CYLINDRICORUM SUPER PLANO &c. 433

SOLUTIO .

Manentibus denominationibus in praecedente problemate factis, coll-ideretur centrum inertiae I ut quiefcens, circa quod defcripta iit fphaera,cujus pundhmi verticale Z, et circulus verticalis fixus ZDX, in quo reiilacentralis IL initio litum ID tenuerit. Elapfo autem tempore t ea perve-nerit in L, ac ponatur arcus ZL — f et angulus XZL = atque hincitus axium principalium, quorum poli fint A , B, C ita definitur, ut fintarcus LA = LB = ^, LC = $, et anguli ZLA = f, ZLB = y, ZLC= h, qui funt quantitates confiantes, ex quibus cum arcu variabili ZL = f,ita definiuntur arcus ZA =/, ZB = *u , ZL — » ut fit:

cofl — cof^j coff -fi coff fin^finf; cofm — cofjj coff + cofgfin fj finf; co fn = cofA co/f -fi coff) fin A finf.

Quod fi jam momenta inertiae corporis reJ|>ctflii axium principalium IA, IB,lC fint Man, M bb, Mrc exifiente M mafia corporis, n autem fit preffio,et fedfio in qua ea versatur ab I antrorfum difiet intervallo s, quod quiaeft variabile, in fuperioribuS formulis loco h scribi debet s. Gyretur nunccorpus circa polum 0 celeritate angulari — g in fenfum<ftBC, pofitisquearcubus OA =r «, OB — /8, OL — y fit a cofct = x, a cof/3 = y, n

i .1 . . Z' fdd . cos- N

coly = z, ac primo habemus n = M + -—— J,

fias tres aequationes

nadx -fi (rc — bb) yzdt = — dt fIn f £ fil1 ? +

tum vero

M"

dt (coff fin geo fq — cofg fin f )bbdy + («n — «) xzdt = —dt fin g fin q fin f -fi

M

dt (cosg fin >; coff — cof», finf)-mfg

ecdz + (bb — ad) xydt —

M

dt fin(j fin $ fin q +

M '

angj-

M

dt (cofij fin B coff — cosA finf).

Praeterea habemus has tres aequationes

dt fin l — dt (y co fu - Z co fm) — dq (cofg fin f — coff fin g coff)dm fin m = dt (a cos/ — x cos» ) — dq (cofyj finf — cofg fin», coff)dn fin» == dt (xcofm — y cof /) — dq (cofA finf —coff) fin A coff)

quarum autem binas tantum fumfifie fufficit, ita ut fuperfint fex aequatio-nes, ex quibus variabiles totidem x, y, z, n» s et f ad datum tempus

Iii t de-