Elementary arithmetic, with brief notices of its history... by Robert Potts.

INTRODTUCTIOF.

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12. Gaelic: aou, da, tri, ceithar, koig, sia, seachd, ochd, nai, deich.
13. Erse: aen, da, tri, keathair, kuig, se, secht, ocht, noi, deich.
14. lceso-Gothic: ains, twai, thrins, fidwor, fimf, saihs, sibun, ahtan, nihun,
taihun.
15. High German: ein, tue, thri, fiuuar, finfe, sehs, sibun, ohto, niguni, tehan.
16. Anglo-Saxon: an, twa, threo, feower, fif, six, seofon, eahta, nigon, tyn.
17. English: one, two, three, four, five, six, seven, eight, nine, ten.
On examining and comparing these names of the first ten
numerals, it will be apparent that in some there is a complete or
partial identity, and in others a diversity with more or less resemblance.1 The use of the same or somewhat similar sounds to
express the same ideas by the successive generations of men, suggests
the high probability that they had a common origin, while the diversities are such as might avise from some confusion at a very remote
period in the original language. The resemblances and diversities
i The close relation of the English names of the first ten numbers with those of
the Anglo-Saxon, High German, and Mceso-Gothic is obvious. With respect to the
names of numbers greater than ten, it may be remarked that the word eleven, AngloSaxon, endlufon, signifies leave one (that is above ten) being derived from ein, one,,
and the old verb liben, to remain. The word twelve is of like derivation, and means.
lecave two.
The words thirteen, fourteen, &c., to nineteen, are formed from-three and ten,
four and ten, &c.
The word twenty is derived from the High German twentig, bis decem, or fron
the more distant Mceso-Gothic twcaintegumn. In the same way are formed thirty,
forty, &c., to ninety.
Hundred is a form of the Low German hunmdert, and is related to the High German and Anglo-Saxon hund.
Thousand: Anglo-Saxon, thn6send, German, tauesend, from the wceso-Gothic, tigos
hlnzad, or tailthns hund, ten times a hundred.
Million comes from the Italian gnillione. The introduction into Italy of the
Indian figures brought in a knowledge of numbers which neither the Latin nor the
Italian language had names to express. This circumstance rendered some additions
to the names of number necessary. The word 'millione has its origin in the Latin mille,
and by the analogy of the Italian language the word millione means a great thousand,
or, in a numerical sense, a thousand thousands. The units of the higher orders,
billione, trillione, &c., are obviously formed from the word millione, with the Latin;
his, tris, &c., prefixed, and thus forming a series of numerical words, of which each
succeeding term is a million times that which immediately precedes it.
The numerical language of the Italians proceeding by thomuscends and by millions
led to the custom of dividing numbers into periods of three figures and of six figures,
and this mode of numeration being adapted to most of the languages of Europe, came
into universal use with the terms million, billion, &c., borrowed from the Italian.
Bp. Tonstall in his work " De Arte supputandi," published in 1522, speaks of the
word million as a word in common use, and Dr. Robert Recorde, in his " Grounde
of Artes," published in 1542, employs the word without any further remark than
explaining its meaning, and dividing numbers into periods of three figures. The
French system of numeration dillbrs from the English by making the billion equal to
a thousand millions, a trillion, a thousand billions, and so on.
The name cipher (rTipa) is borrowed from the Arabic tsqalecarc,, which means
blank or void, and is identical with the Sanscrit word sunyac. In the Sanscrit
notation the cipher was denoted by a point or by a small circle, which latter itf.appears from Planudes was preferred. The word cipher (Italian zifra, French chilfre)
has several equivalents in use, as nothing, noyght, zero. It was written zefro by
the Spanish Moors, and might easily be changed into zerro or zero, at the time
when the notation was translated from the Arabic by Spanish 3Moors and Jewish
merchants.
The word cipher, from its importance in the system, has received a more extended
meaning than its original sense. All the nine digits have been subjected to tho
general name of ciphers, from which the verb to cipher has been formed, having the
same sense as to calculate with these figures.