W. D. Henkle, Names of the Periods in Numeration, 1860  

Following is the article Names of the Periods in Numeration from pages 151-153 of The Ohio Educational Monthly, vol. 9 published in 1860. The author is most probably William Downs Henkle, from Ohio and born in 1828.

The portion quoted here concerns the "Chuquet" number-names.

This article refers to:

Nicolas Pike, A New and Complete System of Arithmetick, 1822.

Benjamin Greenleaf, National Arithmetic, 1835.

Noble Heath, A Treatise on Arithmetic, 1856.

Alfred Holbrook, The Normal or Methods of Teaching, 1859.

Silas L. Loomis, Normal Arithmetic, 1859.

This article is referenced by:

Edward Brooks, The Philosophy of Arithmetic, 1876. (The reprinting of Henkle's list includes several corrections, some additions, and a single deletion)

Rudolf Ondrejka, Renaming the Numbers, 1968.

Note that several typos are corrected in an erratum printed the following month, here shown on "page 184". The location of each error is marked with a dagger (†) in the original text.

— [page 129] —




MAY, 1860.

— [page 151] —

Mathematical Department.



  I propose in this article to point out a mistake which has been fallen into by a few writers on Arithmetic in reference to the names of the periods beyond duo-decillions, and also to suggest a new set of names for these periods.

In order that the mistake above referred to may be clearly seen, I append the names usually given: Millions, Billions, Trillions, Quadrillions, Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, and Duodecillions. These names seem to be well established by general usage. The only departure that I have seen from these names, is the single instance of Quatrillions, given by Pike in his octavo Arithmetic, and this is only another spelling of Quadrillions. Taking, then, these words as established, we should name the other periods in an analagous manner. Pike and Greenleaf writes Tredecillions, Quatuordecillions, Quindecillions, Sexdecillions, Septendecillions, Octodecillions, Novemdecillions, and Vigintillions. S. L. Loomis, in his Normal Arithmetic, gives the same, writing Tridecillions and Septemdecillions, and adding Unvigintillions, Duoviginlillions, Trigintillions, Quatuorgintillions, Quingintillions, Sexgintillions, Septemgintillions, Octogintillions, and Novemgintillions. Heath's Arithmetic, and Ray's Higher Arithmetic, follow Pike and Greenleaf, except in the word Novemdecillions, in which n is used instead of m. Heath adds Viginti-unillions, Viginti-billions, Viginti-trillions; Trigintillions, Triginta-unillions, Triginta-billions; Quadragentillions, Quadraginta-unillions; Quinquagentillions; Sexagentillions; Septu†gentillions; Octogentillions; Nonagentillions, and Centillions.

Thomson writes "Tredecillions," and Tracy "Tridicillions." Holbrook, in his Normal, gives Tridecillions, Quadrodecillions, Quindecillions, Sexdecillions, †

†There were errors here, as outlined on "page 184" below:

"Septugentillions" should be Septuagentillions

"Sexdecillions" should be followed by Septodecillions

— [page 152] —

Octodecillions, Nonodecillions, Vi†gintillions, Unvi†gintillions, Duo-vi†gintillions, Trigintillions, Quadrogintillions, Quingintiilions, Sexagintillions, Septangintillions, Octogintillions, Nonogintillions, Centillions, Uncentillions, Duocentillions, and Millillions.

These are the only instances which I have found in consulting about fifty Arithmetics, in which the names of periods above Duodecillions are given. I object to these names† which the reader will observe are not uniform, because they are formed on the names of the Latin cardinal numbers, and not upon the names of the ordinal numbers. Analogy, derived from the formation of the names up to Duodecillions, plainly demands the use of the ordinal numbers. From Millions to Quadrillions inclusive, there is no analogy. Quintillions, Sextillions and Nonillions, are plainly formed, not from quinque, sex and novem, but from quintus, sextus and nonus. This being the case, we are authorized in considering Septillions, Octillions, Decillions, Undecillions and Duodecillions, as formed from setimus, octavus, decimus, undecimus, and duodecimus, by striking off imus and avus and adding illions.

I give below the names commencing with millions, which is the base of the English system of numeration. The names of the periods after millions denote the respective powers of a million. For the benefit of those readers that are not familiar with the Latin ordinal numbers, I insert, in a parenthesis, afler each name, Arabic numerals denoting the ordinal numbers used in forming the name. The value of one of the period is a million raised to a power denoted by the ordinal number.


  Millions (1), Billions (2), Trillions (3), Quadrillions (4), Quintillions (5), Sextillions (6), Septillions (7), Octillions (8), Nonillions (9), Decillions (10), Undecillions (11), Duodecillions (12), Tertio-decillions (13), Quarto-decillions (14), Quinto-decillions (15), Sexto-decillions (16), Septo-decillions (17), Octo-decillions (18), Nono-decillions (19), Vigillions (20), Primo-vigillions (21), Secundo-vigillions (22), Tertio-vigillions (23), Quarto-vigillions (24), Quinto-vigillions (25), Sexto-vigillions (26), Septi†-vigillions (27), Octo-vigillions (28), Nono-vigillions (29), Trigillions (30).

Quadragillions (40), Quinquagillions (50), Sexagillions (60), Septuagillions (70), Octogillions (80), Nonagillions (90), Centillions (100), Primo-Centillions (101), Decimo-centillions (110), Undecimo-centillions (111), Duodecimo-centillions (112), Tertio-decimo-centillions (113), Quarto-decimo-centillions (114), Vigesimo-Centillions (120).

Primo-vigesimo-centillions (121), Trigesimo-Centillions (130), Quadragesimo-centillions (140), Quinquagesimo-centillions (150), Sexagesimo-centillions (160), Septuagesimo-centillions (170), Octogesimo-centillions (180), Nonagesimo-centillions (190), Ducentillions (200), Trecentillions (300), Quadringentillions (400), Quingentillions (500), Sexcentillions (600), Septingentillions (700), Octingentillions (800), Nongentillions (900).

Millillions (1000), Centesimo-millillions (1100), Ducentesimo-millillions (1200), Trecentesimo-millillions (1300), Quadringentesimo-millillions (14OO), Quinges†tesimo-millillions (1500), Sexcentesimo-millillions (1600), Septingentesimo-mill-

†There were errors here, as outlined on "page 184" below:

"Vigintillions" should be Vingintillions

"Unvigintillions" should be Unvingintillions

"Duo-vigintillions" should be Duo-vingintillions

Add a comma after "I object to these names"

"Septi†-vigillions" should be Septo-vigillions

"Quingestesimo-millillions" should be Quingentesimo-millillions

— [page 153] —

illions (1700), Octingentesimo-millillions (1800), Nongentesimo-millillions (1900), Bi-millillions (2000), Tri-millillions (3000), Quadri-millillions (4000), Quinqui-millillions (5000), Sexi-millillions (6000), Septi-millillions (7000), Octi-millillions (8000), Novi-millillions (9000), Deci-millillions (1O,000), Undeci-millillions (11,000).

Duodeci-millillions (12,000), Tredeci-millillions (13,000), Quatuoi†deci-millillions (14,000), Quindeci-millillions (15,000), Sexdeci-millillions (16,000), Septi-deci-millillions (17,000), Octi-deci-millillions (18,000), Novi-deci-millillions (19,000), Vici-millillions (20,000), Semeli-vici-millillions (21,000), Bi-vici-millillions (22,000), Tri-vici-millillions (23,000), Quo†dri-vici-millillions (24,000), Trici-millillions (30,000), Quadragi-millillions (40,000), Quinquagi-millillions (50,000).

Sexagi-millillions (60,000), Septuagi-millillions (70,000), Octogi-millillions (80,000), Nonagi-millillions (90,000), Centi-millillions (100,000), Semeli-centi-millillions (101,000), Bi-centi-millillions (102,000), Dis†centi-millillions (200,000).

Trecenti-millillions (300,000), Quadri†genti-millillions (400,000), Quingenti-millillions (500,000), Sexcenti-millillions (600,000), Septingenti-millillions (700,000), Octingenti-millillions (800,000), Nongenti-millillions (900,000), Milli-mill†ions (1,000,000).

It will be observed that words ending in o represent numbers to be added, and those ending in i represent multipliers. When two words end with i, the sum of the numbers indicated is to be taken as the multiplier. In each the last word indicates the number to be increased or multiplied.

It is desirable that writers of Arithmetic should adopt these names when they pretend to give those above duodecillions, and that teachers should use them when exercising their pupils in reading very large numbers. The highest number of figures ever encountered by any mathematician in his investigations is 618†. The reading of such a number demands the names of the periods to primo-centillions in the English method, and primo-ducentillions in the French.

†There were errors here, as outlined on "page 184" below:

"Quatuoideci-millillions" should be Quatuordeci-millillions

"Quodri-vici-millillions" should be Quadri-vici-millillions

"Discenti-millillions" should be Ducenti-millillions

"Quadrigenti-millillions" should be Quadringenti-millillions

"Milli-millions" should be Milli-millillions

"618" should be 607

— [page 162] —




JUNE, 1860.

— [page 184] —

ERRATA. — In our article in May number, the following typographical mistakes should be corrected: Last line of the second paragraph, insert in the first word a before the g, and Septodecillions after the last word on p. 151. Insert n before g in the last three words of the first line on p.152. Insert a comma after "names," line 7, p. 152. In names of periods, change i to o in name before (27), s to n in (1500), i to r in (14,000), o to a in (24,000), is to u in (200,000); insert n before g in (400,000), and change "milli-millions" to "milli-millillions. Also 618 to 607.

Communications for this department should be addressed to W. D. Henkle, Lebanon, Ohio.


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