[48] Geschichte der Math., Vol. I, 2d ed., p. 595.
[49] L. von Schroeder, Pythagoras und die Inder, Leipzig, 1884; H. Vogt, "Haben die alten Inder den Pythagoreischen Lehrsatz und das Irrationale gekannt?" Bibliotheca Mathematica, Vol. VII (3), pp. 6-20; A. Bürk, loc. cit.; Max Simon, Geschichte der Mathematik im Altertum, Berlin, 1909, pp. 137-165; three Sūtras are translated in part by Thibaut, Journal of the Asiatic Society of Bengal, 1875, and one appeared in The Pandit, 1875; Beppo Levi, "Osservazioni e congetture sopra la geometria degli indiani," Bibliotheca Mathematica, Vol. IX (3), 1908, pp. 97-105.
[50] Loc. cit.; also Indiens Literatur und Cultur, Leipzig, 1887.
[51] It is generally agreed that the name of the river Sindhu, corrupted by western peoples to Hindhu, Indos, Indus, is the root of Hindustan and of India. Reclus, Asia, English ed., Vol. III, p. 14.
[52] See the comments of Oppert, On the Original Inhabitants of Bharatavarṣa or India, London, 1893, p. 1.
[53] A. Hillebrandt, Alt-Indien, Breslau, 1899, p. 111. Fragmentary records relate that Khāravela, king of Kaliṅga, learned as a boy lekhā (writing), gaṇanā (reckoning), and rūpa (arithmetic applied to monetary affairs and mensuration), probably in the 5th century B.C. [Bühler, Indische Palaeographie, Strassburg, 1896, p. 5.]
[54] R. C. Dutt, A History of Civilization in Ancient India, London, 1893, Vol. I, p. 174.
[55] The Buddha. The date of his birth is uncertain. Sir Edwin Arnold put it c. 620 B.C.
[56] I.e. 100·107.
[57] There is some uncertainty about this limit.