Mifcellanea Curiofa, 149 



COROL IE 



If n be expounded by any Term of the 

 following Series, 2, 3,4, 5, 6', &c. then the 



— 271 , — — • — 

 Curve whofe Ordinate is x y rr< — xx 7 or 



x \l rr-\-xx y is exa&ly fquar'd by this 

 Theorem. 



COROL. III. 



If m be expounded by any Term of the 

 following Series, — 2, o, 2, 4, 6, 8, &c. then 

 the Quadrature of the Gurve whofe Ordinate 



is x V * rr—*xx^ depends upon the Circle, but 



the Quadrature of the Curve whofe Ordinate 

 m 



is x yrr~\-xx 7 depends upon the Hyper- 

 bola. 



COROL. IV, 



If m be expounded by any Term differ- 

 ent from thofe already taken notice of; 



then the Curve whofe Ordinate is x V rr^xx, 3 

 m 



or x y rr-\ ~xx 7 depends neither upon the 

 Circle nor the Hyperbola, but is reduced ta 

 a more JImple Curve. 



L 3 , THEO- 



