484 Methodus inveniendi Lineas Curvas 

Conftat hine quod quoties X + Sf Xdx perfedta integratione 
a 
dx 
habeatur ope 





per arcus circulares dum 
\ tl 
x2 fee ai 
lutam admittat integrationem curva fit algebraica, fi vero aliter 
evenerit tranfcendens. 
CN "dy 
—C?N?* 
admittat integrationem curva eft debris in aliis cafibus  * 
4 
¥, 
* 'y 
h 
| 
Quoties = fit integrale logarithmicum et — abfolutam 

tranicendens. 
1—C?N?4 d= 

Et quoties [2 per logarithmos inveniatur, 
Z 
k 
=apagt a : 2CN' dz : 5 
lute fit integrabilis pariter ac ———— curva eft algebraica, alias 
I+CN 
tranfcendens. 
— §s_—>»-——— 
2. P= ane oe 

Exempl. 1. Si fit variatio curvature T = erit 
arb 
Peta = oe ee =*) = aveas sVe—e hve me 
. oa Te oi eee ee ey ee an e 
[YY Gk OWT . 
Paka delle —— HE ponatur y= oe habetur y+ Sf Tdxx 
a 
+45)7 2 ae: 2y ir Fae Bf 4 3hd 
oe, “adhibendo theorema —__ aa (= 
arb 6 —a*x V a—x 
3 
—=_) = ane a ce et integrando f=. +C= 
Te ae Mi — a+b — xP Vg — x 
;» cujus termini funt arcus circulares quorum finus 






VviI- 4 
(tA: oe b ¢ 
av « : 
J/1 — p= = ee GE cofinus p = 3 ee evanefcente ‘ ‘ 
Vitzo —a’x" a . 
: dx 2st bv Ge 
arcu conftanti C, quare y (= {2 —)= l\w= — bv at j 
Je 4 ( Vvi-?" We =) MNT ag My 
et in hoc cafu curva eft ellipfis. 
4 Exempl 

