r AD CURVAS INVENIENDAS ABSOLUTA.rur, habebiturque o=A

-P + d -ß-

dx

79

iAK + d ll - &c

dx 1 - ^ dx' aC *

quae multiplicetur per dp = q dx , ad eamque addatur o = —dZ-\-P dp -\’Qdq + Rdr + Sds->rSic. quo facto prodibit ista,aquatio integrabilis

o =Ai f —dZ + iJQj— — &c.

“j ~Q^dq 4” Rtd r 4* Sds 4“

cujus integrale erit

o =Ap — B — Z 4 Qjq

4 Rr4 Ss

ßdR, . qd d S o _

d X ”*■ 'd x l ' 0cc '

r d Sdx

seu o = Ap — B — z+Qq — +

qddS - dqdS-^-Sddq qd'T - dqddT-\-dTddq — Td'ct

d x'~ d x ä

Casus VT

K8- Sit & M= o & N—o & P = o, ita ut sit dZ ^f^d q 4" Rd r 4 S d s 4 T d t 4"

Ob N=o & P— o, per Casum fecundum,dua integrationes lo-

cum habent, eritque aquatio, pro curva quahta, hac ,

'_ j u t d B. i d d s _ d r n

o = Ax — B+d—,$+ -T-r— XT + &C.

ad quam per dq = rdx multiplicatam si addatur o = d Z — Q dep■— Rdr — Sds — T dt — &c. habebitur ista aquatio dcnuo-Integrabilis:

o=Axdq — Bdq+dZ—rdR + r ^?+ &c -

:— Rdr — S ds — Tdt —&c.

cujus integrale est

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