350 On the Curves of Trisectron. 
of compasses, opened to the distance of CE, or radius of 
the interior circle, set off this same distance from the point 
of intersection of the rule, and interior circle towards the 
exterior circle. If, for instance, the rule intersect the ecir- 
cle in H, then set off the radius EC or HC, from H to m 
Then will m be one point of the: curve. In this way may 
a sufficient number of points be found to enable one with a 
steady hand to draw the curve. 
3. This curve may also be described meena ai by a 
continued motion, as follows. Let a straight rule CH in 
figure 4, be fastened by a pin at C so as to ie preset 
about et Hm be another rule of the same length, with 
a hole at m for a pencil to pass through. Let this rule be 
pinned to the rule CH atH so as to move about H, as C 
moves about the centre C. Let EG be another straight 
rule, a little longer than three times CH, with a slit through 
the length of it, and moveable about E, where it is fastened 
with a pin, the distance EC being equal to CH. In the 
slit of this rule let Hm be placed, so as to slide in it with 
ease and yet with accuracy. 
‘he instrument being thus constructed, put a pencil 
ths 1 the perforation at m, and by p ushing the rule with 
on one side and to o on the other, the curve will be 
Seied. But when the point m is ato, the rule CH will 
be in the poetinn CE, and the rules EG and Hm in the po- 
sition 
As he largest angle, which can be trisected by means of 
this curve, is an angle of 135 the given angle. is larger 
than 135°, it must be paar es the parts trisected sepa- 
rately 
. Let ACB, in figure 3, be the given angle to be trisected. 
Describe the curve of sines, which intersects the side CA 
inm. From the point m raise mI perpendicular to AC. 
The perpendicular ml is. the sine of one third of the angle 
ACB. From the centre C draw or Of course the nA 
AT is one third of the are AIB, and the angle ACI 
third of the angle ACB. Wherefore by bisecting 1B, or 
setting off the arc AI towards B, and joining the point t t thus 
found with the centre C, the angle AC will be trisected. 
c demonstration of which is as follows. 
