calculus

calculus

English

Etymology

• Borrowed from Latin calculus (“a pebble or stone used as reckoning counters in abacus”) [1], diminutive of calx (“limestone”) + -ulus.[2]
• Mathematical topic is from differential calculus.

Pronunciation

• (UK) IPA^(key): /ˈkæl.kjʊ.ləs/
• (General American) IPA^(key): /ˈkæl.kjə.ləs/

• Audio

  (file)

Noun

calculus (countable and uncountable, plural calculi or calculuses)

1. (dated, countable) Calculation; computation.
2. (countable, mathematics) Any formal system in which symbolic expressions are manipulated according to fixed rules.

   lambda calculus

   predicate calculus

3. (uncountable, often definite, the calculus) Differential calculus and integral calculus considered as a single subject; analysis.
4. (countable, medicine) A stony concretion that forms in a bodily organ.

   Synonym: stone

   Hyponyms: kidney stone, nephrolith, gallstone, cholelith, sialolith, urolith

5. (uncountable, dentistry) Deposits of calcium phosphate salts on teeth.
6. (countable) A decision-making method, especially one appropriate for a specialised realm.
   • 2008 December 16, “Cameron calls for bankers’ ‘day of reckoning’”, in Financial Times:

     The Tory leader refused to state how many financiers he thought should end up in jail, saying: “There is not some simple calculus."

Synonyms

• (calculation, computation): ciphering, reckoning; see also Thesaurus:calculation
• (in analysis): infinitesimal calculus
• (in medicine): stone
• (in dentistry): dental calculus, tartar

Derived terms

• absolute differential calculus
• all students take calculus
• calculus of moving surfaces
• calculus of sums and differences
• calculus of variations
• dental calculus
• differential calculus
• felicific calculus
• finite-difference calculus
• fractional calculus
• hedonic calculus
• hedonistic calculus
• implicational propositional calculus
• infinitesimal calculus
• integral calculus
• jackstone calculus
• join calculus
• Kirby calculus
• lambda calculus
• logical calculus
• modular calculus
• multivariable calculus
• noncalculus
• operational calculus
• pi-calculus
• precalculus
• predicate calculus
• propositional calculus
• renal calculus
• Ricci calculus
• Schubert calculus
• sequent calculus
• stochastic calculus
• tensor calculus
• tuple calculus
• utility calculus

 

Related terms

• calcify
• calcium
• calculate

Translations

formal mathematical system

Afrikaans: analise, calculus Arabic: حسبان‎ Armenian: համարողություն (hy) (hamarołutʿyun) Catalan: càlcul (ca) m Chinese: Cantonese: 微積分學 Mandarin: 微積分學／微积分学 (zh) (wēijīfēnxué) Czech: počet (cs) m Finnish: laskenta (fi) French: calcul (fr) m Gallurese: calculu Georgian: კალკულუსი (ḳalḳulusi), აღრიცხვა (aɣricxva) German: Kalkül (de) m Greek: λογισμός (el) m (logismós) Hungarian: kalkulus Irish: calcalas m Italian: calcolo (it) Japanese: 計算 (ja) (keisan) Korean: 미적분 (ko) (mijeokbun), 미적분학 (mijeokbunhak) Maori: tuanaki Norwegian: beregning m or f Polish: rachunek (pl) m Portuguese: cálculo (pt) Romanian: calcul (ro) n Russian: исчисле́ние (ru) n (isčislénije) Sardinian: Campidanese: calculu, càrculu Logudorese: calculu, càrculu Sassarese: càlcuru Serbo-Croatian: Cyrillic: ра̀чӯн m Roman: ràčūn (sh) m Slovak: počet Spanish: cálculo (es) m Swedish: kalkyl (sv) c Tagalog: tayahan Welsh: calcwlws m Yiddish: קאַלקולוס‎ m (kalkulus)

differential calculus and integral calculus considered as a single subject

Afrikaans: analise, calculus Arabic: حسبان‎, التفاضل والتكامل‎ Bengali: কলনবিদ্যা (bn) (kôlônôbidẏa) Catalan: càlcul (ca) m Chinese: Mandarin: 微積分／微积分 (zh) (wēijīfēn) Czech: počet (cs) Farefare: kɛkrɛ-biire Finnish: differentiaalilaskenta (fi) French: calcul (fr) m Gallurese: calculu Georgian: დიფერენციალური აღრიცხვა (diperencialuri aɣricxva) German: Kalkül (de) m Greek: λογισμός (el) m (logismós) Gujarati: કલન (kalan) Hebrew: חדו"א‎ (ẖédva) Hindi: कलन (hi) (kalan) Icelandic: deilda- og heildareikningur m, diffur- og tegurreikningur m, örsmæðareikningur m, reiknivísi f Ido: kalkulo (io) Italian: calcolo (it) m Japanese: 微積分 (ja) (bisekibun) Maori: tuanaki Marathi: कलन (kalan) Norwegian: matematikk (no) m Persian: حساب دیفرانسیل و انتگرال‎ (hesâbe diferânsyal o entegrâl) Polish: rachunek różniczkowy i całkowy m Portuguese: cálculo (pt) m Romanian: calcul diferențial (ro) n Russian: математический анализ (ru) (matematičeskij analiz) Sardinian: Campidanese: calculu, càrculu Logudorese: calculu, càrculu Sassarese: càlcuru Serbo-Croatian: Roman: infinitezimalni račun m Slovak: matematická analýza Spanish: cálculo diferencial m Swedish: analys (sv) c Tagalog: tayahan Thai: แคลคูลัส (th) Telugu: కలన గణితం (kalana gaṇitaṁ) Turkish: kalkülüs Yiddish: קאַלקולוס‎ m (kalkulus)

stony concretion in an organ

Bulgarian: камък (bg) m (kamǎk) Catalan: càlcul (ca) m Chinese: Mandarin: 結石／结石 (zh) (jiéshí) Finnish: kivi (fi) French: calcul (fr) m, lithiase (fr) f German: Konkrement (de) n Greek: λιθίαση (el) f (lithíasi) Gujarati: અશ્મરી (aśmarī) Icelandic: steinn (is) m Japanese: 結石 (ja) (kesseki) Latin: lapillus m, calculus m Macedonian: ка́мен m (kámen) Portuguese: cálculo (pt) m Romanian: piatră (ro) f, calcul (ro) m Russian: ка́мень (ru) m (kámenʹ) Serbo-Croatian: Cyrillic: каме́нац m Roman: kaménac (sh) m Spanish: cálculo (es) m Thai: นิ่ว (th) (nîu) Turkish: taş (tr)

deposits on teeth — see dental calculus

See also

• algebra
• analysis
• concretion

References

1. Douglas Harper (2001–2023), “calculus”, in Online Etymology Dictionary.
2. https://simplymaths.wordpress.com/2012/06/20/what-does-it-mean-calculus/

• calculus in The Century Dictionary, New York, N.Y.: The Century Co., 1911

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Latin

Etymology

From calx, calcis (“limestone, game counter”) +‎ -ulus (diminutive suffix).

Pronunciation

• (Classical) IPA^(key): /ˈkal.ku.lus/, [ˈkäɫ̪kʊɫ̪ʊs̠]
• (Ecclesiastical) IPA^(key): /ˈkal.ku.lus/, [ˈkälkulus]

Noun

calculus m (genitive calculī); second declension

1. diminutive of calx
2. pebble, stone
3. reckoning, calculating, calculation
4. a piece in the latrunculi game

Declension

Second-declension noun.

Case	Singular	Plural
Nominative	calculus	calculī
Genitive	calculī	calculōrum
Dative	calculō	calculīs
Accusative	calculum	calculōs
Ablative	calculō	calculīs
Vocative	calcule	calculī

Derived terms

• calculārius
• calculensis
• calculō
• calculōsus

Descendants

• → Catalan: càlcul
• → English: calculus
• → French: calcul
  • → German: Kalkül
    • → Czech: kalkul
  • → Romanian: calcul
  • → Swedish: kalkyl
• → Gallurese: calculu
• → Georgian: კალკულუსი (ḳalḳulusi)
• → Hungarian: kalkulus
• → Irish: calcalas
• → Italian: calcolo
• → Portuguese: cálculo
• → Sardinian: calculu, càrculu
• → Sassarese: càlcuru
• → Spanish: cálculo
• → Welsh: calcwlws
• → Yiddish: קאַלקולוס‎ (kalkulus)

References

• “calculus”, in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press
• “calculus”, in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
• calculus in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition with additions by D. P. Carpenterius, Adelungius and others, edited by Léopold Favre, 1883–1887)
• calculus in Gaffiot, Félix (1934) Dictionnaire illustré latin-français, Hachette
• Carl Meißner; Henry William Auden (1894) Latin Phrase-Book‎, London: Macmillan and Co.
  • to go through accounts, make a valuation of a thing: ad calculos vocare aliquid (Amic. 16. 58)