ae 
On the Curves of Trisection. 355 
these, 4 therslose aright angle, and FA is perpendicular to 
points CAF. It is evident that FAC is an angle in a semi- 
Neon which is a right angle, FA is therefore perpendicular 
to HC. 
A perpendicular on the opposite side of AC, drawn from 
the same point A, will necessarily be equal to AF, and cut 
off an arc equal to the are HF; that is, will cut off an arc, 
HR, measuring one third of the given ang a 
he whole curve therefore, BoAE, though formed by a 
complex operation, may well be called the Trisecting 
Curve of Sieh. : 
By making in the same manner a corresponding curve on 
the other side of the diameter, the curve of sines will be 
completed, and the whole figure will resemble in form, 
though not in properties, the Cardioide of Carre. 
In figure 8 the two trisecting curves, completed on each 
side of the diameter, are placed together. DoF np is the 
Trisecting Curve of Secants, and EmBsp is the Trisecting 
Jurve of Sines. Any angle may be trisected with the great- 
By inverting the position of one of these curves, (as the 
Curve of sines, so that its point B shall be at D), it is obvi- 
ous, that while the angles ACB, HCB may be trisected by 
