Libr. I. Sect. I,

a4d u

si nyydf-f sin u d y/

___ rtan g 'yj r sin u

u 2 cos \ (v — y/) cos|-(u + y/) — p pcos ip ^

DifTerentiando perinde aequationem XI, inter variationes differentiales quan-titatum u, y/, N emergit relatiodN _i_\

uu u )

X

d NX

< 4

e(i +•

(uu —i) sin u/

du 4 ---£-dy/, siue

2 u cos y/

r r sin v

d u -f — - _. , ■ d y/

bu VA “' r 7 >cosy/

Hinc eliminando d u adiumento aequationis praecedentis obtinemusd N rr

dv+[

bb tang yj

du =

bb tang y/X. rr

bb tang yj

TF7

( r\ r sin v

V+7J Tco.~ <1 ¥'-

dV

dN

( b b \ si

b cos yjsinu tang y/

+ ^\ r / smy/

os y/■ dyj

d yj

28.

DifTerentiando aequationem X, omnibus r, b, e , u pro variabilibus habitis,sin yj

bstituendo de= — cbs y/ £ " e ^ j ninandoque du adiumento aequationis inter d N,

du, d y/ in art. praec. traditae, prodit

bb e (uu — i)

dr

b d5+ 2 X ur

d N

+ " 9 co!y/' { (« + ^)siny/ — (u— sinu } dy/

Coefficiens ipsius diV per aequ. VIII transit in - „ coefficiens ipsius dy/ au-

tem, substituendo per aequ. IV, //(sin?//—sinu) = sin(y/—u), — (siny/ + sinu) =

i sini// cos u ncosu

sin (*// + e), mutatur m- - — 2 ^ — —- : - ita vt habeatur v

A ' ’ cos y/ smy/ ’

, r 7; sin u 7 ? cos u

dr = —dT» — diV-j- - g.—-- dy/

^siny/

1//

„ N , N

Quatenus porro A' vt functio ipsarum b et t spectatur, fit d N — -j- d i — \. d b,

quo valore substituto, dr, ac perinde in art.'praec. du, per dt, d fi, dy/ expres-sae habebuntur. Ceterum quod supra monuimus etiam hic repetendum est, scilicet