[58] This problem deserves more study than has yet been given it. A beginning may be made with Comte Goblet d'Alviella, Ce que l'Inde doit à la Grèce, Paris, 1897, and H. G. Keene's review, "The Greeks in India," in the Calcutta Review, Vol. CXIV, 1902, p. 1. See also F. Woepeke, Propagation, p. 253; G. R. Kaye, loc. cit., p. 475 seq., and "The Source of Hindu Mathematics," Journal of the Royal Asiatic Society, July, 1910, pp. 749-760; G. Thibaut, Astronomie, Astrologie und Mathematik, pp. 43-50 and 76-79. It will be discussed more fully in Chapter VI.
[59] I.e. to 100,000. The lakh is still the common large unit in India, like the myriad in ancient Greece and the million in the West.
[60] This again suggests the Psammites, or De harenae numero as it is called in the 1544 edition of the Opera of Archimedes, a work in which the great Syracusan proposes to show to the king "by geometric proofs which you can follow, that the numbers which have been named by us ... are sufficient to exceed not only the number of a sand-heap as large as the whole earth, but one as large as the universe." For a list of early editions of this work see D. E. Smith, Rara Arithmetica, Boston, 1909, p. 227.
[61] I.e. the Wise.
[62] Sir Monier Monier-Williams, Indian Wisdom, 4th ed., London, 1893, pp. 144, 177. See also J. C. Marshman, Abridgment of the History of India, London, 1893, p. 2.
[63] For a list and for some description of these works see R. C. Dutt, A History of Civilization in Ancient India, Vol. II, p. 121.
[64] Professor Ramkrishna Gopal Bhandarkar fixes the date as the fifth century B.C. ["Consideration of the Date of the Mahābhārata," in the Journal of the Bombay Branch of the R. A. Soc., Bombay, 1873, Vol. X, p. 2.].
[65] Marshman, loc. cit., p. 2.
[66] A. C. Burnell, South Indian Palæography, 2d ed., London, 1878, p. 1, seq.
[67] This extensive subject of palpable arithmetic, essentially the history of the abacus, deserves to be treated in a work by itself.