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 not so easy as we might suppose at first thought, may be inferred from the fact that, of other nations, not even the keen-minded Greeks possessed one like it. We inquire, who invented this ideal symbolism, and when? But we know neither the inventor nor the time of invention. That our system of notation is of Indian origin is the only point of which we are certain. From the evolution of ideas in general we may safely infer that our notation did not spring into existence a completely armed Minerva from the head of Jupiter. The nine figures for writing the units are supposed to have been introduced earliest, and the sign of zero and the principle of position to be of later origin. This view receives support from the fact that on the island of Ceylon a notation resembling the Hindoo, but without the zero has been preserved. We know that Buddhism and Indian culture were transplanted to Ceylon about the third century after Christ, and that this culture remained stationary there, while it made progress on the continent. It seems highly probable, then, that the numerals of Ceylon are the old, imperfect numerals of India. In Ceylon, nine figures were used for the units, nine others for the tens, one for 100, and also one for 1000. These 20 characters enabled them to write all the numbers up to 9999. Thus, 8725 would have been written with six signs, representing the following numbers: 8, 1000, 7, 100, 20, 5. These Singhalesian signs, like the old Hindoo numerals, are supposed originally to have been the initial letters of the corresponding numeral adjectives. There is a marked resemblance between the notation of Ceylon and the one used by Aryabhatta in the first chapter of his work, and there only. Although the zero and the principle of position were unknown to the scholars of Ceylon, they were probably known to Aryabhatta; for, in the second chapter, he gives directions for extracting the square and cube roots, which seem to indicate a knowledge of them.