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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Von verbeß. Fernröhren.
"/>
a zu b kleiner ſeyn, als m - 1 zu m; </
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<
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xml:space
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">es kann
<
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2
<
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>
gleich ſeyn, oder auch 3
<
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>
größer, aber dennoch
<
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/>
kleiner, als m zu m - 1; </
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>
<
s
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xml:space
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">und 4
<
emph
style
="
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">to</
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>
gleich mit m
<
lb
/>
zu m - 1, oder 5
<
emph
style
="
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">to</
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>
endlich größer, als dieſes.
<
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</
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<
s
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xml:space
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">Im erſten Falle iſt {m - 1/a} > </
s
>
<
s
xml:id
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echoid-s1068
"
xml:space
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">{m/b}, und {m/a} > </
s
>
<
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xml:space
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<
lb
/>
{m - 1/b}, folglich ſo wohl u′, als u″ poſitiv. </
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>
<
s
xml:id
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xml:space
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<
lb
/>
Im zweyten wird {m - 1/a} = {m/b}, und {m/a} > </
s
>
<
s
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xml:space
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">
<
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/>
{m - 1/b}; </
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>
<
s
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"
xml:space
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">läßt man alſo den Theil, in welchem
<
lb
/>
ſich a befindet, hinweg; </
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>
<
s
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echoid-s1073
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xml:space
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">hat man {1/u′} = 0, und
<
lb
/>
u′ = ∞, doch bleibt annoch {1/u″}, und u″ po-
<
lb
/>
ſitiv. </
s
>
<
s
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xml:space
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">Im dritten Falle iſt {m - 1/a} < </
s
>
<
s
xml:id
="
echoid-s1075
"
xml:space
="
preserve
">{m/b}, und
<
lb
/>
{m/a} > </
s
>
<
s
xml:id
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xml:space
="
preserve
">{m - 1/b}; </
s
>
<
s
xml:id
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xml:space
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">derowegen u′ negativ, und u″
<
lb
/>
poſitiv. </
s
>
<
s
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echoid-s1078
"
xml:space
="
preserve
">Im vierten bleibt annoch {m - 1/a} < </
s
>
<
s
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"
xml:space
="
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">
<
lb
/>
{m/b}, doch wird {m/a} = {m - 1/b}, {1/u′} negativ, {1/u″}
<
lb
/>
= 0, und u″ = ∞. </
s
>
<
s
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xml:space
="
preserve
">Endlicy in dem fünften
<
lb
/>
iſt {m - 1/a} < </
s
>
<
s
xml:id
="
echoid-s1081
"
xml:space
="
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">{m/b}, und {m - 1/b} > </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">{m/a}; </
s
>
<
s
xml:id
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xml:space
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">werden
<
lb
/>
alſo beyde Werthe u′, und u″ negativ.</
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</
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<
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">Aus dem, was wir itzt geſagt ha-
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ben, fließet folgender Lehrſatz: </
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>
<
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">Gläſer, die bey-
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/>
derſeits conver, oder planconver, oder </
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>
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