350 CAPUT XV. DE MOTU LIBERO

SOLUTIO,

Fig.89. In fpatio abfoluto concipiatur fpliaera immobilis, in cujus centro ver-

fetur corporis centrum inertiae I, in eaque affumatur circulus fixus maxi-mus ZXVY, in eoque pundum fixum Z, quo fitus axium principaliumquovis tempore referatur. Ac nunc quidem eia pio tempore t refpondeantcorporis axes principales in fphaera immobili pundis A, B, C, a quibusfi ad Z ducantur arcus circulorum maximorum, vocentur ii ZA = l, ZB= m et ZC = n, tum vero fint anguli XZA = a, XZB = ^ et XZC = v.Nunc autem reperiatur axis gyrationis in O, ut fit AO = ct, BO = /3 etCO = y, circa quem corpus gyretur in fenfum ABC celeritate angulari— tempulculo ergo dt polus A vertetur per arculuin Aa — ait fin«,exifiente ha ad arcum OA normali, ita ut fit

cofy

et

fin B An

fiii«

At cft fin Z AB — —-et

fin/

unde colligitur

cof/3 cofiji-f cofiy cof«

cofy co Im — cof/3 cof,z

cofZAa

fin« fin/

fin« fin/

finZAo =

Dudo jam ex a ad arcum ZA perpendiculo a<z, erit

(cofy co fm — cof/3 cof») et acc

co fm -j- cofy cofir).

Verum eft A« = — dl et act — — dh fin /

ideoque hinc et ob analogiam fequentes concluduntur diflferentialiumvalores:

dl fin/ = adt (cof/3 eofrr — cofy cofjw); dh fin/ 2 — — adi

(cof/3 cof m + cofy cof/z)

dm fin m = «z/t (cofy cof/ — cof« cof,/); fin m 1 ~ — adt

(cofy cofrr 4 - cof a cof/)

dn fin n — adt (cof ce cofw — cof/3 cof/); d v fin,/ 2 — — adt(cof ce cof/ + cof/3 co fm).

Harum autem ternarum priorum binas rcfolviffe fufficit, cum fit cof/ 2+-coftn 2 + cofw 2 — 1, iisque refolutis unica reliquarum totum nego-tium abfolvit.

COROLL.