Errata in geometry books

The purpose of this page is to collect mistakes in known geometry books. I have put it up after I noticed a few mistakes which could be quite irritating to the reader. At the moment, this page is in an experimental state. Feel free to inform me of any more mistakes you find.


Nathan Altshiller-Court, College Geometry, 2nd Edition, New York 1952 / 2007

Page 30, Problem 25: The problem asks to construct a line through a given point R cutting a given line in D and a given circle in E and F such that RD = EF. This problem is not solvable with compass and ruler as shown on MathLinks by JPE and Yetti. Thanks to Ryan Filips to letting me know that this false problem appeared in Altshiller-Court.

Page 110, Fig. 72: This graphic contains a typo: The upper of the two points labelled Ga should actually be called Gc. Note that this typo is repeated on the front cover of the book, where a part of Fig. 72 is shown.

Page 269, Problem 4: "Isogonal conjugates" must mean "isogonal conjugates with respect to the angles BA'C, CB'A, AC'B " (and not, as one would probably think, with respect to the angles C'A'B', A'B'C', B'C'A') to make the problem correct.

Page 284, Problem 6: I quote the problem:
"Show that the circumcenter O of ABC, the Lemoine point K1 of the medial triangle A1B1C1, and the circumcenter Z' of the anticomplementary triangle A'B'C' are collinear, and OK1 = K1Z."
Does anyone have an idea what this problem was supposed to say? In the above form, it is completely wrong.


Roger A. Johnson, Advanced Euclidean Geometry, 1929 / 1960 / 2007

Page 169, 264, Proof of the last Theorem: Johnson is quite right in the footnote: This theorem (that of all triangles inscribed in a given acute-angled triangle A1A2A3, the orthic triangle has the smallest perimeter) tends to attract flawed/incomplete proofs. Alas, the proof given in 264 is one of these. Can you spot the mistake? I do not mean the omitted (easy) argument why the point Q1 really lies inside the segment A2A3 and not on its extension. There is a more serious flaw. Here (footnote 1) is the explanation.

Page 246, 405, Theorem: "Orthocenter" has to be replaced by "circumcenter" in order to make the theorem hold.

Page 246, 405, Corollary: Unfortunately, deriving the Feuerbach theorem from the preceding results is equally incorrect as its flawed derivation from 396 in 401. One could imagine a case when the nine-point circle and the incircle (i. e. the pedal circle of the incenter) have two points of intersection, one of them being L (to be precise, the point L from 402 when P is the incenter), and the other one a "random" point.


Ross Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry, 1995

Page 95, 9.5, italicized text: "and the center of the second Lemoine circle is the circumcenter O of triangle ABC" should be replaced by "and the center of the second Lemoine circle is the symmedian point K of triangle ABC".

Page 120, 10.5 (a): Strike out the lines "We note in passing that the Steiner point of a triangle is the center of mass of the system obtained by suspending at each vertex a mass equal to the magnitude of the exterior angle at that vertex". This is a property of a so-called "Steiner point" indeed, but of a different "Steiner point" than the one defined before. Unfortunately, there are at least three different triangle centers all called "Steiner points" in some literature.

Page 151, 13.2 (ii): The reference to Figure 189(c) should be a reference to Figure 189(b).


Errata in geometry books

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Darij Grinberg