MAX. ET M 1 N. RELATIVA.

rrZ

o = B +o = B dx -f-

_I_

n v'( i +pp)_ dx _

nt'Ci -h i'p)

+ d. — jTTZü —>>^udx n f (i + ppj

y d p _ y l pdx

Hh

n(.+») ,:> n'm+n)

9

ex nna aequatione (i dcnuo n = sy dx exterminare velimus ,prodret a?q n acio d'sse r emia is tertii ordinis , ex qua multo mi*nus quicquam ad Curvam cognoscendam deduci posset.

S C H 0 L 1 0 N II.

65 . Quanquam, in hac Propositione posuimus [2] esse func-tionem determinatam quantitatum x, y->p, q, &c. tamen Me-thodus solvend’ patet, si hec ipsa quantitas [Z] fuerit functioirdesinita tbrmulas integrales in se complectens. Ponamus enimin formula n = f[_Z^d x, quas omnibus curvis debet essecommunis, esse

d l Z] — [L]dn+ [Af]^ + [3n^+[P]^+[Q]^-f &c.existente w ■==■/[ a] dx, &

d £&]] = \_m~\dx [_n~\dy \_p~\ d p \_q~\d q SiC.

Maximum minimumve autem esse oportere formulam sZdx texistente : dZ = Ldn 4- Mdx, 4- Ndy 4- P d p 4- Ac.Jam formula f\_Z~\dx continetur in Casu secundo §. 7 Cap.praec: inde ergo si cap ia cur integrale /'iLjdx e)u{quc valor res-pondens abscisse x~a y ad quam solutio debet accommoda-ri, ponatur = [ff], atque [//]— /1LJ dx = [ V]i ha-bebitur formulas f\_ z]dx va'or disserentiaus = n r. dx ([N]

. r„~\ryi _ diL£L+ M Q1> + dd.Clk. 3+ MLvl)

d x dx *

— &c. \ Deinde vero maximi •minimive formula sZdx con-tinetur in Casu tertio loci citati; ad ejusque valorem disserentia-lcm inveniendum, ponatur formale /Ldx valor abscisse x^=arespondens ac H — /Ldx~-V. J tm capiatur integrale

s{L\Vdx ■= Hs[L]dx — s[L}dxsLdx sitque, positox—4, valor formule s[ L) dx/Ldx “ K, eodem autemcasu formulas siL}dx valor est — s H] , ex quo form si e

Dd i j\Li