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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Abhandlung.
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dreyzehn daraus entſtehen werden, derer zwey
<
lb
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{1/a
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}, vier {1/a} in ſich enthalten, ſieben aber von
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dem a befreyet ſind. </
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<
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">Zwey, in denen {1/a} ſich
<
lb
/>
befindet, ſind folgende {d m/d M} X (2 + {4/M}) {1/a},
<
lb
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und {d m/d M} X (m - 1) (4 + {4/M}) {1/a}: </
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<
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<
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in dem letzten die wirkliche Multiplication mit
<
lb
/>
m - 1, laſſen ſie ſich leicht alſo ausdrücken
<
lb
/>
{d m/d M} X 4 [m (1 + {1/M}) - {1/2}] {1/a}. </
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<
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">Eben ſo
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lb
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bekommen jene zwey aus den letzten, die {d m
<
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style
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>
/d M
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style
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emph
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}
<
lb
/>
in ſich halten, dieſe Geſtalt {d m
<
emph
style
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emph
>
/d M
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emph
style
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} X [3 m (M
<
lb
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+ 1) - M]; </
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<
s
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">die drey aber, bey denen man
<
lb
/>
{d m/d M} antrifft, werden alſo ausſehen {d m/d M} X
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lb
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m (3 m - 2 + {2 m/M}). </
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<
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xml:space
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">So wird demnach die
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Gleichung, wenn man ſie in die Ordnung bringt,
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lb
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{1/a
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super
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>
} - {{m - 1/M - 1} X (2 m + 1) - {d m
<
emph
style
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">2</
emph
>
/d M
<
emph
style
="
super
">2</
emph
>
X (2 M + 1) + {d m/d M} X [4 m (1 + {1/M}) - 2]/{m - 1/M - 1} X (1 + {2/m}) - {d m/d M} X (1 + {2/M}) X</
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