30 DOCUMENT
23
SEPTEMBER 1896
"
a2
-
b2
+
c2
29
cos ß
= =
TI
=
0,8055
2ac
36
log
cos
ß
=
9,9061
-
10
ß
=
36° 20'
a2 + b2
-
c2
43
cos
y =
-;
=
-
2ab 48
log
cos
y
=
9,95226
-
10
y =
26° 23'.
Berechnung
der
Seite
a
Da
2^a stumpf,
so
ist
a
=
2r
.
sin
(180°
-
a)
log
a
=
log
20
+ log
sin
(64°
43'
38")[4]
=
1,30103 + 9,94884
-
10
=
1,24987
a
=
17,77.
AUFGABE 2.[5]
Nennen wir den Abstand
eines
solchen Kreises
aus
dem
gegebenen System
vom Mittelpunkt p, so
ist
sein
Radius
=
-Jr2
-
p2.
Seine
Gleichung
ist:
(x
-
p)2
+
r2
-
p2
y2
=
r2
-
p2
x2
-
2px
+
p2
+
y2
=
r2
-
p2
x2
-
2px
+
y2
=
r2
-
2p2.
[4] "64°"
underlined
twice.
"Fehler
im Ab-
schreiben" and "Resultat
richtig." are
written
in
the
left margin.
[5] The
problem,
recorded with
slight
varia-
tions
by
other
examinees, is:
Consider
a
circle
of radius
r,
centered
on
the
origin
of
a
rectangular
coordinate
system.
At each
point
along
the
x-axis,
another
circle
is
constructed,
with
center at
this
point
and diameter deter-
mined
by
the intersections of the
perpendic-
ular
to
the x-axis with the
original
circle.
The
circles
so
constructed
are enveloped by an
ellipse
of
semiaxes
r
and
r^/2.
When the
dis-
tance
of the
centers
of the
circles
from the
origin
exceeds
a
certain maximum
value,
the
circles
cease
to
touch the
envelope.
Prove
the last
two
statements and determine this
maximum
value.
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