vigesimal

adj

1. (not-comparable)Occurring in intervals of twenty.

   “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. (not-comparable)To the base twenty.

   “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.”

   “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.”

   “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; […]”

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

noun

1. A twentieth part.

   “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.”

   “[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.”

   “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.”

   “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.”

2. “vigesimal”, in Merriam-Webster.com Online Dictionary, Springfield, Mass.: Merriam-Webster, 1996–present.
3. “vigesimal”, in OED Online ⁠, Oxford: Oxford University Press, launched 2000.
4. “vigesimal”, in The American Heritage Dictionary of the English Language, 5th edition, Boston, Mass.: Houghton Mifflin Harcourt, 2016, →ISBN.