The Number Concept eBook

Levi L. Conant
This eBook from the Gutenberg Project consists of approximately 185 pages of information about The Number Concept.

The Number Concept eBook

Levi L. Conant
This eBook from the Gutenberg Project consists of approximately 185 pages of information about The Number Concept.

    10. hamar.
    20. hogei.
    30. hogei eta hamar = 20 + 10.
    40. berrogei = 2-20.
    50. berrogei eta hamar = 2-20 + 10.
    60. hirurogei = 3-20.
    70. hirurogei eta hamar = 3-20 + 10.
    80. laurogei = 4-20.
    90. laurogei eta hamar = 4-20 + 10.
   100. ehun.
  1000. milla.

Besides these we find two or three numeral scales in Europe which contain distinct traces of vigesimal counting, though the scales are, as a whole, decidedly decimal.  The Danish, one of the essentially Germanic languages, contains the following numerals: 

    30. tredive = 3-10.
    40. fyrretyve = 4-10.
    50. halvtredsindstyve = half (of 20) from 3-20.
    60. tresindstyve = 3-20.
    70. halvfierdsindstyve = half from 4-20.
    80. fiirsindstyve = 4-20.
    90. halvfemsindstyve = half from 5-20.
   100. hundrede.

Germanic number systems are, as a rule, pure decimal systems; and the Danish exception is quite remarkable.  We have, to be sure, such expressions in English as three score, four score, etc., and the Swedish, Icelandic, and other languages of this group have similar terms.  Still, these are not pure numerals, but auxiliary words rather, which belong to the same category as pair, dozen, dizaine, etc., while the Danish words just given are the ordinary numerals which form a part of the every-day vocabulary of that language.  The method by which this scale expresses 50, 70, and 90 is especially noticeable.  It will be met with again, and further examples of its occurrence given.

In Albania there exists one single fragment of vigesimal numeration, which is probably an accidental compound rather than the remnant of a former vigesimal number system.  With this single exception the Albanian scale is of regular decimal formation.  A few of the numerals are given for the sake of comparison:[337]

30. tridgiete = 3-10. 40. dizet = 2-20. 50. pesedgiete = 5-10. 60. giastedgiete = 6-10, etc.

Among the almost countless dialects of Africa we find a comparatively small number of vigesimal number systems.  The powers of the negro tribes are not strongly developed in counting, and wherever their numeral scales have been taken down by explorers they have almost always been found to be decimal or quinary-decimal.  The small number I have been able to collect are here given.  They are somewhat fragmentary, but are as complete as it was possible to make them.

  AFFADEH.[338]

    10. dekang.
    20. degumm.
    30. piaske.
    40. tikkumgassih = 20 x 2.
    50. tikkumgassigokang = 20 x 2 + 10.
    60. tikkumgakro = 20 x 3.
    70. dungokrogokang = 20 x 3 + 10.
    80. dukumgade = 20 x 4.
    90. dukumgadegokang = 20 x 4 + 10.
   100. miah (borrowed from the Arabs).

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The Number Concept from Project Gutenberg. Public domain.