SQUARING THE CIRCLE 23 



its fifth part FG be added, the whole line AG will be equal 

 to the circumference described with the radius CA, within 

 one-seventeen-thousandth part. 



The following construction gives even still closer results : 

 Given the semi-circle ABC, Fig 2 ; from the extremities 

 A and C of its diameter raise two perpendiculars, one of 

 them CE, equal to the tangent of 30, and the other AF, 

 equal to three times the radius. If the line FE be then 



Fig. 2. 



drawn, it will be equal to the semi-circumference of the 

 circle, within one-hundred-thousandth part nearly. This is 

 an error of one-thousandth of one per cent, an accuracy 

 far greater than any mechanic can attain with the tools 

 now in use. 



When we have the length of the circumference and the 

 length of the diameter, we can describe a square which 



