126
§. 7. Seine Kectifications - Methode.
2 mal das n te Trapez
c 2n —b 2 c 2 “ -2 o_i_
; - -. X 2 +
2b 2 "
a 2 c 2 —a 2 b 2 b 2D ~ 2 c 2 — b 2 “
■. a’
bc 2 c 2 “x 2
Bezeichnen wir die Summe aller dieser Trapeze mit 2 , also diedoppelte Summe mit 2 . 2 , so haben wir:
2. 2 =\ . x 2
~ * b 2
[
_^x 2 [l +
a 2 c 2 — a 2 b 2
1 +
c 2b 2
bUHb»
+ ••• + ( 1-,
+ n.
bc
+
a 4
2x**
[
+ ... +
'b 2 '
1 +( r2 )+... + '
b 2 .
c 2 \n—1'
bl.
c 2 -\n-r
.b 2
2x 2 b 2a 2 "c 2
o2
oder2..S= J .^j.x 2
[■+G0+-+GQ"]<
i—i
-J.x 2 .
+
2x 2
>-(?
a* b 22x 2 ’o 2 '
('bn
+ n ■
a 2 c 2
a 2 b 2
bc
oder2.^= ‘x 2 Q 2 —lj . -
~(b 2 ) a 2 c 2 —a 2 b 2
+ n •
c;
b*
bc
a * r b 2 ^v 1—1 Gr»)
+ 2x 2> V o>y* 1 _b* 5
^ o V c 2 "—b 2n 2 , na 2 c 2oder 2 . 2 = —— • x H-
n 2 a 2 b 2
+
-b 2n
2b 2n 1 bc 1 2c 2n x 2
Dies soll also das n-fache sein von 2 . BHJS. Nun ist, da FH
ist,
__^AD 2 -Ja 2 . 2
EH = “Vs» + ^Kä+bVT-^ VT =bK| + s
SJ = ^V2 + C c
:^ 2 + oV j —— cKJ + a Kj-
K2
f™ A E= b -^ a Vä i AS = *=*. Kb
b c *
also RS = ^.Kj- b 2 ~ a Vj= gjb-a^ -b^+a^ K |.
c ' b bc