différentiel

Forms

différentiel m (plural différentiels)^[1] Adjective: feminine différentielle, plural différentiels, différentielles.^[1]

Etymology

It is formed from French différence + -iel, after Late Latin differentialis.^[2][3] The TLFi derives it from Latin differentia with the suffix -el,^[4] Wiktionary from différent,^[1] while Rey and the Petit Robert treat it as borrowed from Late or scientific Latin.^[5][6] Middle French had differential (“relating to a dispute”) in the 16th century.^[4][5]

Earliest recorded meaning

It is first recorded in calcul différentiel in the Trévoux dictionary (1732), perhaps already in 1696 in the marquis de L'Hôpital's Analyse des infiniment petits.^[4][5]

Semantic evolution

Introduced in mathematics, the adjective spread to tax law (droit différentiel, 1849, Proudhon), to psychology (1851, Cournot) and to technology (thermomètre différentiel, 1860).^[4][5] The Académie recorded quantité différentielle and tarif différentiel from 1798.^[4]

In technology it became a masculine noun (1895) by ellipsis for engrenage différentiel, the gear that joins the two halves of a vehicle's axle;^[5][6] the feminine noun différentielle is the mathematical differential.^[5][4] The noun has also come to mean the gap, as a percentage, between two quantities.^[6]

Timeline

• 1696 – Calcul différentiel possibly used by L'Hôpital.^[4]
• 1732 – Calcul différentiel in the Trévoux dictionary.^[4][5]
• 1849 – Droit différentiel in tax law.^[4][5]
• 1851 – Used in psychology.^[4][5]
• 1860 – Used in technology.^[4][5]
• 1895 – The masculine noun for the gear.^[5][6]
• 1908 – Le différentiel in Maurey's Le Chauffeur.^[7]

Meanings

Adjective

1. Relating to or marking differences or variations: un diagnostic différentiel.^[6][4][8]
2. (mathematics) Proceeding by infinitely small differences: calcul différentiel, équation différentielle.^[4][6][1]
3. (mechanics) Produced by the difference of two motions: mouvement différentiel.^[4][6]
4. (economics) Varying according to origin, distance or productivity: droit différentiel, tarif différentiel.^[4][3]

Noun

1. (automobiles) The differential gear, which lets the driving wheels turn at different speeds in a bend.^[4][6][1]
2. A difference between two quantities, expressed as a percentage: différentiel d'inflation.^[6][1]
3. (ice hockey) Plus-minus.^[1]

Related words

• différence
• différent
• différer
• intégral

Usage notes

The feminine noun différentielle is the infinitely small increase of a function corresponding to an infinitely small increase of the variable.^[4][8]

References

1. ^ a b c d e f g h Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ Rey, Alain, ed. (2005), Le Grand Robert de la langue française, electronic version, Paris: Le Robert
3. ^ a b Guilbert, Louis; Lagane, René; Niobey, Georges, eds. (1971–1978; 1989), Grand Larousse de la langue française, Paris: Larousse
4. ^ a b c d e f g h i j k l m n o p q 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
5. ^ a b c d e f g h i j k Rey, Alain, ed. (1992), Dictionnaire historique de la langue française, Paris: Le Robert
6. ^ a b c d e f g h i Rey-Debove, Josette; Rey, Alain, eds. (2007), Le Petit Robert de la langue française, Paris: Le Robert
7. ^ Quemada, Bernard, ed. (1959–2006), Datations et documents lexicographiques (Base historique du vocabulaire français, BHVF), Paris: Klincksieck / CNRS / Champion; ATILF
8. ^ a b Littré, Émile (1873–1877), Dictionnaire de la langue française, 4 vols. and supplement, Paris: Hachette