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'arithmetique," _Memoires pour l'histoire des sciences et des beaux arts_, Trevoux, 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 Archaeology_, 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'universite de Grenoble_, 1907, Vol. XIX, pp. 657-674, also a note in _Revue Archeologique_, 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. [126] _Alphabetum Barmanum_, Romae, MDCCLXXVI, p. 50. The 1 is evidently Sanskrit, and the 4, 7, and possibly 9 are from India. [127] _Alphabetum Grandonico-Malabaricum_, Romae, MDCCLXXII, p. 90. The zero is not used, but the symbols for 10, 100, and so on, are joined to the units to make the higher numbers. [128] _Alphabetum Tangutanum_, Romae, MDCCLXXIII, p. 107. In a Tibetan MS. in the library of Professor Smith, probably of the eighteenth century, substantially these forms are given.