Mr. P. Newton on the Trisect ion of an Arc. 



11 



celebrated foreigners, — that nearly all these authors, ancient 

 and modern, should concur in observing a profound silence 

 on trisection ; or that none of them should speak or write 

 thereon, but confidently to pronounce its impossibility, except 

 so far as chiefly relates to a right angle; is discouraging in the 

 extreme, and is sufficient to damp the ardour of the most re- 

 solute, zealous, aspiring mind. Hopeless, however, as the per- 

 formance of this task which I have assigned myself, may still 

 appear to the reader, yet what I have observed permit me to 

 communicate. I am, gentlemen. 



Your very obedient servant, 



Paul Newton. 



Widi any radius AF, or FB, describe the given circle 

 AEHRB, &c. With half the radius of AF, or of FB, de- 

 scribe the circle cnmtoD, &c. Let the arc AH, or the arc 

 HB, be that of a quadrant, and let the arc AE be equal 

 to the arc RB, the co-arc EH will in consequence be equal 

 to the co-arc HR. It is required to find a third part of the 

 quadrantal arc AH, or HB, a third part of the arc AE, or RB, 

 a third part of its co-arc EH, or HR, and a third part of the 

 arc AR, or of its equal BE. 



To find a third part of the quadrant AH, or HB.— Draw 

 the diameter HG perpendicularly to the diameter AB. Draw 

 the chord HcL througli the point c, in which the circumference 

 of the circle cnmfoD bisects the radius AF, to meet the given 



B 2 circle 



