ANNUAL RECORD 



OF 



SCIENCE AND INDUSTRY. 



1876. 



A. MATHEMATICS AND ASTRONOMY. 



ON THE CISSOID OF DIOCLES. 



From the inaugural dissertation of Dr. W. Bohmer, enti- 

 tled "Studies upon the Cissoid of Diodes," we quote the fol- 

 lowing method of describing this curve, as given by Sir Isaac 

 Newton : 



Through the centre of a circle whose plane is vertical 

 draw a horizontal line and a vertical one. Lay off to the 

 left a point at a distance from the centre of twice the radius 

 of the circle. Along the vertical line let there glide one end 

 of a bar whose length is the diameter of the circle, and whose 

 opposite end is fixed at right angles to a second bar of in- 

 definite length, and which is forced always to pass through 

 the point just found on the horizontal line. Under these 

 conditions the centre of the first- named bar describes the 

 cissoid required. This method of describing the curve is 

 easily executed mechanically, and by its means we are able, 

 as w^as first shown by Diodes himself, to solve the problem 

 which so troubled the Greek geometers, viz., the construc- 

 tion of a cube containing exactly twice the contents of a 

 given cube. This problem is sometimes known as the prob- 

 lem of Apollo, or of Delphi, since at one time, it is said, Apollo, 



A 



