équation

Forms

équation f (plural équations)^[1] Old French equaciun, equacium.^[2][3]

Etymology

It is borrowed from Latin aequātiō (“equalizing, levelling”), which in Medieval Latin also meant “account, calculation” (11th century).^[3][2] The Latin noun is formed from aequō (“to make equal”), from aequus (“equal”), the source of égal.^[2][4] The algebraic sense was taken from the Latin of the sciences.^[5][6]

It is an old borrowing that was scarcely used before the 17th century;^[2][5][4] Bloch and Wartburg and the Grand Robert date the lasting word to 1613 and treat the 13th-century record as isolated.^[2][5][4]

Earliest recorded meaning

It is first found about 1250 as equacium, in an astronomical sense, in Thomas of Kent's Alexander romance.^[3][2] The Grand Robert glosses this isolated record as “equality”.^[4]

Semantic evolution

After the isolated 13th-century use, the word came back in the early 17th century,^[5][4] and Descartes used it in his Géométrie (1637) for the algebraic relation between two quantities that holds only for certain values of the unknowns.^[3][2] This is still the main sense.^[7]

From mathematics it spread by analogy to other sciences:^[2] in astronomy the équation du temps is the difference between true and mean time, and the équation personnelle (1864) the delay, varying from one observer to another, between seeing a phenomenon and recording it.^[8][2] From this the équation personnelle came to mean each person's own way of observing a fact, a phrase that has recently become fashionable jargon.^[2] Chemistry (19th century) has the équation chimique, which shows the substances that react and those produced.^[2][8]

The adjective équationnel (1897) is a rare learned derivative.^[2]

Timeline

• c. 1250 – Equacium appears in an astronomical sense in Thomas of Kent.^[3]
• 1613 – The word reappears and stays in use.^[5][4]
• 1637 – Descartes uses it in algebra in La Géométrie.^[3][2]
• 1864 – Équation personnelle in psychology and astronomy.^[2]
• 1897 – The derivative équationnel appears.^[2]

Meanings

Noun

1. (mathematics) An equation, a conditional equality between two expressions containing one or more unknowns: résoudre une équation, équation du second degré, système d'équations, as in Elle a posé une équation à deux inconnues pour trouver la réponse.^[7][3][8]
2. (chemistry) Équation chimique: a formula showing the substances that react and those produced.^[8][2]
3. (astronomy) A correction added to or taken from a mean motion to obtain the true one: équation du temps, the difference between true and mean time.^[8]
4. Équation personnelle: the delay, varying between observers, between seeing and recording a phenomenon, and by extension a person's own way of seeing things.^[2][8]

Word family

• équationnel

Related words

• égal
• péréquation
• Latin aequātiō

References

1. ^ a b Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l m n o p q Rey, Alain, ed. (1992), Dictionnaire historique de la langue française, Paris: Le Robert
3. ^ a b c d e f g Trésor de la langue française informatisé (2004), ATILF – CNRS & Université de Lorraine, atilf.fr/tlfi; electronic version of Imbs, Paul; Quemada, Bernard, eds. (1971–1994), Trésor de la langue française, Paris: CNRS / Gallimard
4. ^ a b c d e f Rey, Alain, ed. (2005), Le Grand Robert de la langue française, electronic version, Paris: Le Robert
5. ^ a b c d e Bloch, Oscar; Wartburg, Walther von (1989), Dictionnaire étymologique de la langue française, 8th ed., Paris: Presses universitaires de France
6. ^ Guilbert, Louis; Lagane, René; Niobey, Georges, eds. (1971–1978; 1989), Grand Larousse de la langue française, Paris: Larousse
7. ^ a b Rey-Debove, Josette; Rey, Alain, eds. (2007), Le Petit Robert de la langue française, Paris: Le Robert
8. ^ a b c d e f Littré, Émile (1873–1877), Dictionnaire de la langue française, 4 vols. and supplement, Paris: Hachette