346 On the Curves of T'risection. 
dius be supposed to move from F at an equal distance from 
the centre C and B in the circumference of the outer semi- 
circle, and as it moves towards D in the moving radius, al- 
ways to keep at an equal distance from the centre C and 
from the are BHAD, this last distance being measured on 
the moving radius ;—the point thus carried around from F 
to D, continually receding from the inner semi-circle and ap- 
proaching D until it touches the outer semi-circle at D, will 
describe the trisecting curve of secants. 
Or the generation of this curve may be expressed as fol- 
lows: Let the radius DB revolve on D, and the radius CB 
on C, in such a manner as that the distance from F to B on 
DB shall be always equal to the distance from F toC on CB. 
The point of intersection of these radii describes the curve. - 
When DB is in the position DG, and CB in the position 
CA, FB will be enlarged to oG and FC to oC. When DB 
is in the position Dg, and CB in the position CD, FB be- 
comes Dg, and FC becomes DC. 
2. This curve may be described by points, thus. Take 
iwo thirds of the exterior semi-circle, which is found by ex- 
tending the radius twice along the arc from B. In figure 1, 
two thirds of the exterior semi-circle will be the are BGg. 
Divide this are into any number of equal parts, and to each 
point of division draw a straight line from D. Divide the 
whole interior semi-circle into the same number of equal 
parts, and from the centre through each point of division 
draw a straight line to the exterior semi-circle : or, whichis 
the same thing, divide the whole exterior semi-circle into 
the same number of equal parts, and draw the lines from 
the centre. Theintersection of these lines from D and from 
the centre, will give points of the Curve of Secants, through 
which points with a steady hand the curve may be drawn. 
3. This curve may be described mechanically, by a con- 
tinued motion, as follows. In figure 2, let CG bea straight 
rule, moveable about the centre C, where it is fastened by a 
pin. Let this rule have a fixed part, or perpendicular rule, 
HK, attached to it at H, aad let there be a slit through this 
perpendicular rule, which slit meets CG at H at an equal 
distance from C and G. 
Let CA be another rule, moveable about C, fastened by 
the pin, which fastens CG, and having a slit through a little 
more than half of it from A towards C. 
