!i3o DE PRINCIPIO VELOCITATDM vmTUALIUM , ETC. 

 methodo momenlorum acquatio eiit 

 Pcos(P,7)J7-i-P'cos P',9y7'+P"cos(P",<7")Jy"+etc. ==o (i) 

 dein ex geometria analytica habebitiu- 

 cos(P,<7)=cos(P,a)cos(^,.r)-t-cos(P,j')('os(<7.j)+cos(P,z) 

 cos(y,z);cos(F,9'j=cos(P',x)cos 9',.r)+cos(P',j';cos(j'',j') 

 +cos(P ,z)cos(9',s);etc. 

 allunde notum est diffcrentialia dx, dy, dz esse pro- 

 jectiones in axcs coordinatariun respective spatioli dq^ 

 et sic de caeteris; igitur habentui' 

 dqco^{q,x)-=d.t;dq'coi(q' , i£)=dx';etc.;dqco&((/.y)s=dy ; 

 d()'cos(g\y)=dy';etc.;df/cos(q,z)^=dz;dq'cos(q,z)^=:dz';<iiC. 

 Ponantur iiisuper , brevitatis ergo , 



Pcos(P.x)=X;P'cos(P>)=X';etc.Pros,P,7)=Y; 

 P'cos(P',j^=Y',-eto.;Pcos(P,z)=Z;PVos(P',c)=Z';erp. 

 tandem reponantur haec omnia in (i) et haec abit iti 

 sequentem 



Hdx+Ydy-+-ZJz-i-lCdx'-*-Y'dy+Z'dz'-*- 

 X"J.r"+YV7"+ZVz"-4-etc.=o. (2) 

 ' 'Connexionis leges analytice expressae non snnt nisi 

 Óna vel plures aequatioues inter coordinatas x , y , z\ 

 sf, y, z' ; etc. in quibus si, coordinatae infmitae parum 

 immutatae abeant in x-*-dx, y-^dy,t\.c. , novae quae exur- 

 genit aeqiiationes reprasenfabunt systematis statura cum 

 Snsceperint puncta A , A' , etc. velocitates virtuales 

 Compossibiles juxta connexionis leges: porro ex hac 

 aoquationum posteriori serie si demantur respective 

 quae priorcra componunt, scilicet i." prioris ex 1.^ pos- 

 terioris, et sic deinceps, tertia series coUigetui- aequa- 



