1. The translations of the Elements are by T. Heath, The Thirteen Books of Euclid’s Elements, 3 vols., Cambridge, England, 1925.
2. John Philoponus, In Aristotelis Analytica Priora Commentaria (ed. by M. Wallies), Berlin, 1905, 246.3–4, gives a similar illustration of the fifth anapodeiktos: ‘The side is either equal to or greater than or less than the side; but it is neither greater nor less; therefore it is equal’. For details on the anapodeiktoi and other aspects of Stoic logic, see B. Mates, Stoic Logic, Berkeley 1961.
3. These divisions and their names are taken from Proclus, In Primum Euclidis Elementorum Librum Commentarii (ed. by G. Friedlein), Leipzig, 1873, 203.1–210.16. The rigidity which they suggest is fully confirmed by Euclid’s Elements; and the terms them-selves, or forms of them, can all be found in third-century mathematical works. For references, see C. Mugler, Dictionnaire Historique de la terminologie geomitrique des grecs, Paris 1958.
4. As in D. Hilbert, Foundations of Geometry (transl. by L. Unger), La Salle, 111., 10th ed., 1971.
5. J. Łukasiewicz, Aristotle’s Syllogistic, Oxford, 2nd ed., 1957, p. 1, asserts that Aristotle does not allow singular terms in syllogisms. If Lukasiewicz is right, then no Euclidean argument would be an Aristotelian syllogism.