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 language, or that of the Latins, which was in fact their language in a later time, was the same as the Sanscrit of India. This I have proved not merely by the uncertain mode of shewing that their words are similar, but by the construction of the language. The absolute identity of the modes of comparison of the adjective, and of the verb impersonal, which in my proof I have made use of, cannot have been the effect of accident. The words which I have used above for the first calculation, and for the instruments used in its performance, calculus and calculation, are Latin, the language of the descendants of the Etruscans, and thus may have been readily derived from the earliest people of the world, whether Asiatic or European. I name this to shew that there is no objection to the names merely because they are the names of a modern language.

6. During the time that man was making this calculation, his attention would be turned to the Sun and Moon. The latter he would perceive to increase and decrease; and after many moons he would begin to think it was what we call periodical; and though he had not the name of period, he would soon have the idea in a doubtful way, and with his calculi he would begin calculation. He would deposit one every day for twenty-eight days, being nearly the time one moon lived, and is the mean between the time of her revolution round the earth, twenty-nine days twelve hours and forty-four minutes, and the time she takes to go round her orbit, twenty-seven days, seven hours and forty-three minutes. Any thing like accuracy of observation it would be absurd to expect from our incipient astronomer. After a few months’ observation he would acquire a perfect idea of a period of twenty-eight days, and thus he would be induced to increase his arithmetic to twenty-eight calculi. He would now try all kinds of experiments with these calculi. He would first divide them into two parts of equal number. He would then divide them again, each into two parts, and he would perceive that the two were equal, and that the four were equal, and that the four heaps made up the whole twenty-eight. He would now certainly discover (if he had not discovered before) the art of adding, and the art of dividing, in a rude way, by means of these calculi, probably at first without giving names to these operations. He would also try to divide one of the four parcels of calculi into which the Moon’s age was divided still lower, but here for the first time he would find a difficulty. He could halve them or divide them into even parcels no lower than seven, and here began the first cycle of seven days, or the week. This is not an arbitrary division, but one perfectly natural, an effect which must take place, or result from the process which I have pointed out, and which appears to have taken place in almost every nation that has learned the art of arithmetic. From the utmost bounds of the East, to the Ultima Thule, the septenary cycle may be discovered. By this time, which would probably be long after his creation, man would have learned a little geometry. From the shell of the egg, or the nut, he would have found out how to make an awkward, ill-formed circle, or to make a line in the sand with his finger, which would meet at both ends. The spider, or experiment, would certainly have taught him to make angles, though probably he knew nothing of their properties.

7. Avery careful inquiry was made by Dr. Parsons some years ago into the arithmetical systems of the different nations of America, which in these matters might be said to be yet in a state of infancy, and a result was found which confirms my theory in a very remarkable manner. It appears, from his information, that they must either have brought the system with them when they arrived in America from the Old World, or have been led to adopt it by the same natural impulse and process which I have pointed out.

8. The ten fingers with one nation must have operated the same as with the other. They all, according to their several languages, give names to each unit, from one to ten, which is their determinate number, and proceed to add an unit to the ten; thus, ten one, ten two, ten three, &c., till they amount to two tens, to which sum they give a peculiar name, and so on to three tens, four tens, and till it comes to ten times ten, or to any number of tens. This is also practised among the Malays, and indeed all over the East: but to this among the Americans there is one curious exception, and that is, the practice of the Caribbeans. They make their determinate period at five, and add one to the name of each of these fives, till they complete ten, and they then add two fives, which bring them to twenty, beyond which they do not go. They have no words to express ten or twenty, but a periphrasis is made use of. From this account of Dr. Parsons’, it seems pretty clear that these Americans cannot have brought their figures and system of notation with them from the Old World, but must have invented them; because if they had brought it, they would have all brought the decimal system, and some of them would not have stopped at the quinquennial, as it appears the Caribbees did. If they had come away after the invention of letters, they would have brought letters with them: if after the invention of figures, but before letters, they would all have had the decimal notation. From this it follows, that they must have migrated either before the invention of letters or figures, or, being ignorant persons, they did not bring the art with them. If this latter were the case, then the mode of invention according to my theory must have taken place entirely and to its full extent with the Americans, (which proves my assumed natural process in the discovery