( 345 ) 
the other Values of z, x, x t x t *.• But by what is alrea- 
dy fet down, it is evident that all their Values will be 
expreft by a and z, and the three Symbols c,c, c : and 
c nfequently all the Values of the reft of the Increments 
of x, viz. * &c • will be exprefs’d by the fame Sym- 
bols. Whence it follows that to determine the Values of 
the Symbols c, c , c ■; there may be takeh three Conditions 
relating to the Values of x. x, *, *, \$c. promifcuoufly, 
as the fourth Proportion airelfts. The fame Rule hblds 
good in the Met od of Fluxions. For Example- having 
given the ^Equation a 4- x z x 6, if it 'be propofed to 
defcribe the Curve that i t belongs tq ; by die fourth Propa- 
fition it may alio be required CsV Condition, tha<- the 
Carve fhall pafs through two ^iven ’^pints'; that it fhall 
touch two given Lines ; that lt-lliall phfs thro a "given 
Point, and when it cuts a given tine fiialf have a given 
Degree of Curvature ; or that it fhall have any other cwo 
Circumftances that depend upon the Values of the third, 
fourth or other Fluxions. Thefe Conditions that attend 
Incremental or Fluxional Equations, I don’t know to have 
been fufficiently taken notice of by any Body : but they 
ought well to be attended to in the Jnverfe Methods ; 
the Solutions of particular Problems bdirtg never pe^fedJ, 
unlefs there be provjfion made for thef fatisfy ing of them, 
by the indetermined Coefficients in the Equation that 
contains the Solution of theProblem. Examples of this 
may be feen in Prop. 17 and 18 , where T give' the- Solu- 
tion of the Problems concerning the /JoperirMter, and 
the Catenaria. 
The fixth Propofition contains the general Explanation 
of the Inverfe Method both of Fluxions and of Incre- 
ments, which confifts in the Solution of this Problem. 
Having given the Relations of the Increments, or of the 
Fluxions of feveral Quantities, whether they be confide- 
