Further reading

  • Saussure, Ferdinand de. Course in General Linguistics. Original: Cours de linguistique générale. Paris: Payot, 1916.
  • Peirce, Charles Sanders. Collected Papers of Charles Sanders Peirce. 8 vols. Cambridge, MA: Harvard University Press, 1931–1958. Volume 2 contains the texts on icon, index and symbol.
  • Peirce, Charles Sanders. The Essential Peirce: Selected Philosophical Writings. 2 vols. Bloomington: Indiana University Press, 1992–1998.
  • Morris, Charles W. Foundations of the Theory of Signs. Chicago: University of Chicago Press, 1938.
  • Duval, Raymond. Sémiosis et pensée humaine: registres sémiotiques et apprentissages intellectuels. Bern: Peter Lang, 1995.
  • Duval, Raymond. A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 2006, p. 103–131.
  • Falkner, Karen P.; Levi, Linda; Carpenter, Thomas P. Children’s understanding of equality: a foundation for algebra. Teaching Children Mathematics, 6(4), 1999, p. 232–236.
  • Mazur, Joseph. Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers. Princeton: Princeton University Press, 2014.
  • Swetz, Frank J. Capitalism and Arithmetic: The New Math of the 15th Century. La Salle: Open Court, 1987. Includes a translation of the Treviso Arithmetic (1478), with the rule of three and gelosia multiplication.
  • Cajori, Florian. A History of Mathematical Notations. 2 vols. Chicago: Open Court, 1928–1929. On the fraction bar, the names of the rule of three and the signs of proportion.

The old texts on this site about fractions, multiplication and the rule of three supplied the etymology of numerator and denominator, Egyptian multiplication, Pacioli’s gelosia and the table of names for the rule of three.

Image sources

Image Source Licence
Portrait of Ferdinand de Saussure Wikimedia Commons public domain
Portrait of Charles Sanders Peirce, Napoleon Sarony (New York Public Library) Wikimedia Commons public domain

The diagrams (fractions, structure of formulas, gelosia, equality, segments, area of the square and registers of the affine function) and the interactive figures were made for this book. They explain concepts and do not reproduce original diagrams by Saussure, Peirce or Duval.

Chapter index · ← How to read a notation: a guide and a glossary · Chapter 3: variables, unknowns and functions →