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1. the following preliminary observations, I have repeated much of what may be found in my work, entitled, but it is so much enlarged, and I hope improved, by additional evidence in its support, that I have found it impossible to avoid the repetition to do justice to my subject. Therefore I hope it will be excused: more particularly as I consider that the removal of all doubt respecting the antiquity of the 16 or Cadmean letter system is necessary, several very important consequences being drawn from it, which have an intimate relation to the doctrines developed in the following work.

2. In an inquiry into the origin of nations, or into the early history of mankind, one of the very first objects which offers itself to our attention is the invention of letters and numbers. Of this we have no actual information to which the least attention can be paid; for I suppose no one listens to such stories as those of their invention by Hermes or Mercury in Egypt, or Hercules in Gaul; it is therefore evident that to theory, and to theory alone, we must have recourse for the solution of the difficulty. A bare probability is the utmost at which we can ever expect to arrive in the investigation of this very interesting subject.

3. There is no likelihood that man would be endowed with these sciences at his creation; therefore it follows as a matter of course, that we must suppose the knowledge of them to have been the result of his own ingenuity, and of the gradual development of his faculties. This being admitted, it surely becomes a matter of great curiosity to ascertain the probable line of conduct, and the gradual steps which he would pursue for their acquisition.

4. After he had arrived at the art of speaking with a tolerable degree of ease and fluency, without being conscious that he was reasoning about it, he would probably begin to turn his thoughts to a mode of recording or perpetuating some few of the observations which he would make on surrounding objects, for the want of which he would find himself put to inconvenience. This I think was the origin of Arithmetic. He would probably very early make an attempt to count a few of the things around him, which interested him the most, perhaps his children; and his ten fingers would be his first reckoners; and thus by them he would be led to the decimal instead of the more useful octagonal calculation which he might have adopted; that is, stopping at 8 instead of 10. Thus, 8 + 1, 8 + 2, 8 + 3, instead of 10 + 1 or 11; 10 + 2 or 12; 10 + 3 or 13. There is nothing natural in the decimal arithmetic; it is all artificial, and must have arisen from the number of the fingers; which, indeed, supply an easy solution to the whole enigma. Man would begin by taking a few little stones, at first in number five, the number of fingers on one hand. This would produce the first idea of numbers. After a little time he would increase them to ten. He would, by placing them in order, and making them into several parcels, by degrees acquire a clear idea of ten numbers. He would divide them into two, and compare them with one another and with the fingers on each hand, and he would observe their equality; and thus by varying his parcels in different ways, he would begin to do what we call calculate, and acquire the idea of what we call a calculation. To these heaps or parcels of stones, and operations by means of them, he would give names; and I suppose that he called each of the stones a calculus, and the operation a calculation.

5. The ancient Etruscans have been allowed by most writers on the antiquities of nations, to have been among the oldest civilized people of whom we have any information. In my Essay on the Celtic Druids, I have shewn that their