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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<
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<
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<
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o
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23
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file
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0027
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n
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27
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rhead
="
Von verbeß. Fernröhren.
"/>
chet, die unendlich nahe bey der Achſe ein-
<
lb
/>
fallen.</
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>
<
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<
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<
s
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xml:space
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">28. </
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<
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xml:space
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">I Zuſatz. </
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<
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xml:space
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">Sey demnach q der Werth
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des x ſür die unmittelbar bey der Achſe einfal-
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lenden Straalen, wo der Bogen A M = e ver-
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ſchwindet, und mithin auch alle mit e
<
emph
style
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super
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>
multi-
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plicirte Größen: </
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>
<
s
xml:id
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echoid-s227
"
xml:space
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preserve
">ſo wird ſtehen q : </
s
>
<
s
xml:id
="
echoid-s228
"
xml:space
="
preserve
">q - a =
<
lb
/>
m p : </
s
>
<
s
xml:id
="
echoid-s229
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xml:space
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preserve
">a p k = m : </
s
>
<
s
xml:id
="
echoid-s230
"
xml:space
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">a k; </
s
>
<
s
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"
xml:space
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preserve
">folglich giebt ſich dieſe
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Gleichung m q - m a = a k q, oder m a =
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/>
m q - a k q, und {1/q} = {1/a} - {k/m}, das iſt
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lb
/>
q = {a m/m - a k}.</
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<
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xml:space
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<
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">29. </
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<
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">II Zuſatz. </
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<
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xml:space
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">Man gebrauche ſich des
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itzt geſundenen Werths des {1/q} anſtatt {1/x} in
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dem dritten Theile des erſten Gliedes der
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oben (26) beſtimmten Proportion, ſo wird
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dieſes Glied x - {e
<
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style
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>
/2 a} + {e
<
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style
="
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">2</
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>
/2 a} - {k e
<
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style
="
super
">2</
emph
>
/2 m} = x
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/>
- {k e
<
emph
style
="
super
">2</
emph
>
/2 m}, und die Proportion wird folgende
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/>
ſeyn x - {k e
<
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style
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super
">2</
emph
>
/2 m} : </
s
>
<
s
xml:id
="
echoid-s236
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xml:space
="
preserve
">x - a = m p - {1/2} m k e
<
emph
style
="
super
">2</
emph
>
:
<
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/>
</
s
>
<
s
xml:id
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echoid-s237
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xml:space
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preserve
">a p k, aus welcher die Gleichung m x p - {1/2}
<
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/>
m k e
<
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style
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super
">2</
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x - m a p + {1/2} m k a e
<
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style
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">2</
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>
= a p k x -
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/>
{a p k
<
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style
="
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">2</
emph
>
e
<
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style
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">2</
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>
/2 m} entſteht, daraus man findet x =
<
lb
/>
{m p a - {1/2} m a k e
<
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style
="
super
">2</
emph
>
- {a p k
<
emph
style
="
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">2</
emph
>
e
<
emph
style
="
super
">2</
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>
/2 m}/m p - a p k - {1/2} m k e
<
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style
="
super
">2</
emph
>
}.</
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>
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xml:space
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</
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<
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">30. </
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<
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xml:space
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">II Anmerkung. </
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<
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xml:space
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">Man kann dieſen
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Bruch in einen weit einfachern verändern, wenn
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man n@e@ket, daß in dem Numerator die </
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