6.R.1. EVERY TRIANGLE IS ISOSCELES
This is sometimes claimed to have been in Euclid's lost Pseudaria (Fallacies).
Ball. MRE, 1st ed., 1892, pp. 33 34. On p. 32, Ball refers to Euclid's lost Fallacies and presents this fallacy and the one in 6.R.2: "I do not know whether either of them has been published previously." In the 3rd ed., 1896, pp. 42-43, he adds the heading: To prove that every triangle is isosceles. In the 5th ed., 1911, p. 45, he adds a note that he believes these two were first published in his 1st ed. and notes that Carroll was fascinated by them and they appear in The Lewis Carroll Picture Book (= Carroll-Collingwood) -- see below.
Mathesis (1893). ??NYS. [Cited by Fourrey, Curiosities Geometriques, p. 145. Possibly Mathesis (2) 3 (Oct 1893) 224, cited by Ball in MRE, 3rd ed, 1896, pp. 44-45, cf in Section 6.R.4.]
Carroll-Collingwood. 1899. Pp. 264-265 (Collins: 190-191). = Carroll-Wakeling II, prob. 27: Every triangle has a pair of equal sides!, pp. 43 & 27. Every triangle is isosceles. Carroll may have stated this as early as 1888. Wakeling's solution just suggests making an accurate drawing. Carroll-Gardner, p. 65, mentions this and says it was not original with Carroll.
Ahrens. Mathematische Spiele. Teubner. Alle Dreiecke sind gleichschenklige. 2nd ed., 1911, chap. X, art. VI, pp. 108 & 119 120. 3rd ed., 1916, chap. IX, art. IX, pp. 92-93 & 109-111. 4th ed., 1919 & 5th ed., 1927, chap IX, art. IX, pp. 99 101 & 116 118.
W. A. Bagley. Puzzle Pie. Op. cit. in 5.D.5. 1944. Call Mr. Euclid -- No. 15: To prove all triangles are equilateral, pp. 16-17. Clear exposition of the fallacy.
See Read in 6.R.4 for a different proof of this fallacy.
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