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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letzten Größen im Vergleiche der erſten, wie auch
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die letzte des Denominators im Anſehen der
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zwey erſten ſehr klein ſind. </
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">Denn es iſt ein
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bekannter Lehnſatz, deſſen man ſich gar oft ge-
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braucht, daß wenn bey zweyen Größen A + y
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und B + z, das y und z gegen A und B ſehr
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klein iſt, man annehmen könne {A + y/B + z} = {A/B}
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+ {- A z + B y/B
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}, mit Hinweglaſſung aller Po-
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tenzen des y und z, die über den erſten Grad
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hinaus gehen, wie es ſich leicht zeigen wird,
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wenn man ſowohl A, als y, mit B + z
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wirklich dividirt.</
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<
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">31. </
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">III Zuſatz. </
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">Nach dieſer Anmerkung
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wird der Bruch des zweyten Zuſatzes alſo aus-
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ſehen x = {m p a/m p - a p k} + {(m p a) {1/2} m k e
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- (m p - a p k) ({1/2} m k a e
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+ a p k
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e
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)/p
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x (m - a k)
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.
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">Der erſte Theil {m p a/m p - a p k} iſt eben {m a/m - a k}
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= q (I Anmerk.)</
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">der zweyte wird durch die
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wirkliche Multiplication alſo ausfallen
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{m
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a
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({k
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/m p} - {k
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>
/m
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a} + {k
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/m
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}) {1/2}e
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}/{(m - a k)
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} =
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{m
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a
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/(m - a k)
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} x ({k
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/m p} - {k
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/m
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a} + {k
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/m
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}) {1/2}e
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=
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q
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({k
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/m p} - {k
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/m
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a} + {k
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/m
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}) {1/2} e
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.</
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