Prohlemata Aslronomiam mechamcam spectantia. 321 



quae esiyy^aa — xx — -• ronatur nunc z constans, ut mtegrationes pateant ad sectiones 



sphaeroidis parallelas aequatori secundum MR factas: hunc in finem ponatur V (aa — ^^j = /), 

 ut /> sit radius hujus sectionis, atque integrationem eousque extendi oportebit, donec fiat x = p. 

 Sit °-^= n, eritque pro hoc casu 



bb 



vis Yr = f-^' fdx (i - "'"^""^'""^^" -H 'Il^^^Slmi-^ y^pp _ ^^), 

 vis;tx = /?^7<fo(i - ''-'^^^'-'^" -^ ^''^^^^''"" '^yipp-xx), ' 



momcntum Yy . CY= f — -^/-^fxxdxY^pp — xx) — f — —-^fxxzzdx V{pp — xx), 

 momentum Xx ,CX = f — -^i^ fzz dx V {pp — xx) — f — ^,^ ' fxxzz dx Y (pp — xx), 



Posita autem ratione diametri ad peripheriam = iin, si post integrationem fiat x=p, erit 

 fdx y {pp — xx) = — npp , /xxdx y {pp — xx) = — np^, 



quibus valoribus substitutis erit 



msYr=f—y-{i 2^^ -H 2^5 j' ' 



mom. 



mom. Fr.CF=/— 2^ dz — y ^, dz, 



. V^ rv /-e^AArflfPP^* j, r ^5rtkkrgp*zz ^ 



uXx,CX=J -, dz — J —f dz. 



Est autem pp = aa — nzz = aa — ^> uti assumsimus, erit ergo aa = nbb et pp = n {bb — zz). 

 Instituatur nunc ultima integratio, ac ponatur r = 6, quoniam est 



•fppdz = nfdz (66 — zz) = |- nb\ fp^ dz = nnfdz (66 — zz)"" = ^jnnb\ 



fppzzdz = nfzzdz {bb — zz) = ^nb\ fp^^zzdz = nnfzzdz {bb — zzy =-^nnb\ 



I 



; integralia quaesita ita sc habcbunt 



L. Enleri Op. pottbama T. II. 41 



