MtjceUanea Curio fa. 1 5*7 



For the Menfuration of a furface dsfcrib J d 

 by the Conversion of a Curve round its Axis J 

 we are to afliime for the Fluxion of it, a Cy- 

 lindrick Superficies, whole Altitude is the 

 Fluxion of the Curve, and whofe diftance 

 from the Axis is the Ordinate Applicate cor- 

 responding to that Fluxion. Ex. gr. Let AG 

 be the Arch of a Circle, which turning round 

 the Axis AD, generates a fphericai;Superficies, 

 which we would meafure. Now DC the 

 Fluxion of the Arch is already found to be 



rx 



= which if we multiply by the 



\l irx—xx 



Periphery belonging to the Radius BC, that 

 is, by ~\Jirx-~xx (putting ~ the Ratio of 

 the Circumference to the Radius) we fhall 



have cx for the Fluxion of the fpherical Su- 

 perficies, and confequently that Superficies it 

 felf, is ex. 



As for Centers of Gravity ; having gotten 

 the Fluxion of the Solid or Surface, and 

 multiplied the fame into its diftance from 

 the Vertex, the flowing Quantity muft be 

 found, which divided by the Solid or Surface 

 it felf, the Quotient will fhew the diftance of 

 the Center of Gravity from the Vertex. Thus 

 to find the Center of Gravity of all the Pa- 

 raboloids; their Fluxion is thus generally 



expreffed 



