CORPORUM RIGIDORUM A VIRIBUS &c. 351

COEO LL. u

81 o. Si ponamus g cofcn = x; a cof /3 — yt t g cofy = Z, ut fitex momentis virium follicitantium P, Q, R,

cc — bb . zgVdt aa — cc seQdt

dx +- ijzdt - -; ch-r- — xzdt=

„a 7 Mflfl J bb Ubb

bb — fia . spRrf/

dz -f- xydt — — -;

cc M cc

nunc fequentes aequationes adjungi oportet,

dl fin / xz dt (y cof» — 3 cof)»' 1 ; dm fin ttt — dt (z cof/ — a: cof») j(/n finK — rfr (# cofw — y cof/)

t/A fin / a - dt (y cof m -f 3 cof»); d^ finm* — - dt (3 cof»+ X cof/); rfy finw a = — rfr (x cof/ -t- y cofw). ,

C 0 R O L L. 2.

811« Si porro ponamus cof/ = p; coft» = q, coftirrr, pofleriores aequationes has induent formas obpp -f qq -f rr = j :

dp -f dt (yr — zq) ~ o; dq + dt (&p — xr) = o ; dr + dt(xq — yp) — o

. dt(yq + zr) dt(zr + xp)

«A + —---= 0 5 d(* + --— o; dv dr

qq -p rr

dt (xp + yp)

pp -p rr

— o;

pp + qq

unjde etiam fit xdp -j- ydq + zdr = o, quemadmodum eft pdp -f qdq+ rdr — 0,

SCHOLION.:

8x2. Etfi hic problema praecedens, qua fi'jam e fiet folutnm, fpe-ifiavi, tamen plerumque ambo problemata conjungi eorumque refolutio-nem timui inflitui oportet, quemadmodum in praecedente capite de motuturbinum ufu venit. Haec fcilicet amborum problematum conjundtio ne-cefiaria efi , quando vires follicitantes a fitu corporis abfoluto pendent,quod quidem, fi vires externae affuerint, femper contingere folet. Hisigitur caiibus, momenta virium P, Q, R arcus /, w, m' ac fortafle etiamangulos A, v involvent: ita ut omnes aequationes coroll. x, exhibitaefimul perpendi debeant, antequam folutio fufeipi queat. Quodfi corpusinfuper motu progreflivo feratur, fieri folet, ut vires etiam ab eo perde-