five, is a notation by fives, or as it is called, a quinary nota- tion. To count by the use of both hands to 10, and thence to reckon by tens, is a decimal notation. To go on by hands and feet to 20, and thence to reckon by twenties, is a vigesimal notation. Now though in the larger proportion of known languages, no distinct mention of fingers and toes, hands and feet, is observable in the numerals themselves, yet the very schemes of quinary, decimal, and vigesimal no- tation remain to vouch for such hand-and-foot-counting having been the original method on which they were founded. There seems no doubt that the number of the fingers led to the adoption of the not especially suitable number 10 as a period in reckoning, so that decimal arithmetic is based on human anatomy. This is so obvious, that it is curious to see Ovid in his well-known lines putting the two facts close together, without seeing that the second was the consequence of the first.
'Annus erat, decimum cum luna receperat orbem. Hic numerus magno tunc in honore fuit. Seu quia tot digiti, per quos numerare solemus: Seu quia bis quino femina mense parit: Seu quod adusque decem numero crescente venitur, Principium spatiis sumitur inde novis.'[1]
In surveying the languages of the world at large, it is found that among tribes or nations far enough advanced in i arithmetic to count up to five in words, there prevails, with scarcely an exception, a method founded on hand-counting, quinary, decimal, vigesimal, or combined of these. For perfect examples of the quinary method, we may take a Polynesian series which runs 1, 2, 3, 4, 5, 5⋅1, 5⋅2, &c.; or a Melanesian series which may be rendered as 1, 2, 3, 4, 5, 2nd 1, 2nd 2, &c. Quinary leading into decimal is well shown in the Fellata series 1 ... 5, 5⋅1 ... 10, 10⋅1 ... 10⋅5, 10⋅5⋅1 ... 20, ... 30, ... 40, &c. Pure decimal may be instanced from Hebrew 1, 2 ... 10, 10⋅1 ... 20, 20⋅1 ... &c. Pure vigesimal is not usual, for the obvious
1 Ovid, Fast. iii. 121.
- ↑ 1
