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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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AB CXJRVAS INVENIENDAS ABSOLUTA. iop'

d. [Z"J dx = m. dx. [!/"] dx c [»"] ^ + "IfJ )

[ Z w 2 dx = m. dx. [I/ v ] dx ( [V]

d. [ 2'} dx = äv. t/x ([//]

&c.

Hinc porro deducitur:

d[p'] , dd[qJx + J ~ s ;

«*s /3

^ x J

, Ml 3 s+ dx\ )

'd nd. n'

n v. dx.

££]

dx 1

d.n = 0». ([ V ]<&. + j£J )

. c^vrt'i +

^[^'3 dd[jQ] ^

dx 5

n'"= nv. dx (£ L" ] C /> 7 3

+ [tf "3

^.n A/ :

+ [L "][/3

x dx

n,. dx([L"'] dx ([*"]

[>] d sLH + 2 fL']d[q\

dx

+OT-

4 n , dJ[Qi i

T* i v « /

dx

m

dx 3dd[q]

d.n' = »y. dx(([L"'}dx + [L»']dx)([*"] J^ +4-[L"l[>] k?3<* [^3 + 2 + j- y* j ^LL) +

^ /f Cl X CL a^a M

&c.

Ex his jam orientur sequentes determinationes |

</. Zdx=.m.dx.

dx 1

V. Zdx^=-m. dx(JJdx. ^ Hh t" )

.. - , . rr ^. rr X ri M J X \n Wl -l-E3)

*: Z dx~m.dx^L dx([L jdx. + -j--' _r -

o z

d.