p6 COMVEND. ANALTSEOS PRO INVEKTIONK 



malis in Bzz ds *£ **?£$ . Qiua autem vis centralis eft ad 

 vim normalem , qnae ex illa refiiltat , vt ds ad dy , o- 

 portet vt vis centralis in B fit — d ~^-rjr~ °l liae dicatnr zzzf. 

 ISimili ratione vis normahs m b m curua vera — : — ^5^-" 

 adeoque vis centralis , ex qua illa generari debet (nam et 

 heic areae circumcentrales temporibus funt proportionales) , vis, 



■ „ ,. dS*d(nxdy:dS) ^xi Cnxd-v: JS) j_ B „ 



lnquam , centrahs — -^j^- — - a *x' dy:As*~Tdx * d 



( nnxxdyKJS* ) = ;S x ^ ( ^Sly ) q iiae dlCatUr = F - M 



artificio transformatur / feu ^ff^f * in 3 x d(xxT?) fevt 

 i n S x ^1tSt^)- Habetnr itaque F-/= ^ ^faM&H- 

 ih *d{ nnxxdy '^ zz.(dS 2 zznn dyt-hdx* , ob nnds 2 zr nndx* 



.A-tindv') — J/ ^^-t-^^ T 1 y J nndy^nnd^_ — nrc , 



-t-nnay ) tdx xd[ nn ^ dy z )-\~ 2 dx* ai < nnxxdy 2 J — 2 dx x « 



( ^-f-^^)-f-ix ^{—-^-n^p) zz (differentiando adu 



■ f j_ - rnt nn ,, dx 7 t f % ,i nn<x z \ 



lpilim xx ) X 3— 2dx xa{ nnxxdy i)— X 3~t- 2 dx * a {nuxxdy*J 



nn — , nn ,, dx 1 N , i jt nndx z x / . , 



~3 Vdx x «dn^r^»)H-.'di wds^,-,) == (quia ob con- 



ftantem » duo poitremi termini fe mutuo deitruunt) "-^r 1 . 



Corollarium i. 



Eft itaque exiftente n inuaiiabili , virium centralium 

 differentia in orbita mobili et immobili reciproce vt cvfi 

 bus communis altitudinis x , ficuti habet Newtonus in 

 propof. 44. operofe et obfcure demonftrata ; fed et infa- 

 per hoc patet , quod Newtonus non docet , fi duae fint 

 orbitae mobiles, quamm velocitates angulares fint vt n ad 

 N, et vtraque ad velocitatem angularem in orbita immo- 

 bili habeat conftantem rationem , fore dinerentiam illam 

 virium in vna ad dirlerentiam virium in altera vt nn-i 

 ad m-l* Co- 



