E 4- FX 1 OO EF\ id est) ll + ppoo fi

FT Z -f- GT Z 00 FG Z - -

GZ 1 + CZ 1 OOGC z -

BX-t-FY-t-GZOO const.

mm+qq 00 ttnn -4- rr OO ««

D ( 6) D

1 unde differen-| uando cmer.gunt pro fluxu

/. ldl+ pdp 00 fit

II. mdm -f- qdq 00 tdt

III, ndn + rdr 00 ttdu,

nn^rroouu ,

'+>*4«00const. "*

I punstslru f,g i tV. dl+dmdno 0o

FX-\~GY+CZ00 const. p+q+rOO const. j Aquationes.ßF-i-FGst-GCX'Const, s+j+sX const. J

j V. dp -f- dq+ dr 00 o[_VI.ds+dt + du 00o

pro quibus , in casu hujus Theorematis , ob fluxum punctorumF, G in rectis KF, LG ( qui rectas BX, FT, GZ, seu l,m,n > in variatasrelinquit, ipsasque proin ö7 ,<//«,cura tota aequatione IV evane-scere facit ) scribendae

1. pdp OO fdsIL qdq 00 tdtIII. rdr 00 « du

V. dp + dq + dr00o

VI. ds 4" dt -f - du 00 o

sic ut sex tantum diflerentialia & quinqueaequationes remaneant , quarum beneficioquatuor ex illis omnifariam tolli, & reliquo -rum duorum ratio ad invicem inveniri potest.Nam ex. gr. per vi habetur duOO — ds—dt ,& perF, dr OQ — dp-dg-, qu i valores in IU locodr Sl du substituti faciunt dt 00 rdp -\-rdg — uds : u ; & hic loco dtsurrogatus in II producit ds 30 rt dp 4- rtd g — qudq: tu ; qui deniquepositus pro ds in i exhibet , ptu — rst,dpOO rft — qfu,dq •, undedp.dq:: rft — qfu.ptu — rft, nec non componendos. dp-{-dq (hocest,<//.<tz) ;; rft — qfu. ptu — qfu], seu, variatis signis secundi & quar-ti termini , df. — dg :: rft — qfu. qfu — ptu. Q_E,D.

Theor. III. Ponantur qm in praced. rursum^ summa retiarumBF4- FG + GC confianter maneat eadem ; sed fluant punäa F, G in pe -ripheriis circulorum super punctu fixis B , C descriptorum, fecum ducentia re -cUs KF,LG; erit incrementum momentaneum recta KF ad decrementummoment. rechn, LG , aut vicifim decrementum illius ad incrementum hujus ; utdifferentia inter duo priora ad differendam inter duo pofteriora trium solido.>rum sub BX, FY,CZ; sub BX, GZ, GY, & sub FY, GZ, FX; hoceU in symbolis , erit df. — dg:;lnir—Inq.lnq—mnp. (Tig.I.)

Dem. Durante fluxu punctorum F, G in peripheriis circaj 3 ,C;cuminvariata? maneant singula? BF, FG,GC, seu s ,t,w, eva-nescantque ad eods,dt , du unä cum aequatione VI Theor. praeced.caeterae ibidem profluxu punctorum indeterminato repertae aequa-tiones ad has quinque reducuntur :

J. Idl