15$ D£ MOTV OSCILLATORIO 



zzVazzk, ct AG = i; crit \Gzzb-i-k ct G_-~ 

 — j^- ; critquc primo pro nexura in A; bj^zbb-Y- 

 bk -f- />/> ; atquc pro flcxura M crit ?c — P/ -f-/j 



dp-jp^^^X-fjy.dp-tSxxdp-, feu P 



( f - J' ) -/P <T = ^&^ + J tJJ *P> vbi no- 

 tandum elt, ii .v — o fieri y zz c ct fi x zz a , rlt j zz o. 

 Sumantur autem differentialia vt prodeat - Vdy--pdy 



Pcdx(b-l~k) d x , ,, c ■ j j • tf" 



rr y fe - -\--j- fy d p. Sumtisque denuo differen- 



tialibus pofito dx conftante habebimus : -P ddy- pddy 

 — dy dp — y - * d - ? - ; quae cll aequatio pro curuatura fli 

 nis OMA. 



§. 4.4.. Si fin>is grauitas euanefcat , vel corpus P fit 

 quafi infinitum rclpcctu ponderis funis p , tum fiet ddy 

 rrio, funiquc in directum extendetur, Lta vt Htyzz 

 f(a ~ x ) , vti fiipra hotauimus. Sin autem funis ad cor- 

 pus finitath habeat ratiohern , ponamus funcm vniformis 

 cralTitici , vt iit p ipfi X proportionalc , fitque pzznx : 

 atque habebi miis — ?ddy -h » x ddy -f- n dx dy -4- zz^j- 

 zzo. Sumatur pro aequatione integrali 

 y — c -f- a.v -+- (3 .v ? -f-y *' -f- £ .vM-e .v 5 -f- £.v 5 -f- ctc. crit 

 2|3P-f-6yP.v-f-i 2oP.v 1 -i--20fiP.v , H-30^P.v 4 -i-+2riP.v etc/) 



-+-2j3w-f- 6y ;/.v.v-|- 1 2o;/.v J +2oe;/.v 4 -f- 3 . '£;;.v ; etc. ' _ 

 -i-a;/-f-2,3'/.v-f-3y"-vM- 4$».v f- 5e«A"*-f- 6<^'.vctc.|~" 

 4,-4. s«* _+- &■* .+- -^ -+- i±£ -+- <-^ etc.j 



hinc ergO crit _(3P_r— ■ a'/ . 6yPz=- +,3;;-~- 1 , 



12 p— — 9y ;/- 7- ; &ogP__ i6$n j etc. At ex 



aequatione — Y dy —pdyzz ^ 1~~ j Jjdx nircl- 



ligitur, iin xzzxi , forc ob p_~-0 et Jydxzzo\ dyzz- 



cdx 



