The site Earliest Known Uses of Some of the Words of Mathematics provides just that, going into great detail where necessary about the history of the words used for concepts:

SUBTRACT. When Fibonacci (1201) wishes to say “I subtract,” he uses some of the various words meaning “I take”: tollo, aufero, or accipio. Instead of saying “to subtract” he says “to extract.”

In English, Chaucer used abate around 1391 in Treatise on the Astrolabe: “Abate thanne thees degrees And minutes owt of 90” (OED2).

In a manuscript written by Christian of Prag (c. 1400), the word “subtraction” is at first limited to cases in which there is no “borrowing.” Cases in which “borrowing” occurs he puts under the title cautela (caution), and gives this caption the same prominence as subtractio.

In Practica (1539) Cardano used detrahere (to draw or take from).
In 1542 in the Ground of Artes Robert Recorde used rebate: “Than do I rebate 6 out of 8, & there resteth 2.”

In 1551 in Pathway to Knowledge Recorde used abate: “Introd., And if you abate euen portions from things that are equal, those partes that remain shall be equall also” (OED2).

Digges (1572) writes “to subduce or substray any sume, is wittily to pull a lesse fro a bigger number.”

Schoner, in his notes on Ramus (1586 ed., p. 8), uses both subduco and tollo for “I subtract.”

In his arithmetic, Boethius uses subtrahere, but in geometry attributed to him he prefers subducere.

The first citation for subtract in the OED2 is in 1557 by Robert Recorde in The whetstone of witte: “Wherfore I subtract 16. out of 18.”

Hylles (1592) used “abate,” “subtact,” “deduct,” and “take away” (Smith vol. 2, pages 94-95).

From Smith (vol. 2, page 95):

The word “subtract” has itself had an interesting history. The Latin sub appears in French as sub, soub, sou, and sous, subtrahere becoming soustraire and subtractio becoming soustraction. Partly because of this French usage, and partly no doubt for euphony, as in the case of “abstract,” there crept into the Latin works of the Middle Ages, and particularly into the books printed in Paris early in the 16th century, the form substractio. From France the usage spread to Holland and England, and form each of these countries it came to America. Until the beginning of the 19th century “substract” was a common form in England and America, and among those brought up in somewhat illiterate surroundings it is still to be found. The incorrect form was never popular in Germany, probably because of the Teutonic exclusion of international terms.

Thanks to Grant Barrett for the link.

Update (Nov. 2020). See also Mathematical Words: Origins and Sources.


  1. The term “algorithm” as a peculiar history (per OED, old ed). An important math book used in Islam and translated into Latin was written by someone from Khwarizm (Chorasmia), i.e. “al-Khwarizm”, the man from Khwarizm. Like “Amerigo’s map”, the man’s name was applied to the thing, algorisms. Then by analogy with arithmatic this became algorithms.
    Khwarizmia was in Uzbekistan. The Uzbekistan–Afghanistan area was a major center of civilization both under Buddhism and under Islam. Avicenna and Fa-Tsang, arguably the greatest Muslim and Buddhist philosophers respectively, both came from there. As late as the post-Tamerlane period it was a center for original astronomy..

  2. Although the current meaning of algorithm has little to do with al-Khwarizm or doing arithmetic with arabic numerals.

  3. Perhaps Mr Hat would be kind enough to look up the current definition of “algorithm” in his copy of the OED? I can only get it second hand that they apparently refer to it as a “pseudo-eytymological perversion”.

  4. Actually the linked site has a very good entry on both “algorism” and “algorithm”. Leibniz was one of the first to use it in its modern sense (i.e. a systematic technique for solving a problem).
    Sorry for cluttering your comments section, Hat!

  5. What a marvellous site. I always wondered why a sine was called a sine, and I never would have guessed such a story.

  6. I like cluttered comment sections!

  7. And as for Khwarezm, it was the home of not only the great mathematician Muhammad ibn Musa al-Khwarizmi (note final -i: ‘the Khwarezmian’) but of the great scientist Abu’l Rayhan Muhammad ibn Ahmad al-Biruni, so it was quite the place to be from… unless Genghis Khan was in the neighborhood.

  8. This is what the OED has under the etymology of “algorism” (slightly modified for easier posting):
    a. OFr. augorisme, algorisme, augorime; ad. med.L. algorism-us (cf. Sp. guarismo cipher), f. Arab. al-Khowarazmi, the native of Khwarazm (Khiva), surname of the Arab mathematician Abu Ja’far Mohammed Ben Musa, who flourished early in the 9th c., and through the translation of whose work on Algebra, the Arabic numerals became generally known in Europe. (Cf. ‘Euclid’ = plane geometry.) Algorisme being popularly reduced in OFr. to augorime, English also shows two forms, the popular augrime, ending in agrim, agrum, and the learned algorism which passed through many pseudo-etymological perversions, including a recent algorithm in which it is learnedly confused with Gr. ‘number.’

  9. Thanks Grant. That was the quote I was looking for.

  10. I have been looking for why “sine” (in trigonometry)is so called and still don’t know. Why is it so called?

  11. How do you say 7 to the 7th Power?
    like example:
    like the second power is = squars
    and the third power is = cube
    so what is the the 7th power….? can some one be so kind to send me an email regarding this issue
    thank you…….

  12. This is what the OED has under the etymology of “algorism”

    They updated the entry in 2012, and this is the new etymology:

    Etymology: In sense 1 [“The Arabic (decimal) system of numbering (characterized by a zero, 0)”] < (i) Anglo-Norman algorism, (with vocalization of -l-) augorime, (with elision of unstressed medial vowel) augrim, augrime and Old French, Middle French algorisme, (with vocalization of -l-), augorisme, Middle French algorime method of calculation using Arabic numerals (early 13th cent.), arithmetic (c1400 or earlier),

    and its etymon (ii) post-classical Latin algorismus Arabic numerical notation (from 12th cent. in British sources; also in continental sources; also as augorismus (a1274, a1349 in British sources), algarismus (first half of the 15th cent. in British sources)), use as common noun of the personal name Algorismus, Algoarismus, Alghoarismus, Alchoarismus (all from 12th cent. in British and continental sources) < Arabic al-Ḵwārizmī (also al-Ḵwārazmī, al-Ḵuwārizmī, al-Ḵuwārazmī), surname of the mathematician Abū Jaʿfar Muḥammad b. Mūsā (fl. 800–47: see note below).

    In sense 2 [= algorithm] an alteration of algorithm n. (compare algorithm n. 2) after -ism suffix.

    Compare Spanish algorismo (a1425; a1276 as †alguarismo), Portuguese algarismo (16th cent.; also †algorismo), Italian †algorismo (end of the 13th cent.), and also Middle High German, early modern German algorismus, all denoting a type of arithmetic. Compare also Spanish guarismo cipher (probably early 17th cent. in this sense; earlier in senses ‘arithmetic’ (c1350) and ‘code, secret language’ (late 16th cent.); shortened < alguarismo). Compare later algorithm n. and the foreign-language parallels cited at that entry.
    Al-Ḵwārizmī’s Arabic surname, which literally means ‘the native of Khorezm’, is < Arabic al the + Ḵwārizm (also Ḵwārazm), the Arabic name of the town of Khorezm (now Khiva in Uzbekistan) + -i suffix2. He is best known for his treatise on algebra (see algebra n.), but also wrote a (now lost) work on the decimal numeral system, which was translated into Latin in several versions. A particularly influential version was John of Seville’s translation Liber Alghoarismi de practica arismetrice; a British version, attributed to Adelard of Bath, is entitled Liber Algorismi de numero Indorum; both of these date from the first half of the 12th cent. It was this latter work on the decimal numeral system, rather than the treatise on algebra, which introduced the Indo-Arabic numerals to Western European scholars.

  13. Jeff Miller’s site on Earliest Known Uses … (the original link) moved (in 2008) to here.

  14. I finally updated the post and changed the link to yours; thanks!

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