Miscellanea Curio fa. 133 



ry 1=2 x rr . And 



yy 



confeqnently if rr >-*yy be thrown into an in- 

 finite Series, and the feveral Members of it 



be multiplied into ry } and then the flowing 

 Quantity of each be taken, we fliall have the 

 length of the Arch AC After the fame 

 manner, giving the verfed Sine, the lame 

 Arch may be found. For refuming the E- 



• • • 

 quation found above 2rx ixx pa iyy, we 



have y rx — xx, but C xx \yy « xx 



yy 



• • • • • • 



rrxx & irxxx + x z xx 



xx 



yy 



rrxx irxxx x^xx 



* . ,- ■ » -;■■ , that is, (reducing all 



to the fame Denominator, and expunging 

 \ • • 



rrxx 



contradi&ory Terms) > , whence 



CDs rx , and confequently the 



XX 



*\firx*~ 



length of the Arch A C may be eafily found 

 from what is faid already. 



, i ' K 3 The 



