134 WPUSCUIA . 
eft s dp = ft.v ; crgo V ds ^ M dx , Q_^/ j 4- N -h m dx erunt 
coordinatarum elementa ; horum quadrata funt P*^/j^-H2 
PM^-^i^ -1- M*^.v% & Jj* -4- 2Q_. N H- w Jj^;v -f- 
N -I- m J^^^S quorum quadratorum fumma haec proveniet 
T^-h(^.ds'-h PM-{-Q..N-{- w.2jjJ.v-l- M'-hN4-^w* 
.dpc^; radix quadrata hujus fummc-e =: \Jdn^-\-dy^ eft ele- 
mentum arcus curvae algebraicse . Ut autem ex hac fiimma 
radix quadrata adlu extrahi polTit , oporteret ut ^PP-h Qj^. 
|/m* N H- = P M -I- Q_ . N m ; & quadrando 
PP -f-Q^Q.M'-!-PP-HQ_Q^. N 4- = P'M*H- 2PMQ. 
. N -f- »2 -f- Q.Q.. N 4- w % ergo QQ.M' — 2 P M Q_. N-!- f?? 
P P . N ~h w o ; Quoniam autem quantitas hxc eft qua- 
dnatum completum , extrahatur ejus radix , ut fit Q_M — P . 
N-f- m =::o,feu^-?--=:^,& fubftitutis valoribus M & N 
erit -h = ^ . Si ita determines Q_ per , ut fit 
'llL diiferentiale logarithmicum , palam eft , integrata fupe- 
liore isquatione, fadoqiie tranfitu a logarithmis ad numeros , 
inveniri P datam algebraice per f\ datis vero algebraice P, 
Q_ per invenientur etiam M & N. 
§. 16. Hoc modo pera(!la determinatione fpeciei Q, & 
%'ocato cury^ arcu = L , estrahatur ^quantitatis inventie radix 
quadrata ds VpYT"^Q. d x ^ W -f- N-f- - d L ; 
addatur %/P* -I- Q\ & dematur xquale ^j. 
fiat d s ^/P-h Q: ' -h s D v/Fh^ — ~ D v^P^ -h Q_^ 4- 
dpc Vi -!- 'N-hm * iL , quse integrata exhibet s %/?' -f- Q! 
|/m*-i- nh=:^' =l. Ex hac; 
& fuperioribus formulis quamplurima Theoremata Eernoullia- 
110 finiilia proficircuntur . 
§. 27. 
