Bošković, Ruđer Josip
,
Abhandlung von den verbesserten dioptrischen Fernröhren aus den Sammlungen des Instituts zu Bologna sammt einem Anhange des Uebersetzers
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
page
|<
<
(24)
of 199
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
de
"
type
="
free
">
<
div
xml:id
="
echoid-div7
"
type
="
section
"
level
="
1
"
n
="
5
">
<
p
>
<
s
xml:id
="
echoid-s241
"
xml:space
="
preserve
">
<
pb
o
="
24
"
file
="
0028
"
n
="
28
"
rhead
="
Abhandlung
"/>
letzten Größen im Vergleiche der erſten, wie auch
<
lb
/>
die letzte des Denominators im Anſehen der
<
lb
/>
zwey erſten ſehr klein ſind. </
s
>
<
s
xml:id
="
echoid-s242
"
xml:space
="
preserve
">Denn es iſt ein
<
lb
/>
bekannter Lehnſatz, deſſen man ſich gar oft ge-
<
lb
/>
braucht, daß wenn bey zweyen Größen A + y
<
lb
/>
und B + z, das y und z gegen A und B ſehr
<
lb
/>
klein iſt, man annehmen könne {A + y/B + z} = {A/B}
<
lb
/>
+ {- A z + B y/B
<
emph
style
="
super
">2</
emph
>
}, mit Hinweglaſſung aller Po-
<
lb
/>
tenzen des y und z, die über den erſten Grad
<
lb
/>
hinaus gehen, wie es ſich leicht zeigen wird,
<
lb
/>
wenn man ſowohl A, als y, mit B + z
<
lb
/>
wirklich dividirt.</
s
>
<
s
xml:id
="
echoid-s243
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s244
"
xml:space
="
preserve
">31. </
s
>
<
s
xml:id
="
echoid-s245
"
xml:space
="
preserve
">III Zuſatz. </
s
>
<
s
xml:id
="
echoid-s246
"
xml:space
="
preserve
">Nach dieſer Anmerkung
<
lb
/>
wird der Bruch des zweyten Zuſatzes alſo aus-
<
lb
/>
ſehen x = {m p a/m p - a p k} + {(m p a) {1/2} m k e
<
emph
style
="
super
">2</
emph
>
- (m p - a p k) ({1/2} m k a e
<
emph
style
="
super
">2</
emph
>
+ a p k
<
emph
style
="
super
">2</
emph
>
e
<
emph
style
="
super
">2</
emph
>
)/p
<
emph
style
="
super
">2</
emph
>
x (m - a k)
<
emph
style
="
super
">2</
emph
>
.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s247
"
xml:space
="
preserve
">Der erſte Theil {m p a/m p - a p k} iſt eben {m a/m - a k}
<
lb
/>
= q (I Anmerk.)</
s
>
<
s
xml:id
="
echoid-s248
"
xml:space
="
preserve
">; </
s
>
<
s
xml:id
="
echoid-s249
"
xml:space
="
preserve
">der zweyte wird durch die
<
lb
/>
wirkliche Multiplication alſo ausfallen
<
lb
/>
{m
<
emph
style
="
super
">2</
emph
>
a
<
emph
style
="
super
">2</
emph
>
({k
<
emph
style
="
super
">2</
emph
>
/m p} - {k
<
emph
style
="
super
">2</
emph
>
/m
<
emph
style
="
super
">2</
emph
>
a} + {k
<
emph
style
="
super
">3</
emph
>
/m
<
emph
style
="
super
">3</
emph
>
}) {1/2}e
<
emph
style
="
super
">2</
emph
>
}/{(m - a k)
<
emph
style
="
super
">2</
emph
>
} =
<
lb
/>
{m
<
emph
style
="
super
">2</
emph
>
a
<
emph
style
="
super
">2</
emph
>
/(m - a k)
<
emph
style
="
super
">2</
emph
>
} x ({k
<
emph
style
="
super
">2</
emph
>
/m p} - {k
<
emph
style
="
super
">2</
emph
>
/m
<
emph
style
="
super
">2</
emph
>
a} + {k
<
emph
style
="
super
">3</
emph
>
/m
<
emph
style
="
super
">3</
emph
>
}) {1/2}e
<
emph
style
="
super
">2</
emph
>
=
<
lb
/>
q
<
emph
style
="
super
">2</
emph
>
({k
<
emph
style
="
super
">2</
emph
>
/m p} - {k
<
emph
style
="
super
">2</
emph
>
/m
<
emph
style
="
super
">2</
emph
>
a} + {k
<
emph
style
="
super
">3</
emph
>
/m
<
emph
style
="
super
">3</
emph
>
}) {1/2} e
<
emph
style
="
super
">2</
emph
>
.</
s
>
<
s
xml:id
="
echoid-s250
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>