3? 
1 
H 
2 
Polest. 
1 = 1+ 0-1-04-0+0 
xx 
yj a 4 —3 
XX lx 6 1.3x 10 1.3.5x 14 1.3.5.7x 18 
etc. 
aa 2 a 6 
2.4a 10_r 2.4.6a 14 2.4.6.8a 18 
•8 
+ -7 + 
12 v 
TT ~ 
11 2 a 
16 x 
Tß 4 ~ 
16 a 
20 
etc. 
•8 
□ a 4 
x _ = i_ + 
x 4 a 8 
2x12 3 X 16 4 x 2o 
a 12 ■ a lb a 2U a . 
X 1 * 3x 1 6 6x 20 10x 24 15x 28 
-j l. u 4 —— etc. 
ai 2 + a 16 a 20 ^ a* a ^ 
4- 
.16 
-4- 
,20 
4- 
ox 
24 
,24 
etc. 
12 
C.a 4 
24 
,28 
hae series interpolentur inter 0 et l am potestatem, ut habeatur 
potestas dimidia 
xx 
^a 4 
quare dy 
_ xx lx 6 
T aa 2a 6 
1.3.5x 14 , 1.3.5.7x 18 t 
+ 4^—. „ ^ etc. 
1.3x 10 
2.4a 10 274.6 a 14 ’ 2.4.6.8a 18 
V a 
xxdx xxdx . l.x«dx + eorum- 
aa 
l.x 7 
que integralia Y = + 
2 a 6 ' 2.4a 10 
1.3 x 11 1.3.5x 15 
etc.; hinc si x 
1.3.5 
4 
- 4 
a et utraque 
1.3.5.7 
11 in2.4a 1 0 
1 
15in2.4.6a 14 
1, erit y 
1 
3 + 2 in 7 
1.3 
2.4.6 in 15 1 2.4.6.8 in 19 
construitur curva elastica, est ay = 
1.3.5x 15 
2.4 in 11 
etc.; sic spatium, cujus rectificatione 
x 3 lx 7 1.3x 41 
3ina + 7in2a 5 1 11 in2.4a 9 
4 
4- 
etc. 
15in2.4.6 a 13 
Haud absimiliter invenitur ratio s ad x, ipsius curvae ad ab- 
scissam, per seriem: 
, aadx 
d s = 
, x 4 dx 1.3x 8 dx 1.3.5x 12 dx 
d x 4- 4 ——— b 
2a 4 
2.4 a 8 
x i 
2.4.6a 12 
1.3.5.7x 16 dx , x 5 1.3x 9 
+ 2.4.6 .8 x 16 etC ' ade ° qUe S = X + 2in5a^ + 
+ 2.4.6tal3 3 ‘* etC ' et P ° Sit0 x = a = 1 re P eritur 5 = 1 + 2in5 
1.3 1.3.5 1.3.5.7 
4 <: 
2.4 in 9 
4 
_!_ 1_ _7 fttc 
2.4.6inl3 ^ 2.4.6.8inl7