[492] However, we can often recognise, in a small artery for instance, that the so-called “circular” fibres tend to take a slightly oblique, or spiral, course.
[493] The spiral fibres, or a large portion of them, constitute what Searle called “the rope of the heart” (Todd’s Cyclopaedia, II, p. 621, 1836). The “twisted sinews of the heart” were known to early anatomists, and have been frequently and elaborately studied: for instance, by Gerdy (Bull. Fac. Med. Paris, 1820, pp. 40–148), and by Pettigrew (Phil. Trans. 1864), and of late by J. B. Macallum (Johns Hopkins Hospital Report, IX, 1900) and by Franklin P. Mall (Amer. J. of Anat. XI, 1911).
[494] Cf. Bütschli, “Protozoa,” in Bronn’s Thierreich, II, p. 848, III, p. 1785, etc., 1883–87; Jennings, Amer. Nat. XXXV, p. 369, 1901; Pütter, Thigmotaxie bei Protisten, Arch. f. Anat. u. Phys. (Phys. Abth. Suppl.), pp. 243–302, 1900.
[495] A great number of spiral forms, both organic and artificial, are described and beautifully illustrated in Sir T. A. Cook’s Curves of Life, 1914, and Spirals in Nature and Art, 1903.
[496] Cf. Vines, The History of the Scorpioid Cyme, Journ. of Botany (n.s.), X, pp. 3–9, 1881.
[497] Leslie’s Geometry of Curved Lines, p. 417, 1821. This is practically identical with Archimedes’ own definition (ed. Torelli, p. 219); cf. Cantor, Geschichte der Mathematik, I, p. 262, 1880.
[498] See an interesting paper by Whitworth, W. A., “The Equiangular Spiral, its chief properties proved geometrically,” in the Messenger of Mathematics (1), I, p. 5, 1862.
[499] I am well aware that the debt of Greek science to Egypt and the East is vigorously denied by many scholars, some of whom go so far as to believe that the Egyptians never had any science, save only some “rough rules of thumb for measuring fields and pyramids” (Burnet’s Greek Philosophy, 1914, p. 5).
[500] Euclid (II, def. 2).
[501] Cf. Treutlein, Z. f. Math. u. Phys. (Hist. litt. Abth.), XXVIII, p. 209, 1883.