As I am reading some old messages sent by Steve about Anallagmatic

Cubics I have found in message 2300 the terms "supplementary" and

"antisupplementary" paired with "complementary" and "anticomplementary".

The last two are well known to me, and Clark in the Glossary at ETC

defines "complement" and "anticomplement" for points collinear with G:

"P is the complement of Q if G trisects PQ and is closer to P than Q"

"P is the anticomplement of Q if G trisects PQ and is closer to Q than

P".

The terms "supplement" and "antisupplement" must denote something like

that but are referred to I at the place of G. I don't find a short

definition of them. I know only that if the supplement of P is Q, P and

Q are homologous in an homology with pole I and axis the tripolar of I

(called sometimes the anti-orthic axis) carrying the vertexs to the

excenters.

Is there a shorter definition and construction of the supplementary and

antisupplementary points?

Greetings from Barcelona

Quim Castellsaguer

qcastell@...