The ancient book was made of parchment; sometimes attached to a wooden roller, but more often a simple roll, whence our word volume, the rolled or revolved thing. The title was a small tag attached to the roller or to the parchment itself. The volumes were kept in a round box which the pedagogue carried for the boy. This arrangement of the rolls in round boxes is still preserved in the Vatican Library at Rome.
The schoolboy's arithmetic consisted of the science of abstract numbers—regarded as especially difficult and seldom acquired by the ordinary man—and the art of reckoning, common to the pursuits of everyday life. The Athenians, who had obtained a wide reputation as bankers, must have acquired proficiency in the keeping of accounts. To the science of abstract numbers is due much of the architectural excellence of the Greek temples and public buildings, whose dimensions were based on some mathematical theory, and in at least one instance—the celebrated Temple of the Olympian Zeus—multiples of seven and five have been found to be the governing principle. The boy was taught to add, subtract, multiply, and divide; though the lack of our Arabic system of notation made the operation much more difficult than now. Mother Nature, here as everywhere, taught the first lesson. The pupil used his fingers in counting, and "counting by fives" came to be the fixed expression for all counting. The units were represented by the fingers, a bent or crooked finger having a fractional significance. Our old-fashioned word digits (fingers) is a telltale relic of this mode of reckoning. The time immemorial practice of counting by fives and multiples of five has survived to this day, and forms the basis of all calculation, pure and applied, and will maintain its sovereignty as long as mankind has fingers and toes.
The Greek boy made straight marks for numbers; at first five lines (|||||) meant five, and then two lines at an angle—the outline of the hand outstretched in counting that number (V); two of these angles with their vertices together (X) meant ten. The higher numbers, as the hundreds and thousands, were represented by the initial letter of the word, as in the Roman system of to-day. The abacus and pebbles were used as an aid in computations with large numbers. The abacus, so called from its resemblance to the marble slab at the top of the Doric pillar, was said to have been introduced by Pythagoras, but was probably of Egyptian origin. There were several forms of the abacus, but the kind most common in the Greek schools was, in principle, exactly like the counting-frame "John Chinaman" uses when he reckons up our laundry bill. There were several straight furrows set with pebbles, a row for each of the orders of units, tens, hundreds, and so on: at the left side of each furrow
