420 CAPUT XVJII. DE MOTU CORPORUM

SCHOLION .

917. Pro cafu ergo ejusmodi corporum pro quibus efl bb — U,

> aa co(<f 2 4 - cc fm? 2,

-, atque J Jifgu, 8 * —

erit » — -, u ':

c c aacc

</zfgu 1 , integralia in genere ita fe habebunt:

fin £ z fin ( 8 't -f- f))

aa

X = <5 cof£ ♦

y=ecor,+0Jcof3fin(*+3)+ J£' c °g^ »"(^ + SO

* = ecoO-®Jcor,Cn(*+ 3 )+

> cc

atque

7 , —Fcol^-l- Gfin^ co5(F/-hq)

^ — F coi tj — G cof£ coi »7 col'(fjV 4g) -s- H«' cof 3 cof(J*V + h)*• = 5 cof 3 - & cof£ cof 3 cof^/ -> g) - H «' cof>7 cof + h).Quare fi initio t ~ o fuct it

p = r Im£cofl; 5 = rfin^cofm, r = r fin3 cofN

reperitur

q rfin»; cof3 cofm_r cof»; fin3 cofn«'fin^ coii)

^ _ r fin£ 3 cofI _ r fin>7 cof^ cof»7 cofnt - r fin3 cof^cof3 cofn

fiu £ 2 cofg

F — rfin^ cof£ coff -f r fiu-7 cof-7 cof IN -i- r fin 3 cof 3 coftt.

At datis angulis l, m, N, fiinul dantur 77, 3

cofj-m) cof(n —f) cof(m-n)cof(f-m)

co:

fin^

fin ((—m)fin(n-i)co f^x _ co^»- Qco f(m- ri)

fin(n — I)fin(m- u)- cof(m - N)

; fi »>/ = —

cofftt - l)

fin 4 —m) iin (n — ()' ■' Jin (nt — u) fin J _ m) 1

. — cof 4 — m)

ijn 3 z —

fin (ti - l) fin (in _ n) '

Ex his autem formulis colligitur, eifc

fin£cof£ cof I + fin >} cofjj cofm -f fin3 cof3 cofn = o,

ita