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# Edward Brooks, The Philosophy of Arithmetic, 1876

Following are excerpts from The Philosophy of Arithmetic as developed from the Three Fundamental Processes of Synthesis, Analysis, and Comparison, by Edward Brooks, Ph.D., published in 1876.

The appendix repeats the "Chuquet" number-names seen in W. D. Henkle, Names of the Periods in Numeration, 1860.

These number-names have long since been supplanted by the Conway-Wechsler system, see full list of individual "zillions".

Dmitri A. Borgmann, Naming the Numbers, 1968.

John Candelaria, Extending the Number Names, 1975.

(From Section II, "Arithmetical Language", Chapter 1, "Numeration, or the Naming of Numbers.")

In a similar manner we name the numbers from one hundred to the next group, consisting of ten hundreds, to which we assign a new name, calling it thousand. After reaching the thousand, a change occurs in the method of grouping. Previously, ten of the old groups made one of the next higher group, but after the third group, or thousands, it requires a thusand of an old group to form a new group, which receives anew name. A thousand thousands forms the next group after thousands which we call million from the Latin mille, a thousand. In the same manner, one thousand millions gives a new group which we call billion, one thousand billions a new group we call trillion, etc.

[...]

In closing this chapter, we remark that the names of the periods above ducentillions have not been fully settled by usage. Prof. Henkle, who has examined the subject with considerable care, finds a law which he maintains should hold in the formation of the names of the higher periods. The terms quintillions, sextillions, and nonillions are formed, not from the cardinals, quinque, sex, and novem, but from the ordinals, quintus, sextus, and nonus. From this he infers that analogy plainly demands that the names beyond duodecillions should be formed from the Latin ordinal numerals. For the names thus formed, see appendix.

APPENDIX

HENKLE'S NAMES OF PERIODS.

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), 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), Septo-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), Quingestesimo-millillions (1500), Sexcentesimo-millillions (1600), Septingentesimo-millillions (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), Quatuoideci-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), Quadri-vici-millillions (24,000), Quniqui-vici-millillions (25,000), Sexi-vici-millillions (26,000), Septi-vici-millillions (27,000), Octi-vici-millillions (28,000), Novi-vici-millillions (29,000), 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), Discenti-millillions (200,000), Trecenti-millillions (300,000), Quadringenti-millillions (400,000), Quingenti-millillions (500,000), Sexcenti-millillions (600,000), Septingenti-millillions (700,000), Octingenti-millillions (800,000, Nongenti-millillions (900,000), Milli-millillions (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 in 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.

List of changes, as compared to the 1860 version:

• "Septo-decillions (17)" is missing from this version.
• "Septi-vigillions" (period 27) changed to "Septo-vigillions"
• "Quniqui-vici-millillions" through "Novi-vici-millillions" (periods 25,000 through 29,000) added
• "Quodri-vici-millillions" (period 24,000) changed to "Quadri-"