. De Morgan on Euclid's fourth postulate. Bulletin of Symbolic Logic. 20 (2014) 250. (Coauthor: Sriram Nambiar) ► JOHN CORCORAN AND SRIRAM NAMBIAR, De Morgan on Euclid's fourth postulate. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu The five "postulates"-as opposed to "axioms" or "common notions"-of Euclid's Elements [2, volume I, pp. 153–240] are specifically geometrical. The first: to draw a line from any point to any point; the fifth: the parallel postulate. The fourth postulate [2, volume I, p. 200] is: Kai pasas tas orthas gonias isas allelais einai. All right angles are equal to one another. One first-order translation in variable-enhanced English (cf. [4], p. 121) is: Given two angles x, y, if x is right and y is right, then x equals y. It is clear to us, as it might have been to Euclid, that the fourth postulate uses equal for a relation of angles to angles and not for a property belonging to angles-as intimated by Euclid's to one another. But, De Morgan (1806–1871) did not see it this way, at least in 1831 [1, pp. 203, 206–219]- before he discovered relational logic [3]. Omitting to one another, he wrote: All right angles are equal. The latter he took as elliptical for: All right angles are equal magnitudes. As if emphasizing his construal of Euclid's fourth postulate as an Aristotelian subject-copulapredicate, universal-affirmative, categorical proposition [1, p. 203], he applied an Aristotelian conversion rule to it, deducing the following [1, p. 206]: Some equal magnitudes are right angles. We examine these and other historically revealing statements in [1]. Our study establishes a zero base-line reference from which to measure the De Morgan's stunning future progress in logical theory. [1] AUGUSTUS DE MORGAN, Study and Difficulties of Mathematics, Open Court, 1831/1943. [2] EUCLID, Elements, 3 volumes (Thomas Heath, translator), Dover, 1956. [3] DANIEL MERRILL, Augustus De Morgan and the Logic of Relations, Kluwer, 1990. [4] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995.