ARITHMOLOGY; OR, THEORY OF COMMON ARITHMETIC, FULLY PROVED WITHOUT ALGEBRA. BY S. E. CASPERSONN, M.B. LONDON: W. H. DALTON, COCKSPUR STREET. 1844. PREFACE. IN presenting this small Work to the public, I will briefly explain my object, and the reason why I wished not to multiply the innumerable crowd of arithmetic books. As to the last, I must confess, all seem to be written by men, whose abilities could not produce better ones, or who appeared to have considered common arithmetic as a matter of too little consequence to take much notice of it. However, all are compositions of a good quantity of rules, which without perpetual practice must be forgotten, or at least confused, as they cannot be understood, but only learned, and the pupils can only thus be trained as animals, not taught, as intelligent beings ought to be. My object was to give a theory of reckoning, I mean not only rules, but an understanding and proof of the correctness of them, in order that he, who understands this theory well, may be able not only to find out all similar cases, not mentioned here, but to renew the rules in his mind, if he has forgotten them. To have shown the way, how to reach this object, was my intention; and only then will I be content, to have published a new arithmetic, when it has caused an alteration in a matter of such general importance, and in which the authors have too long continued in their old way, to the greatest injury of their readers. S. E. CASPERSONN. London, October, 1844. NUMERATION. § I. To number means either to pronounce a given number, or to write down a dictated one. To do the first, we only require to know, how six numbers are to be pronounced, and this we can do, if we know, that from the right to the left the first figure signifies the units, the second the tens, the third the hundreds, the fourth the thousands, the fifth the tens of thousands, the sixth the hundreds of thousands. If we divide a given number from the right to the left into classes of six figures, we give to each class, except to the first, a peculiar name; that of the second class is "million," of the third "billion," of the fourth" trillion," of the fifth "quadrillion," and so on, "quintillion," "sextillion," "septillion," "octillion," "nonillion," "decillion," &c. Now we can easily pronounce every given number after this rule: we divide the number from the right to the left into classes of six figures, B |