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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25
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file
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0029
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29
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rhead
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Von verbeß. Fernröhren.
"/>
<
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<
s
xml:id
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echoid-s251
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xml:space
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preserve
">Setze man nun in dieſem Ausdrucke des
<
lb
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zweyten Theils nach {k
<
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/m p} hinzu + {k
<
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">2</
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/m
<
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">2</
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p} -
<
lb
/>
{k
<
emph
style
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">2</
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>
/m
<
emph
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super
">2</
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p}, ſo wird er q
<
emph
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({k
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/m p} + {k
<
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">2</
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/m p} - {k
<
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">2</
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/m
<
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="
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">2</
emph
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p}
<
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/>
- {k
<
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">2</
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/m
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a} + {k
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">3</
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/m
<
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>
}) {1/2}e
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.</
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>
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</
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<
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<
s
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="
echoid-s253
"
xml:space
="
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">Weil aber - {k
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/m
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a} + {k
<
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">2</
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>
/m
<
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">2</
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>
p} = {k
<
emph
style
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super
">2</
emph
>
/m
<
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">2</
emph
>
}
<
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/>
(- {1/a} + {1/p}) (das iſt, wegen k = {1/a}
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/>
- {1/p}) = {k
<
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/m
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} x - k = - {k
<
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/m
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}; </
s
>
<
s
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xml:space
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">kann
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man auch ſchreiben q
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({k
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/m p} - {k
<
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/m
<
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>
} - {k
<
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">2</
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>
/m
<
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style
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">2</
emph
>
p}
<
lb
/>
+ {k
<
emph
style
="
super
">3</
emph
>
/m
<
emph
style
="
super
">3</
emph
>
}) {1/2}e
<
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>
= q
<
emph
style
="
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">2</
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>
(- {m - 1/m
<
emph
style
="
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">3</
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>
} x (k
<
emph
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">3</
emph
>
-
<
lb
/>
{m k
<
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">2</
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/p}) {1/2}e
<
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style
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>
= - q
<
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">2</
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>
x {m - 1/m
<
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">3</
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>
} (k
<
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style
="
super
">3</
emph
>
-
<
lb
/>
{m k
<
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style
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">2</
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>
/p}) {1/2}e
<
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>
. </
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>
<
s
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xml:space
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preserve
">Auf dieſe Weiſe hat man x =
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q - q
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x {m - 1/m
<
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style
="
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">3</
emph
>
} (k
<
emph
style
="
super
">3</
emph
>
- {m k
<
emph
style
="
super
">2</
emph
>
/p}) {1/2}e
<
emph
style
="
super
">2</
emph
>
. </
s
>
<
s
xml:id
="
echoid-s256
"
xml:space
="
preserve
">Setzet
<
lb
/>
man φ = {m - 1/m
<
emph
style
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">3</
emph
>
} (k
<
emph
style
="
super
">3</
emph
>
- {m k
<
emph
style
="
super
">2</
emph
>
/p}) {1/2}e
<
emph
style
="
super
">2</
emph
>
, ſo
<
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/>
wird endlich x = q - q
<
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>
φ.</
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>
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<
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<
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">32. </
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<
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">III Anmerkung. </
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>
<
s
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"
xml:space
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">Dieſe Formel kommt
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in allem mit des Herrn Clairaut ſeiner, die
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man zu Ende der zweyten Aufgabe ſeiner Ab-
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bandlung vom Jahre 1756 findet, überein, </
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