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A system of numeration was thus established which may be looked at from a double point of view; in the first place from its sexagesimal base, which certainly adapts itself to various requirements with greater ease than any other; in the second from the extreme facility with which not only addition, but all kinds of complex calculations may be made by its use.
It will be seen that on the twelve parallel wires there are 144 balls, alternately black and white. By these the elements of arithmetic may be taught as follows: Numeration.
As a basis for the notion of a whole made up of equal parts, nothing so readily suggests itself as the hand with its five, or the hands with their ten, fingers; upon this rests the decimal system. We have already observed that these elements of all numeration and measuring reach back not merely beyond the separation of the Greek and Latin stocks, but even to the most remote primeval times.
We can discover no reason why the number ten should be chosen rather than any other for the term of numeration, except this primitive practice of counting by the fingers." The whole of his observations on this subject are well worthy of minute consideration. On such elements, the provision of nature, are founded the most sublime and important sciences.
Blessed they who, like this little maiden, are awakened, not only by His voice, but by His touch, and to find, as she did, their hand in His! The third of these miracles, which Matthew seems to reckon as the second in the group, because he treats the two former as so closely connected as to be but one in numeration, need not detain us long. It is found only in this Gospel.
And here it should be remarked that in this recombination of the notion of equality with that of multiplicity, by which the first steps in numeration are effected, we may see one of the earliest of those inosculations between the diverging branches of science, which are afterwards of perpetual occurrence.
I am far from placing the languages of the New World in the same rank with the finest languages of Asia and Europe; but no one of these latter has a more neat, regular, and simple system of numeration, than the Quichua and the Aztec, which were spoken in the great empires of Cuzco and Anahuac.
I shall always think the better of Cadell for this, not merely because his feet are beautiful on the mountains who brings good tidings, but because he showed feeling deep feeling, poor fellow he who I thought had no more than his numeration table, and who, if he had had his whole counting-house full of sensibility, had yet his wife and children to bestow it upon I will not forget this if I get through.
In vases of agate were heaped diamonds beyond numeration, the smallest of which was larger than a pigeon's egg. On alabaster tables lay amethysts, topazes, rubies, beryls, and all other precious stones, wrought by the hands of skilful artists, beyond power of computation.
I do not particularize further, because I know that good teachers will at once see the principle aimed at, and supply the other requisite lessons: the object of this book being rather to shew the principle of the thing, than to go into detail. The arithmeticon How applied Numeration Addition Subtraction Multiplication Division Fraction Arithmetical tables Arithmetical Songs Observations.
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