Buch 
Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti / auctore Leonhardo Eulero
Seite
89
JPEG-Download
 

r AD CURIAS INVENIENDAS ABSOLUTA 89

d. Z dx = L dx. d nd. Z' dx = Udx.dn'd. Z" dx = L" dx. dn"d. Z" dx = U" dx. dii"d. Z /V d x = V'dx.dri"

Quodsi jam loco difserentialium dn, dri, dn", d n" &c. va-lores supra inventos ex translatione puncti n in v ortos substi-tuamus obtinebimus.

Zdx = nv. 11 dx*. ßd. Z'dx = nv.LVx 1 (&Ü-d.Z // dx=tiyX'"dx 2 ( [ ßl-d. Z'dx = nv.L n, dx 2 ( ^

' s sc

4 sr]+ fd[r] x

3 i g [^]+ 1 ? 4~ti -4- io^r7* r ^

dx* * /

_ 2[Xl+iSU

4[r] + i d-2oii[r] + jod'sr ] .

dx* '

i&d, =n, !*< Ep - [gZ3+|itga + [ffl t aWft aafl

** d oc d OC d X 9

IlYr\"l 4/',<n 4>c« , <f*OT 4-VI)

rf.2 <fc=n,.L <& ([iP-] Jjj 4-j^i;-73.- + -35* - 7*.}

&c.

Sequentium scilicet terminorum incrementa eadem hac lege pro-grediuntur. Addantur jam senorum priorum terminorum incre-menta , prodibit terminorum Z d x+ Z dx -f- Z' dx + Z"dx+ Z n ' dx A' dx incrementum totale =

. mddL^dmdL^+^ddiR^

uy.ax ^ -j-z k- j x i ~

; [$'] d 3 V. + 4d [S']ddL" + 6dL"dd + tf W [ 5 ']

d

Euleri de Max. & Min M -f-

M