100. cant.
MANX.[332]
10. jeih.
20. feed.
30. yn jeih as feed = 10 + 20.
40. daeed = 2-20.
50. jeih as daeed = 10 + 40.
60. three-feed = 3-20.
70. three-feed as jeih = 60 + 10.
80. kiare-feed = 4-20.
100. keead.
1000. thousane, or jeih cheead.
BRETON.[333]
10. dec.
20. ueguend.
30. tregond = 3-10.
40. deu ueguend = 2-20.
50. hanter hand = half hundred.
60. tri ueguend = 3-20.
70. dec ha tri ueguend = 10 + 60.
80. piar ueguend = 4-20.
90. dec ha piar ueguend = 10 + 80.
100. cand.
120. hueh ueguend = 6-20.
140. seih ueguend = 7-20.
160. eih ueguend = 8-20.
180. nau ueguend = 9-20.
200. deu gand = 2-100.
240. deuzec ueguend = 12-20.
280. piarzec ueguend = 14-20.
300. tri hand, or pembzec ueguend.
400. piar hand = 4-100.
1000. mil.
These lists show that the native development of the Celtic number systems, originally showing a strong preference for the vigesimal method of progression, has been greatly modified by intercourse with Teutonic and Latin races. The higher numerals in all these languages, and in Irish many of the lower also, are seen at a glance to be decimal. Among the scales here given the Breton, the legitimate descendant of the ancient Gallic, is especially interesting; but here, just as in the other Celtic tongues, when we reach 1000, the familiar Latin term for that number appears in the various corruptions of _mille_, 1000, which was carried into the Celtic countries by missionary and military influences.
In connection with the Celtic language, mention must be made of the persistent vigesimal element which has held its place in French. The ancient Gauls, while adopting the language of their conquerors, so far modified the decimal system of Latin as to replace the natural _septante_, 70, _octante_, 80, _nonante_, 90, by _soixante-dix_, 60-10, _quatre-vingt_, 4-20, and _quatrevingt-dix_, 4-20-10. From 61 to 99 the French method of counting is wholly vigesimal, except for the presence of the one word _soixante_. In old French this element was still more p.r.o.nounced.
_Soixante_ had not yet appeared; and 60 and 70 were _treis vinz_, 3-20, and _treis vinz et dis_, 3-20 and 10 respectively. Also, 120 was _six vinz_, 6-20, 140 was _sept-vinz_, etc.[334] How far this method ever extended in the French language proper, it is, perhaps, impossible to say; but from the name of an almshouse, _les quinze-vingts_,[335] which formerly existed in Paris, and was designed as a home for 300 blind persons, and from the _pembzek-ueguent_, 15-20, of the Breton, which still survives, we may infer that it was far enough to make it the current system of common life.
Europe yields one other example of vigesimal counting, in the number system of the Basques. Like most of the Celtic scales, the Basque seems to become decimal above 100. It does not appear to be related to any other European system, but to be quite isolated philologically. The higher units, as _mila_, 1000, are probably borrowed, and not native. The tens in the Basque scale are:[336]
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. tikk.u.mga.s.sih = 20 2.
50. tikk.u.mga.s.sigokang = 20 2 + 10.
60. tikk.u.mgakro = 20 3.
70. dungokrogokang = 20 3 + 10.
80. duk.u.mgade = 20 4.
90. duk.u.mgadegokang = 20 4 + 10.
100. miah (borrowed from the Arabs).
IBO.[339]
10. iri.
20. ogu.