I. Weidler, Spicilegium observationum ad historiam notarum numeralium, Wittenberg, 1755, derives them from the Hebrew letters; Dom Augustin Calmet, "Recherches sur l'origine des chiffres d'arithmétique," Mémoires pour l'histoire des sciences et des beaux arts, Trévoux, 1707 (pp. 1620-1635, with two plates), derives the current symbols from the Romans, stating that they are relics of the ancient "Notae Tironianae." These "notes" were part of a system of shorthand invented, or at least perfected, by Tiro, a slave who was freed by Cicero. L. A. Sedillot, "Sur l'origine de nos chiffres," Atti dell' Accademia pontificia dei nuovi Lincei, Vol. XVIII, 1864-1865, pp. 316-322, derives the Arabic forms from the Roman numerals.
[120] Athanasius Kircher, Arithmologia sive De abditis Numerorum, mysterijs qua origo, antiquitas & fabrica Numerorum exponitur, Rome, 1665.
[121] See Suter, Die Mathematiker und Astronomen der Araber, p. 100.
[122] "Et hi numeri sunt numeri Indiani, a Brachmanis Indiae Sapientibus ex figura circuli secti inuenti."
[123] V. A. Smith, The Early History of India, Oxford, 2d ed., 1908, p. 333.
[124] C. J. Ball, "An Inscribed Limestone Tablet from Sippara," Proceedings of the Society of Biblical Archæology, Vol. XX, p. 25 (London, 1898). Terrien de Lacouperie states that the Chinese used the circle for 10 before the beginning of the Christian era. [Catalogue of Chinese Coins, London, 1892, p. xl.]
[125] For a purely fanciful derivation from the corresponding number of strokes, see W. W. R. Ball, A Short Account of the History of Mathematics, 1st ed., London, 1888, p. 147; similarly J. B. Reveillaud, Essai sur les chiffres arabes, Paris, 1883; P. Voizot, "Les chiffres arabes et leur origine," La Nature, 1899, p. 222; G. Dumesnil, "De la forme des chiffres usuels," Annales de l'université de Grenoble, 1907, Vol. XIX, pp. 657-674, also a note in Revue Archéologique, 1890, Vol. XVI (3), pp. 342-348; one of the earliest references to a possible derivation from points is in a work by Bettino entitled Apiaria universae philosophiae mathematicae in quibus paradoxa et noua machinamenta ad usus eximios traducta, et facillimis demonstrationibus confirmata, Bologna, 1545, Vol. II, Apiarium XI, p. 5.