vigesimal

Maya numerals from 0 to 19. The Mayan number system is vigesimal (base 20).

From Latin vīcēsimus (“twentieth”) (from *vīcēnssos, from Proto-Indo-European *wi(h₁)ḱm̥ttós, with the -imus ending of decimus (“tenth”)) +‎ -al (“suffix forming an adjective”). Compare Latin vīgintī (“twenty”), from Proto-Indo-European *h₁wih₁ḱm̥ti, from *dwi(h₁)dḱm̥ti(h₁), *dwi(h₁)dḱm̥ti (“two tens; two decades”).

• (Received Pronunciation, General American) IPA^(key): /vɪˈdʒɛsɪm(ə)l/, /vaɪ-/, /-sə-/
• Hyphenation: vi‧ge‧sim‧al

vigesimal (not comparable)

1. Occurring in intervals of twenty. [from mid-17th c.]
   • 1899, Thomas Carlyle, “On History Again”, in Critical and Miscellaneous Essays: In Five Volumes, volume III, London: Chapman and Hall Limited, OCLC 855624082, page 172:

     For indeed, looking at the activity of the historic Pen and Press through this last half-century, and what bulk of History it yields for that period alone, and how it is henceforth like to increase in decimal or vigesimal geometric progression,—one might feel as if a day were not distant, when perceiving that the whole Earth would not now contain those writings of what was done in the Earth, the human memory must needs sink confounded, and cease remembering!— […]

2. (arithmetic) To the base twenty. [from mid-17th c.]
   • 1871, Edward B[urnett] Tylor, “The Art of Counting”, in Primitive Culture: Researches into the Development of Mythology, Philosophy, Religion, Art, and Custom. [...] In Two Volumes, volume I, London: John Murray, Albemarle Street, OCLC 913570572, page 236:

     To go on by hands and feet to 20, and thence to reckon by twenties, is a vigesimal notation. Now though in the larger proportion of known languages, no distinct mention of fingers and toes, hands and feet, is observable in the numerals themselves, yet the very schemes of quinary, decimal and vigesimal notation remain to vouch for such hand-and-foot counting having been the original method on which they were founded.

   • 1875, James A[llanson] Picton, “On the Origin and History of the Numerals”, in Proceedings of the Literary and Philosophical Society of Liverpool, volume XXIX, London: Longmans, Green, Reader, & Dyer; Liverpool: D. Marples & Co. Limited, Lord Street, OCLC 873143475, page 87:

     The most remarkable vigesimal scale of numeration is that of the Mexicans. The decimal scale is adopted as far as twenty; that is to say, after ten the primitive digits are repeated, but from twenty onwards the numbers are taken by twenties. Thus 34 is canlahhutukal, literally fourteen and twenty.

   • 1923, Melius de Villiers, “Aryan Numeral-words”, in The Numeral-words: Their Origin, Meaning, History and Lesson, London: H. F. & G. Witherby, 326 High Holborn, London, W.C.; Cape Town; Johannesburg; Port Elizabeth: Juta & Co., OCLC 558087525, page 93:

     With regard to the Danish numeral-words founded on the vigesimal system of numeration, it must be admitted that here the explanation fails which has been given for the divergence of the forms representing 70, 80 and 90 from the forms representing the lower numerals of 10 in the case of some other languages, since in the present case the forms for 50 and 60 also depart from the decimal system; […]

   • 1970, Petr Beckmann, “The Belt”, in A History of π (Pi), Boulder, Colo.: The Golem Press, →ISBN; republished New York, N.Y.: St. Martin's Press, 1971, →ISBN, page 34:

     [I]t is not known whether they [the Maya] progressed beyond a "vigesimal point" to negative powers of 20, i.e. to vigesimal fractions.

• vicesimal

• vigesimally
• vigesimation

vigesimal (plural vigesimals)

1. A twentieth part.
   • 1872, Frederick A[ugustus] P[orter] Barnard, How to Find the Church Festivals without Tables; Being a Letter Addressed to the Chairman of the Committee of the Prayer Book in the House of Clerical and Lay Deputies of the General Convention of the Church, in 1871, Hartford, Conn.: The Church Press; M. H. Mallory and Company, OCLC 33247189, page 4:

     If the years of the incomplete century be divided into twenties, and the excess of twenties resolved into fours, the Dominical Letter will advance three places for every twenty, two places for every four, and six places for every unit of the still outstanding remainder. Hence the Sunday Letter will be found by taking the sum of four numbers, which may be called the centurial, the vigesimal, the quaternial, and the residual.

   • 1876, F[rederick] A[ugustus] P[orter] Barnard, “Easter”, in Frederick A. P. Barnard and Arnold Guyot, editors, Johnson’s New Universal Cyclopædia: A Scientific and Popular Treasury of Useful Knowledge. [...], volume I (A–E), New York, N.Y.: A[lvin] J[ewett] Johnson & Son, 11 Great Jones Street, New York; Pittsburg, Pa.: W. D. Cummings; San Francisco, Calif.: H. D. Watson, OCLC 6846720, page 1463, columns 1–2:

     [column 1] The author of this article has also designed an instrumental contrivance for finding Easter by inspection, for any year from the beginning of the Christian era down to the end of hundredth century, in old style or new. […] [column 2] Around the fixed ring here described is a rotary ring bearing the numbers from 1 to 19 (the golden numbers) twice repeated, and at the left of these the vigesimals, arranged in regular order.

   • 2009, Richard A. Goldthwaite, “The Network”, in The Economy of Renaissance Florence, Baltimore, Md.: Johns Hopkins University Press, →ISBN, page 83:

     They had all attended an abacus school (scuola d'abaco), where the basic training program, well known from the numerous practical treatises on the subject that survive, had taught them above all how to deal in different moneys and to make the four basic arithmetic calculations, using what for them was the standard mensural system based on vigesimals and duodecimals.

   • 2010, Helen Verran, “Yorub and English Number Systems”, in Science and an African Logic, Chicago, Ill.: University of Chicago Press, →ISBN, page 55:

     The Yoruba series of number names generates primarily around a base of twenty. […] The core process in the working of the system is progression from one vigesimal (twenty) point to the next. Multiplication generates multiples of ogún (twenty), or to be more exact, "multiple placing out," as the Yoruba verb embedded in the numeral has it. About the vigesimals, intermediate numerals are generated using tens and fives.

• vigesimal on Wikipedia.Wikipedia