It is proposed to discuss in this paper some properties of the general Frégier-point and point out its connections with well known conics like the Apollonian hyperbola and the nine-point conic of a quadrangle. Incidentally, we discover a pedal conic of a quadrangle which has very intimate relations with the nine-point conic.

Dr T. J. Fletcher’s article in last December’s Gazette [1] was of great interest mathematically in illustrating how an eminently practical problem (here, essentially a combinatorial problem) could be solved using some surprising and unexpectedly theoretical mathematical ideas. (These included the field GF(22), the group (C2)4 and finite geometries, as well as excursions into Pappus’ and Desargues’ theorems.) But to myself, at least, the interest was augmented because the article provided the background for three or four end-of-term lessons with a third year grammar school form. The purpose of this article is to describe how some of the material was adapted.

This product of Queen Anne’s reign consists of five parts: I. Arithmetick, Vulgar and Decimal. II. Algebra or Arithmetick in Species. III. The Elements of Geometry. IV. Conick Sections. V. The Arithmetick of Infinites explained, with its application to Superficial and Solid Geometry. To these is added an Appendix of Practical Gauging, and in the eighth edition is also found the History of Logarithms.

Here is a published example of what I mean by the sinusoidal fallacy: