RECTIFJCATIONEM ELLITSIS REQVIR. 91 



et ^R — l^^^ll^Z^^- et dz=:^:^—~l^ 



y'[cc-f-bb ( 2.V — .V .V ) ] y ( 2 X — .r .v ) 



Hiinc ob rem erit ^—[cc{2.x — xx)^abcc{'i.x-xx) 

 -^ ab^ {^ X- X xf -{-'^ c' -^- z^b"- c^ {^x-xx)-\- ^ b* 



i 2 X — X x)^ ]:[c c -i- bb ( 2 X — X x]]" V ( 2 x ~ x x). Po- 



natur ad fimilcm formiim obtinendam Q^— y^^^j^^ii^;^ 

 qui valor pcr fe euanefcit pofito x — o. 



§. 14. Differentietur nunc Q pofito tantum x va- 



riatili eri t ^^ — [ycc(2x — x x ) -f- ybb (2X~ x x )- -4- 

 y-ccx-h § cc—'yccx- — $ccx):{cc-\-bb(cC'-{-bb(2X 



— xx)yV(2x—xx), Qiiia ergo denominatores iam 

 funt inter fe aequales , fiant numeratores quoque aequa- 

 les, aequandis terminis iii quibus ipfius x {imiles funt 

 dimenfiones; eric 



I. ybb = ab'-^^b*\ 



II. yb^^ab^-^-^Sb*', 



III. ^ybb — 2y cc—^ab^-^-^tb^—cc—ahcc—^tb^c*'.^ 



IV. ^iycc-^cczz^cc-^-^abcc-^-^^^b-c^:, et 



V. $cc—^c\ 



Hinc inuenitur a — l\ §— j-^.j y—-^^, et a^zz 



ce 



$. 15. His ergo valoribus fubftitutis prodibit 

 {bb-^cc) v[^^:+36(7^^=ix)r — ^-T-y— jr:^. Viuia autem elt 



*^ — (i^ rf6V(2;i:— «J ^^ ^ — ab "^ dbilee-i-i/b^zx—xx]] 



M 2 atque 



