of Colin Maclaurin. 105 
1915-16.] The “ Geometria Organica” 
Let the equation to O x P be 
y = tx . 
so that the equation to PQ is of the form 
L 0 + L^ + L 2 ^ 2 = 0 
Let Q0 2 have an equation 
so that 0 2 R has an equation 
M 0 + /aMj = 0 
No + ^ t i = 0 
• (1) 
• ( 2 ) 
• ( 3 ) 
• ( 4 ) 
The condition that (2), (3), and V are concurrent leads to a relation 
f(t, /*) = 0 , 
of the second degree in t and linear in /x- 
afi + bt + c 
• • • • ■ ( 5 ) 
Eliminate t and /x from (1), (4), and (5), when the result follows. 
Cor. 3. If S is taken on PQ such that L PO x S is constant, then S by the 
Lemma describes a straight line and L C^SQ is constant. Hence another 
way of obtaining such a cubic by using S in place of P, and the intersection 
of O x S with 0 2 R. 
Fig. 16. 
Cor, 4. Also thus : Let l and V cut in E. Draw ET (l") making an angle 
a = O x PQ with V, and cutting O x P in T. Then QTO x = QEP is constant. 
