1 1 6 Mtjcellanea Curio fa. 



of Simt, the Roots of thefe Equations are 

 found ; 1 thought convenient to add an Ex- 

 ample or two, by which the Compendium of 

 that; Pra&ife may be rendred manifeft. Let 

 the Equation £.3 - 39^ 2 + 479^ — 1 88i = <?, 

 be propos'd} and the Roots z, are fought. 



Here V ' j, bb-jpz=z V $>i *= V whofe 



double V 377 is the Radius of the Circle*, 

 alfo i 7 &3 '1 " 2 ? — f ^ = 2 1 97 ~t 94° i "~ 3 1 1 3 i> 



V^3. ^fVpi 



24 



or — - - — is the Tabular Sine of the Angle 5 



97 ^ 9i 



that is, making a Divifion by the helpof 

 the Logarithms, Log. 9.5)2515(50, to which 

 correfponds an Angle of 57 0 . 19'. it*". The 

 third part of this is 19 0 . 6'. 24". and of the 

 Complement, is 40°. 53'. 36". The Sines 

 give the Logs, 9.514983 and 9.816011} 



which multiplied into the Radius V 37 m 

 produce Y& and Y&, Log. 0.301030 = 2, 

 and Log. 0.601059 = 4, but the third Y& 

 is equal to the Sum of them, or 6. And 

 therefore the Roots are 1 3 — 4 = 9 ; 1 3 2 

 = 11, 13 -V 6 = 19 of which feveral ones 

 the foremention'd Equation is eompos'd- 

 Where 'tis to be noted that the two lelFer 

 Fvoots, do not exceed f b or 13, becaufe the 

 Center R in the Conftru&ion falls on the 

 right hand of the Axis j that is, £ bp is kfs 

 than | 7 bi i~i q. 



For 



