CORPORUM RIGIDORUM A VIR IBUS &c. zzz

flatui corporis initiali conveniant. Ad hoc confiderentnr vires 'corpus nuncfollicitantes, quarum colligantur momenta inertiae refpedlu axium prin-cipalium corporis: litque

mom. virium refpecflu axis IA in lenium BC — Pmom, virium refpechi axis I B in lenium CA = Q,mom. virium refpechi axis IC in fenfum AB — R,

atque ponendo brevitatis gratia y cof« = x, a cof£ = y, et L cofy = z,ut lit n = </ (aw + yy -f zz), fupra invenimus fore:

dx +

ct — bb

11

^8

t?

2gPdt

cui

Maa

dy +

aa — cc

xzdt —

igQdt

bb

M bb

dz +

bb — aa

L

St

11

•zgKdt

CC

Mcc

quibuscum, pofito cof/ = p, coimzzq ct cof« = r, conjungantur haeaequationes:

dp 4- dt (yr — zq) — o; dq + dt (zp — xr) = o, Jr + dt(xq-yp) = o

, . dt(yq + zr) _ dt (zr + xp) '

d\ + —— “°J — ■ - = o; 4 +

qq -i- rrdt (xp + yp)

rr + pp

— o,

pp + n

quae fi ita resolvi et integrari queant, ut ad quodvis tempus t afiignari pof-Ihit quantitates x, y, Z, p, q, r , A, p, v, problema erit perfedle folu-tmn, In his poftremis autem aequationibus notandum eft, efle pp -f qq-p rr — i, unde pdp + qdq + trdr ~ o, tum vero etiaea xdp + ydq

+ zdr = o. Denique fin(^ — A) = — - ■■■ --- et co((p - A)

lui / Imm

— cof/cof?» ., , . r / \ P

— —z ——-, ideoque tang (p - A) = — ; et tang ( v -p)~ -,

Jm / lui pq qr

tum tang (A — v ) — feu tang(v — A) =

pr

guloruniA» p> r unicum invenifie.

pr

; ita ut fufficiat an-

Yy

SCHO-