[1] Since this paper was first written Euclid, Book I, in the Greek, has been edited with a commentary by Sir Thomas Heath (Cambridge Press, 1920). It is full of interest and instruction.
[2] See my paper on ‘The Socratic Doctrine of the Soul’. Proceedings of the British Academy, 1915-16, pp. 235 sqq.
[3] In the case of the parabola, the base (as distinct from the ‘erect side’) of the rectangle is what is called the abscissa (Gk. αποτεμνομενη, ‘cut off’) of the ordinate, and the rectangle itself is equal to the square on the ordinate. In the case of the central conics, the base of the rectangle is ‘the transverse side of the figure’ or the transverse diameter (the diameter of reference), and the rectangle is equal to the square on the diameter conjugate to the diameter of reference.
[4] This word primarily means an all-round athlete, a winner in all five of the sports constituting the πενταθλον, namely jumping, discus-throwing, running, wrestling, and boxing (or javelin-throwing).
[5] επι δε τουτοις Πυθαγορας την περι αυτην φιλοσοφιαν εις σχημα παιδειας ελευθερου μετεστησεν. {epi de toutois Pythagoras tên peri autên philosophian eis schêma paideias eleutherou metestêsen.} Procli Comment. Euclidis lib. I, Prolegom. II (p. 65, ed. Friedlein).
[6] The word Biology was introduced by Gottfried Reinhold Treviranus (1776-1837) in his Biologie oder die Philosophie der lebenden Natur, 6 vols., Göttingen, 1802-22, and was adopted by J.-B. de Lamarck (1744-1829) in his Hydrogéologie, Paris, 1802. It is probable that the first English use of the word in its modern sense is by Sir William Lawrence (1783-1867) in his work On the Physiology, Zoology, and Natural History of Man, London, 1819; there are earlier English uses of the word, however, contrasted with biography.
[7] The remains of Alcmaeon are given in H. Diel’s Die Fragmente der Vorsokratiker, Berlin, 1903, p. 103. Alcmaeon is considered in the companion chapter on Greek Medicine.
[8] Especially the περι γυναικειης φυσιος, On the nature of woman, and the περι γυναικειων, On the diseases of women.
[9] περι ἑβδομαδων. The Greek text is lost. We have, however, an early and barbarous Latin translation, and there has recently been printed an Arabic commentary. G. Bergstrasser, Pseudogaleni in Hippocratis de septimanis commentarium ab Hunnino Q. F. arabice versum, Leipzig, 1914.
[10] περι νουσων δ.