History of the New World Called America (Volume 2); Book II. Aboriginal America (Continued) (Paperback)

This historic book may have numerous typos, missing text or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1899. Not illustrated. Excerpt: ... when the collective unit comes to be multiplied by itself, Book II. or 'squared, ' would it be necessary to choose between Aboriginal them. Amerua. Up to this point the denary and vicenary systems are Relative equally convenient, the numbers below the collective unit e tewo being easily added to or used as multipliers for it, as may systemsbe required. When, however, the two systems are compared with reference to the facilities afforded by each for expressing numbers higher than the collective unit multiplied by itself, and for constituting a progressive scale of compound terms by the continuous multiplication of the product thus obtained, the inconvenience of the vicenary system is manifest. The multiples increase too rapidly. It has as its first compound term, instead of the useful 100, the rarely required number 400, and as its second, instead of i.coo, the number 8,000, which is so seldom reached in the reckonings of common life that the mind scarcely attaches to it any definite idea; and here its supply of multiples practically ends. A vicenary arithmetic, though more favourable to mental advancement in a low stage because exercising the imagination in a higher degree, is less favourable to notation by compound terms than the system of multiplication by 10 in successive stages (100, 1,000, io, oco, and so forth); and while it might be expected to prevail rather than a denary arithmetic at a certain stage of culture, there must be a tendency to abandon it for the latter as advancement proceeds. It recalls the cycle passed through by objective gender, which is unknown in the lowest stages of language, and has a prominent place as advancement proceeds in the languages of certain peoples whose circumstances suggest it 1, but is either reduced to its lowest terms, ...