Subject: [HM] The Unfortunate Wallace!
From: Antreas P. Hatzipolakis (xpolakis@otenet.gr)
Date: Thu Mar 30 2000 - 11:59:20 EST
A well-known point in the complete quadrilateral is Miquel Point:
The point where the circumcircles of the four triangles of the quadr. meet.
A. Miquel wrote about this point in J. math. pures appl. (1) 3(1838), p. 486,
but 10 years before, J. Steiner had discovered it (Annales de Gergonne XVIII,
1827-28, p. 302).
[The references from: P. D. Ladopoulos: Elements of Projective Geometry
[in Greek]. Athens, 1966, p. 155, footnote #77]
In the biography of William Wallace (1768 - 1843) at St. Andrews archive at:
http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Wallace.html
we read that:
<quote>
Wallace's work was on geometry and Simson's line (which is definitely not
due to Simson!) appears first in a paper of Wallace in 1799. One of
Wallace's theorems,
if 4 lines intersect each other to form 4 triangles (omit one
line in turn) then the circumcircles of the triangles have a
point in common,
was generalised to 2n lines by Clifford.
</quote>
This point is the Miquel Point. Where had Wallace published this theorem?
In the 1799 paper? If so, he is very unfortunate:
His line is named after Simson, and his point after Miquel!
Antreas
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