Abacus, among ancient mathematicians, signified a small table covered in dust on which they traced their maps and their figures, according to the testimonies of Martianus Capella, [1] and of Persius, Satires, I, v. 131.

Nec qui abaco numeros & facto in pulvere metas
Scit risisse vafer.

Nor do I want a man who thinks it funny to laugh at calculations with an abacus and cones traced in the sand. [2]

This word seems to come from the Phoenician abk,  [3] dust or powder.

1. D’Alembert gives the name of this fifth-century scholar as “Martius Capella.”

2. Adapted from the translation of G.G. Ramsay in his Juvenal and Persius (London: William Heinemann, 1918), p. 331. A.E. Housman mentions this passage from Persius in a paper on “The Manuscripts of Propertius [III].” While discussing a passage in Propertius, Housman quotes the passage from Persius: “[I]t is possible that we ought to transpose in with Paley and read ‘qui nunc se tumide iactando in uenit honorem’: for a similar transposition of in see Pers. 1 131 where instead of ‘nec qui abaco numeros et secto in puluere metas’ one family of MSS gives ‘nec qui in abaco numeros et secto puluere metas’” (F.R.D. Goodyear, The Classical Papers of A.E. Housman [Cambridge: Cambridge University Press, 2004], vol. 1: 1882-1897 , p. 321). We see from this that d’Alembert has mistranscribed or, perhaps, misremembered the passage he cites, reading facto for secto. As for d’Alembert’s interpretation of an abacus as “a small table covered in dust,” it is (or would have been) considered an error by A.J. Macleane (who also read secto rather than facto ), and d’Alembert would not be the last to make this mistake. Macleane wrote: “’Abacus’ was a board or tray, with raised border and wooden divisions, used for calculating numbers with pebbles. The way of doing it is given conjecturally in Dict. Antiqq. The author of the article ‘Abacus’ in that dictionary has mistaken this passage. It is clear that the first sentence refers to arithmetical computations on an ‘abacus,’ and the second to geometrical figures drawn on sand, for which an ‘abacus’ was also used. ‘Metas’ are cones, but any diagrams may be understood. ‘Scit risisse vafer’ is sarcastic, like ‘possit dicere’ above. ‘Sit’ has been proposed, for which Heinrich quotes authority, but I prefer the common reading: ‘He knows how to laugh, the clever fellow, at arithmetic and geometry . . . ‘” (A.J. Macleane, ed., Decii Junii Juvenalis et A. Persii Flacci Satirae [London: Whittaker, 1867], p. 388 n.131). By “Dict. Antiqq.” Macleane means William Smith, ed., A Dictionary of Greek and Roman Antiquities, first published in 1842. According to this interpretation, the table to which Persius refers was used for calculation only; cones and other geometrical figures were drawn on sand. (Paper would not produced in the West before the 13th century.)

3. The Encyclopédie gives the three letters aleph, bet, and qof of the Hebrew (not the Phoenician) alphabet, written right to left: אבק. The Semitic word abk means ‘sand’ or ‘dust’. Phoenician and Hebrew, along with Ammonite, Moabite (a dialect of Hebrew), and Edomite, are members of the Canaanite subgroup of Northwest Semitic languages. Modern acquaintance with the Phoenician alphabet dates from the 17th century, but it was not identified as such until the 19th century; thus it is not surprising that d’Alembert uses Hebrew. Prior to the 19th century, Phoenician script was believed to be a variation of Egyptian hieroglyphics. Phoenician script developed from the 13th century BCE to the 3rd century BCE and is one of the main branches of the North Semitic cycle of scripts; another was what is now known as Paleo-Hebrew, for which evidence exists from the 10th century BCE to the 5th century BCE, when the Aramaic alphabet became the predominant system for writing Hebrew. The script presently used for Hebrew evolved from the Aramaic alphabet. See Albertine Gaur, A History of Writing, rev. ed. (New York, London, and Paris: Cross River Press/Abbeville Press, 1992), pp. 90-95.