6.R.3. LINES APPROACHING BUT NOT MEETING
Proclus. 5C. A Commentary on the First Book of Euclid's Elements. Translated by Glenn R. Morrow. Princeton Univ. Press, 1970. Pp. 289-291. Gives the argument and tries to refute it.
van Etten/Henrion/Mydorge. 1630. Part 2, prob. 7: Mener une ligne laquelle aura inclination à une autre ligne, & ne concurrera jamais contre l'Axiome des paralelles, pp. 13 14.
Schwenter. 1636. To be added.
Ozanam-Montucla. 1778. Paradoxe géométrique des lignes .... Prob. 70 & fig. 116-117, plate 13, 1778: 405-407; 1803: 411-413; 1814: 348-350. Prob. 69, 1840: 180-181. Notes that these arguments really produce a hyperbola and a conchoid. Hutton adds that a great many other examples might be found.
E. P. Northrop. Riddles in Mathematics. 1944. 1944: 209-211 & 239; 1945: 195 197 & 222; 1961: 197 198 & 222. Gives the 'proof' and its fallacy, with a footnote on p. 253 (1945: 234; 1961: 233) saying the argument "has been attributed to Proclus."
Jeremy Gray. Ideas of Space. OUP, 1979. Pp. 37-39 discusses Proclus' arguments in the context of attempts to prove the parallel postulate.
6.R.4. OTHERS
Ball. MRE, 3rd ed, 1896, pp. 44-45. To prove that, if two opposite sides of a quadrilateral are equal, the other two sides must be parallel. Cites Mathesis (2) 3 (Oct 1893) 224 -- ??NYS
Cecil B. Read. Mathematical fallacies & More mathematical fallacies. SSM 33 (1933) 575 589 & 977-983. There are two perpendiculars from a point to a line. Part of a line is equal to the whole line. Every triangle is isosceles (uses trigonometry). Angle trisection (uses a marked straightedge).
P. Halsey. Class Room Note 40: The ambiguous case. MG 43 (No. 345) (Oct 1959) 204 205. Quadrilateral ABCD with angle A = angle C and AB = CD. Is this a parallelogram?
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