what is more numerous. Thus, three and one or three and two take the place of four and five. This method was actually incorporated into the systems of theand the ancient Hindus. Indeed, the habit persists in the minds of people later on, when they possess many number symbols and the ability to use them in calculation. While the more acute nowadays can without great difficulty comprehend four and five, yet five will frequently be apprehended better as a combination of two and three, while almost inevitably six will be thought of as a combination of three and three, and seven as made of three and four.
Nevertheless as the mind of man becomes more powerful, and the need for calculation becomes more frequent, larger numbers are made use of, even though they can only be comprehended as combinations of smaller ones. The designation of these number ideas soon becomes necessary, and it must be made both for the eye and for the ear. For the eye this may be done by symbols; for the ear by words. Thus, the Greeks may write Ὡ (90) and call it ὲνενῄκοντα; the Romans XL, and call it quadraginta.
The designation of these number ideas either by symbol or by sound is exceedingly difficult for the reason that number ideas are necessarily abstract. It is true that the lower, which represent a few objects, can be designated by pictures. So, man may originate the symbols for his lower numbers in the same manner that he first makes the symbols for his words, by ideographs or picture-drawings. In old Chinese the rude representation of a man designates man. Similarly the Chinaman writes a simple stroke to represent a single object; two strokes to represent two objects; and three, to represent three:
The Hindu once employed the same device, except that his strokes were usually perpendicular:
These symbols were used wherever men began to write their numbers. They were employed by the Latin peoples, and as the Roman numerals are still in common use. In cursive form they are the numerals which we use to-day:
Such graphic designation of number cannot be carried very far, however, and arbitrary symbols must soon be employed. Thus, for four the Hindu wrote two strokes crossed: