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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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r AT> CV&VAS INVENIENDAS ABSOLVTA. 85

Ex his nunc colligentur incrementa valorum n , n', n ", n 1 "»-&c. qux recipiunt ex translatione puncti n in ; erit scilicet

d. nd, n':

d. 1 /

d.ri"

4-

, [T]

nv. dx.

dx*

m

: nv. dx (

dx*

nv. dx{

dx

; 4 s r'] +Jpr] .

^*5 '

3[s"] + 45'] . 6sm + 44r f 14r]

dx*

'//

+ +

dx

3[S ,// ]+^[S ,/ ]d[S' } __

d X^

[Q_ ['o ,v l4-^ro ,// 1 OT+z^lX" ]

dx z dx*

4 1"! +6J[T"]'

4d[f] 4- [df\

)

)

d,Ti'=n y .dx ( L ~j x

dm

t g v ]+3 d[s"']-3d[s")+d\s'} , It v ]+44.t"} -6d[rq+4d[T] -441

dx* d x s ^

- ilp +

fsg'M

^5C 1 dx 1

4X V J affin+WJ d[s^u^"] 4- 34^4^

dx* dx*

d [? v ] 4 d\r"] + 6d sr v ] 4 din + d[T] N

' TZs " )

d X s

Huic autem incremento arqualia sunt incrementa omnium se-quentium valorum, nempe ipsorum n w/ , n '" 1 ", n IX , &c. At-qui valoris ji V/ & omnium sequentium incrementum idem erit

_ , / r Xf 1 ' n d[F fV l , dd{Q'"] d* 1

= nv. <3!Jf ( [Ä J - + -- J - - L V " J

dx 1 d x z dx*

4 - ^ ^ -3 ). Poterunt autem ha:c incrementa ad ea-

dx* d x* J

dem signa reduci, respectu litterarum [Psl, [Q], [i?jy,& [T]j sicque prodibit

d.w