480. ‘Methodus inveniend! Lineas Curvas 


Exempl. 1. Invenienda fit curva ubi variatio curvature T=. 
2) Bu; 2 Se z he PR te Lee 
 BLOETATAL eee. Lt fimphicier -reddatur’.caleulus; poner 
aii Z 3 
avo ie ae 
3 Ss . é pens e4 
- “2 z_ O42 ea bap 
. bar 278)" =4 et at=b erit = - = ie eee te Mee Ze 





18 VO u=4o. 
ct [Tas ivan a2 Gt ‘conftans ize At 
Téz=——__ = + A; fit conftans hee =4, quod 
accidit evanefcente we Waza = 0, abetur 7 per — theorema 
du /b duSb 4 
SG = = et integratione ae : C= = j 
“he re isa S Vile . 


5 cUjus zquationis Paes guum fint arcus circulares 

Te 
4b a/b 
quorum finus ¢ Oe —p =——— et cofinus p= 7, » pofito arcu 
conftanti C=o, ebtinetur y (= Spas) =f du /b eB) 
Yu—4b Vb 4bhV/b 
a nai oa a pofita y=o et w= 46, atque (= 
du ugh hu asl 
fads/i—p a = [= aia 3 ES a quibus zequationibus ex- 
terminata w et fubftituta a habetur y* = ax° zquatio pro parabola 
~ 
ccubica. 
Exempl. 2. Si fit variatio curvature T= erit " Tas (= 
a 
f2® aU AEE it Ze ae = qerit conftans A= a, atque 
E a 
; . ] : ; 
vi theorematis os = (= =) == Pee et Te 
a 7: Taz V1I—p 
dz 
Jz —3+C= “pa = pofito arcu conftanti C=o cateri 
a Pe V1 
funt equales corumque finus et cofinus, unde /i p= 
a . en Cae Zz 
aa et dx (=dz I-p)= ————— et d = 
» P V a +2 \ v p) Vg? ly ( a 
2 | pas) 


rae 

