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

12

INTRODTUCTION.

"Why do all men, barbariarns as well as Greeks, numerate up to
'ten, and not to any other number, as two, three, four, or five,1 and then
repeating one and five, two and five, as they do one and ten, two and
ten, not counting beyond the tens, from which they again begin to.repeat? For each of the numbers which precedes is one or two, and
then some other, but they enumerate however, still making the
number ten their limit. For they manifestly do it not by chance, but.always. The truth is, what men do upon all occasions and always,
-they do not from chance, but from some law of nature. Whether is
it, because ten is a perfect number? For it contains all the species of
Number, the even, the odd, the square, the cube, the linear, the
plane, the prime, the composite. Or is because the number ten is a
principle? For the numbers one, two, three, and four when added
-together produce the number ten. Or is it because the bodies which
are in constant motion, are nine? Or is it because of ten numbers in
continued proportion, four cubic numbers2 are consummated, out of
which numbers the Pythagoreanss say that the universe is constituted?
-Or is it because all men from the first have ten fingers? As therefore
men have counters of number their own by nature, by this set, they
numerate all other things."
Besides the idea of the division of numbers by tens, the names of
the first ten numbers as they have descended to modern times are
suggestive of questions for consideration to the student. The following list contains the names of the first ten numbers as preserved in
seventeen languages, some of them being no longer spoken:1. Hebrew: echad, shnayim, shlosha, arbaa, khamisha, shisha, shiva, slimona,
tisha, asara.
2. Arabic: wahad, ethnan, thalathat, arbaat, khamsat, sittat, sabaat, thamaniat,
tessaat, aasherat.
3. Syriac: chad, treyn, tlotho, arbo, chamisho, shitho, shavo, tmonyo, tesho,
cesro.
4. Persian: yak, du, sih, chahar, panj, shash, haft, hasht, nuh, dab.
5. Sanscrit: eka, dwi, tri, chatur, panchan, shash, saptan, ashtan, novan, dasan.
6. Greek: e's, Vo, rpets, refaapes, 7rerTe, E, eTrr, oKTa, evea, seca.
7. Latin: unus, duo, tres, quatuor, quinque, sex, septem, octo, novem, decem.
8. Italian: un, due, tre, quattro, cinque, sei, sette, otto, nove, dieci.
9. Spanish: uno, dos, tres, quatio, cenco, seis, siete, ocho, nueve, diez.
10. French: un, deux, trois, quatre, cinq, six, sept, huit, neuf, dix.
11. Welsh: un, dau, tri, pedwar, pump, chwech, saith, wyth, naw, deg.
I This refers to the quinary scale of notation, instances of which are found in
Homer, Odys. iv. 412; in AEschylus, Eumen. 738, and in other Greek writers.
2 In Euc. viii. 10, it is demonstrated that if, beginning with unity, ten numbers
are formed in continued proportion, four of these numbers will be cubic numbers.
3 The Pythagorean philosophers indulged in fancies the most absurd, in the
extraordinary powers they attributed to numbers; and among other absurdities they
maintained that, of two combatants in the Games, the victor would be that man the
letters of whose name, numerically estimated, expressed the greater number. In
later times they were fond of forming words so that the numeral value of the letters
-should be equal to the same number, and there is an instance in the Greek Anthology
(vol. ii., p. 412, Jacobs) in which a poet has applied the idea to describe a pestilent
fellow. Having observed that the letters of his name Aaya-1ypas (mob orator) and
Aoe/Lbs (pestilence) denoted, in the Greek notation, the same number, the following,epigram declares, that when weighed in the balance, the latter was found to be the
Jlighter.
Aaeuaaypav Kalc doiuvv lGo7pqbv rTs a'Kov'oas
'Eor-~r' -&o-aiOTEp' s-bv rpTov CK Kavc'os.
'Ets Tsb lAepos 8e KaiOeIAKET' &aveXKvaOE Vb TA adrVov
Aactay4dpov, Aouby d' eVpeP ZA-pdTrspoV.