z, mit 3 r
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δ e
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gleich werde.</
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<
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">Es iſt noch übrig, daß wir den Punkt
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C beſtimmen, wo die Tangente D B mit der
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Brennlinie zuſammen ſtoſſet. </
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">Es muß aber
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folgende Proportion ſtatt haben B O
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: </
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">B E
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=
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O C
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: </
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<
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">E D
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, oder vermöge ihrer Gleichung,
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= I O
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: </
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">I E
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, welche auch richtig iſt, ſo fern
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I O dem vierten Theile von I E gleich genom-
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men wird. </
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">Denn man gebe der Linie E I 12
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gleiche Theile, ſo kommen der Linie I O derer
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3 zu, und (aus vorigem Artikel) der B E 8;
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</
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">der Linie B I aber 4, und 1 der BO. </
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demnach B O : </
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">8, und I O : </
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">E I =
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1 : </
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">4, folglich iſt ſowohl B O
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zu B E
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, als
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I O
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zu I E
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, wie 1 zu 64.</
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">Eben dieſes giebt auch die Berechnung,
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wenn man gerade ſetzet I O = h z. </
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">Denn es
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wird B E = {2/3}z, B I = {1/3}z, B O = ({1/3} - h)z,
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und ſtehet die vorige Proportion in folgenden
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Ausdrücken ({1/9} - {2/3}h + h
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) z
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: </
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">{4/9} z
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= h
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z
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:
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</
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">z
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= h
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: </
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= {1/9} - {2/3} h + h
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