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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0089
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89
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Von verbeß. Fernröhren.
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E X = A H - E H - A X = {1/2}a - {e
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/4a}
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- {2a
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t + e
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t/4a t + 8e} - {e
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/2a} (das letzte Glied {e
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/2a}
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iſt der Werth von A X vermöge (21)) =
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{2a
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e - 2a e
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t - 3e
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/2a
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t + 4a e}. </
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">Man ſetze dieſen
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= z, und die Länge A B = c, ſo ſtehet wie-
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derum E X (z): </
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">E B (A B + E X + A X,
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oder c + z + {e
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/2 a}) = M X (e): </
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xml:space
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">B D =
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{c e/z} + e + {e
<
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/2 a z}. </
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<
s
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">Nennen wir den itzt ge-
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fundenen Werth r, wird z = {c e + e
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/2 a}/r - e} =
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{4 a
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e - 4 a e
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t - 6 e
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/4a
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t + 8 a e}, oder {c + {e
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/2a}/r - e} =
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{a - e t - {3e
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/2a}/a t + 2 e}, welche Gleichung den geſuch-
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ten halben Durchmeſſer a giebt, ſo fern man
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aus dem Verſuche c, e, r, das iſt A B, B D
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und MX, oder die halbe Oeffnungsbreite weiß,
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wie auch t, den Sinus des halben ſcheinbaren
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Durchmeſſers der Sonne, nach dem halben
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Durchmeſſer = 1 gerechnet: </
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xml:space
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">und weil dieſer
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bey nahe 15{1/2} Minuten faſt allezeit </
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