190 DE CONSTRVCTIONE 



intcgralls eft SzzA-lKe-^-f^z-^c] "''-^^ , cxiftentc x 

 conftanti quantitate , hinc elicitur x ( rr RS ) ::= A 

 [(^^y)2^^.]-^:^-h/_-i_, exifta vero deriuatur fequens 



[(^z^f^z-^cY-^^^^^iex-^h^-zze Azz. ex acquatione vero 

 a-^-hz-^-cx-^ezx^-fy—o, obtinetur {e-^-f^z-^-czz. 

 ^cfx-(cef-^ff)y--^<^~<^f qu^re inuenta aequatio abit in 



{cfx-^-efi^-i-jjj-^-ae-^-af-^-hc)' x {ex-^-hYzizC , vbi C 

 crt alia quantitas conftans. 



Exemplum q. 



Si quaeratur curua huius proprietatis , vt quaelibet 

 eius tangens, fit ad partem axis inter tangcntem et ini- 

 tium curuae , in data ratione « ad i , inuenietur aequatio 

 diiferentialis eius effe nxdy-nydxzzyds , quae iterum 

 conftrui poteft ponendo dyzzzdx, et fi praeterea fiat nn 

 V{zz-\-i) , mutabitur aequatio in nzx-nyzzry, eritquc 



adeoP^^, etQ=.. Atqui'^^^"^-,-^:^,.^-^- 

 (propter zz-rr-i )^:-^^=\-ir-^-ir^-^^ 



rr^nr 



r—\ 



r^^n 



, binc elicitur R=(;-- 1 f' "- x(r-f-;/): (rH- 1 f-^ -^^rzz^c. 

 Vel [r- 1 )^- ' [r-^n)~ rx (r-Hi f 2 , vel (/'- 1 )\ [r-^nf 

 zzrrxx {r-^-if , fed aequatiow.rs— wj=^^ praebet szz 

 2; 1=1 «;/Ar 1' -4- Q j' : nnxx—yy , exiftente Q.= 

 'V[nnxx-\-nnyy—yy) adeoque r(zznxz—Tiy : j)ziz nyy-\- 

 nQx : nnxx —yy. Qiiod fi in praecedenti aequatione 

 fubftituatur , proueniet ( nyy -{-yy — nnxx -H «Qa^)" 



