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Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti / auctore Leonhardo Eulero
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M A X. ET Mite RELATIVA. iSt

erit valor differentialis ipsius q'

n ydx

ipsius

O Ci)

At 1

Zu vdx* 3

ipsius q V

2 o m . n vdx l ~ ~d^

ipsius'^ v/ -= Hocque modo similiter progredi licet ad

sequentes quantitates r, x, &c. cum suis derivativis; hinequenascetur sequens Tabella, qua singularum harum quantitatum va-lores differentiales exhibentur.

d.

r

= nv

d.

y

=z 0 C*>

d.

r

_ n v

d X

d.

r

= -

n v ,

0 u

d x

d.

/

= -

o ca

d x

d.

= +

n v

dx*

///

d, <fd. qd. qd. q K '

n i>

2Mv

0 Udx\

n ydx*o u

2 0 ca

d. r"d. r"d. r' vd. r'

3 m > , o u

+ d ^ 1

= +

dx l

d x*n v

dx* J__ o &»

dx\

3 0 £k>

d x*3 o co

d X J

X

d. s'd. s"

J '//

^r. j, /v

^ dx*

._ 4» X

dx*i 6 n v

+ 7^

._4 « v

<fx 4

, n V

, + j?-

Hb

o &>dx*

4 o ud x 46o^ x 44 Qa)dx\

d. x V

&C.

+

O L)

<k 4

Ex hac Tabella perspicitur, in valoribus differentialibus totidemterminos particula o u affectos occurrere, ac particula n y; at-que in utrisque pares adesse coefficientes : discrimen vero inhoc consistere, ut cuilibet termino particula o u affecto relpon-

Z 3 deati