MOMENTANEA AXIS GYRATIONIS A &c. 267

cof« tangS-

J\* } ‘ + fi)

linde fittang COS =:

aabb (aa — bb)fm cofm cof«’

ccfn(bb (bb — cc)fm 2 + aa (aa — cc) cof m z )tefn (aa (aa- cc) cofm 2 -s- bb (bb - cc)fm z )

(aa - bb ) fm cofm (aabb cofw 2 -f cc(aa + bb)fn z — c*fn zPorro ex eodem triangulo OCS colligitur,

/*„ cofs coffm + *) \cof/ = cof(m -f tf) cof?i cof A + fnfb —/A +•-tang^'- J

f n(aabb - (aa + bb) cc + c*) __ (aa-cc) (bb-cc)fnf$aabb * aabb

feu cofr=

unde fit da —

an (aa — bb) (aa — cc) (bb — cc)f m cofm fn cof?i*

aabbcc

. dt*

adt

Denique pofitis 0 A = «; OB — C, OC = y erit arculus 0 o = .

/■/a 4 /i 4 («a - W) 2 cof» * cof^ 244 (o«—f 0 * c0 ^« 2 c °fy 24 f 4 () 2 cofS* cofy 1V. — (aa — bb) 2 (aa — cc) z (bb — cc) z cof x z cofC 2, cofy 2

aabbcccc)

7 2

- (aa — M) 2 (aa — rr) 2 (W; — cc ) 2 c

88 (aa — bb) (aa — cc) (bb — cc) cof« cofScofy

et «8 — " ■ - --—-- --- - — - dt,

aabbcc

Verum fi cx o ad CO perpendiculum ducatur op, per regulas trigono-inetriae fphaericae, arculi dementares Op et op ita rationaliter exprimun-tur ut fit:

8 (aa bb) dt cof» cof Q(aabb — (aa — cc) (bb — cc) cofy 2 )

Op —

*p

aabbcc Rny

gdt cofy (aa(aa — cc) cof a 2 -\-bb(bb — cc) cof£ 2 )

aabbfy

C O R O L L. i,

aa(aa — bb) (aa—cc) (bb — cc) coftfcofficofy

670, Cum fit da— ---—- — - 1

aabbcc

dt patet fi trium momentorum principalium duo fuerint inter fe aequalia,tum celeritatem angularem plane non immutari,

C O R O L L, 2.

6yi. Introdudlis difiantiis a, C, 7 poli O a polis principalibus A,B, C erit

Ll r tang