1060 



<p^(.v, y) = O 

 the satellite point Si {xivi',yiV'i) will be on the curve (p of order n 



If Pi describes the curve 7, Si describes the curve (f\ hence the 

 proposition : 



If a curve C{p,q) intersects an arbitrary curve (p of order ?i, the 

 satellite points of the intersections lie on a curve of order n. As 

 the transformation of Pi in Si is an affine transformation, (p is 

 affine with fp. 



If q is odd the satellite points of the points of Jcl lie on the 



conic IcL' 



(q — ;)) .vy -\- p^v^x — qXvPy = 0. 



The tangents in the points of hi pass through the point {Ivi', (ivi). 

 This point L' is the satellite point of L, and for any curve 

 C{p,q) — {q odd) — the propositions hold: 



I. If Pj, P^, P3 are the points of contact of the tangents from L 

 to a curve C{p,q), the tangents in the satellite points of P,, P^, I\, 

 pass through the satellite point L' of L. 



If in the satellite points of the satellite points the tangents to 

 C{p,q) are drawn, they pass again through a point L" ; this process 

 can be continued ad infinitum; the points L' , L" etc. lie on CL{p,q)- 



II. If Pi, P,, P3, are the points of contact of the tangents from 

 L to C{p,q), the three straight lines passing through P^, P, and Pj, 

 which touch .C{p, q) outside these points, pass through one point 

 viz. L^. 



The Hague, September 1917. 



