De motu corporum circa punctum fixum mohilium. 



57 



hinc vis 



sec. Oa 

 sec. O^ 

 scc. Oy 



praebet per resolutionem : 



vim sec. OA 



'idlHddX 



dfi 

 'idMddY 



dfi 

 'idlHddZ 



COsJa 

 COS J/3 



CQsJy 



vim sec. OB 



'idMddX 



dfi 

 '2dMddY 



dfi 

 IMdc 



COS Bcc 

 COS B,S 



'idMddZ n 



-— - cos By 



vim soc. OC 



'idMddX 



cos Ccc 



cos C/3 



da ^««^J^- 



dfi 

 2dMddY 



dt^ 

 'idMddZ 



6V. His viribus colIig;endis orientur pro elemento in Z — dM 



- xmd%-^y%dd^ -f- z%dd(i 



I. Vis sec. OA = 



2d7W 



IL Vis sec. OB 



III. Vis sec.OC 



df2 



^dM 

 dt^ 



^dM 



x®dd® -H y(^dd^ -+- z(Bdd2 



x^dd^-i-y^dd^ 

 x(^dd^ -+- j@dc/@ 

 x^dd® -+-y^dd^ 



x(^dd^-i~y(^dd^ 

 x^dd^ -^ y^dd(§, 

 x^dd(B -H y^dd^ 



z^dd(^ 



z(§dd^}=y'iZq 



z^dd^ 



z(^dd(§, 



z^dd^ }= vi Zr 

 z^dd^ 



ideoque ad motum elementi Z = c?M requiruntur hae tres vires Zp, Zq et Zr (Fig. 12^). 



65. Quia punctum corporis fixum retinetur, ratione motus non tam ipsae hae vires, quam 

 earum momenta respectu ternorum axium OA, OB et OC spectari debent. 



Praebet autem vis Zp momenta circa 



vis Zq « « 



vis Zr (i a i 



OB=Zp.z in plagam CA 

 OC = Zp.y 



OC = Zq.x 

 OA = Zq.Z 



0A = Zr.y 

 OB = Zr,x 



BA 



AB 

 CB 



BC 

 AC 



66. Hinc ergo resultant ex motu particulae in Z = dM pro tribus axibus OA, OB, OC se- 

 quentia tria momenta: 



in plagam 

 -xy^^^dd^-^^dd^^-^^dd^^y 



-xz{^dd%-^(gdd^-^^dd(B) 



1 M ' nj 2dM )-^yy{^dd^-^^dd(i-^3dd^)[ „., 



I. Mom. circa OA = -^ < > Bt 



d^' ]---zz(^dd(B-i-(§,dd^-i-JQdd2)l 



- yz (Scide -4- ^dd^ -h ^dd^) 



^yz{^dd^-h-^dd(§-*-^dd^)J 



L. Ealeri Op. posthnma T. II. 8 



