110 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Also RDQ is constant = 7 r — a, and R0 2 Q = a. Hence in Cor. 3 replace 
the right angle RDQ by ir — a, and R0 2 Q by a. 
Cor. 5. (The Strophoid.) 
Let a = /3, and let D coincide with the centre of the circle 0 1 R0 2 . Draw 
0 2 T parallel to l cutting DQ in T. 
Then 
0 2 QT = 0 2 RD = R0 2 D = (RPD i Q0 2 T. 
Hence 
TQ = T0 2 . 
Hence (Barrow’s) generation of the curve 
D is a fixed point in the plane, and T any point on a fixed line 0 2 T. 
If Q is taken on DT so that TQ( = TQ') = 0 2 T, the locus of Q is the 
strophoid (oblique, or right when D0 2 is perpendicular to 0 2 T). 
Cor. 7. In this corollary Maclaurin generalises the construction of 
Cor. 5 by taking for the point 0 2 any point in the plane, T being still 
on the line l , while TQ = T q = 0 2 T. 
When the origin is taken at D, with the y - axis parallel to l, Teixeira 
gives the equation to the locus of Q as 
