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 orvigesimal 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!—[…]
To go on by hands and feet to 20, and thence to reckon by twenties, is avigesimal 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.
The most remarkablevigesimal 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 iscanlahhutukal, literally fourteen and twenty.
1923, Melius de Villiers, “Aryan Numeral-words”, inThe Numeral-words: Their Origin, Meaning, History and Lesson, London: H. F. & G. Witherby, 326High Holborn, London, W.C.; Cape Town; Johannesburg; Port Elizabeth: Juta & Co.,→OCLC,page93:
With regard to the Danish numeral-words founded on thevigesimal 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;[…]
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,page 4:
If the years of the incomplete century be divided intotwenties, and the excess of twenties resolved intofours, the Dominical Letter will advancethree places for every twenty,two places for every four, andsix 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 thecenturial, thevigesimal, thequaternial, and theresidual.
[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 thevigesimals, arranged in regular order.
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 onvigesimals and duodecimals.
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 ofogún (twenty), or to be more exact, "multiple placing out," as the Yoruba verb embedded in the numeral has it. About thevigesimals, intermediate numerals are generated using tens and fives.
