192 
Exemplum Ill. 
f. 10. Integrare expressionem 9/—04%y (1 +) 
elementum arcus Ellypseos, cujus semi - axis transversus 
Z a, ét semi-axis conjugatus —b, denotantem.. 
Solutio. 
Posito Ps k, et reducta quantitate radicali y (1 +2.) 
in seriem infinitam, obtinebitur : 
VU+)= 1,5 LP ete fe prete. 
Bx4 
vel = 1 Ne ES “siemens ot: it Le ee mat etc., ubi 
a, BB, y» 0, €, à etc. coëffcientes I, EG) 1G-9DG=2), 
1. 2 1. 2. 3 
1G—1)G—2)G—3) 
1. 2. 3. 4 
significant. His praemissis erit : 
ax? 0x Gx+ox yx69x% 
Of = OL sh qe —asjte quon + et. 
Quodsi jam quantitates (a?—x?) *,(a—x?) *,(a—x°) * etc. 
etc. respective in: À, À?, À°, kt etc. ductos, 
in series infinitas resolvantur, ac in suos coëéfficientes du- 
cantur, valor 9 f abit in: 
aeos x4 x6 æ2(m— 32) 
ed (1 es pre at 5h 46 ss... mL) 
sex REA 3x4 4x m(x)2 (mr 
Meten (1 ae Hasta. 
y6ax aval 6x4 7 1ox6] pe x2(M—1) 
te ( Er) + 4. a° x sous A æt mn), 
ÿx30x 4x2? 10 x4 20% m(m+:) m+2)x? es) 
Date MD ns Macbr De REC ns — eat) 
+ etc. 
mx2(M—31)  m(m+:) x2(M—1) 
ami) ? F'anPie o2 (M— 1) etc, 
ubi notandum est, quantitates 
terminum generalem uniuscujusque seriei exprimere. Su- 
