page_title: Léon Lalanne
section_title: Mathematics
hierarchical_section_title: Léon Lalanne / Works / Mathematics
caption_attribution_description: English: "Universal calculator" of Léon Lalanne, a nomogram.
context_page_description: Léon Louis Lalanne was a French engineer and politician.
context_section_description: With Philbert Maurice d'Ocagne Lalanne is considered the inventor of the nomogram. The intention was to replace the slide rule. In a paper of 1846 Lalanne contributed to the subject the ideas of anamorphosis and the use of projective transformations. There were applications to the solution of the cubic equation. He called his nomographic device the "abac". This "universal calculator" had 60 functions implemented graphically. Half a century later Maurice d'Ocagne provided a general theory, founded in projective geometry, for the nonlinear scales related by nomography.
  In 1840 Lalanne announced balanced ternary as an arithmetical system, in Comptes Rendus; this followed earlier work on signed arithmetic by John Leslie and Augustin Cauchy. Also in 1840 he devised a mechanical computer capable of solving numerically polynomial equations up to degree seven.
  Charles Darwin cited a paper by Lalanne from the same year 1840 on the geometry of honeycombs, in his Natural Selection manuscript.
caption: Léon Lalanne's "abacus" or "universal computer", 1843
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