FIGURES, AND NUMBERS.
Respecting the origin of the numeral figures 1, 2, 3, 4, 5, 6, 7, 8, 9, there are various opinions, but the one most generally received is, that they were brought into Europe from Spain; that the Spaniards received them from the Moors, the Moors from the Arabians, and the Arabians from the Indians.
Bishop Huet, however, thinks it improbable that the Arabians received figures from the Indians, but, on the contrary, that the Indians obtained them from the Arabians, and the Arabians from the Grecians; from whom, in fact, they acquired a knowledge of every science they possessed. The shape of the figures they received underwent a great alteration; yet if we examine them, divested of prejudice, we shall find very manifest traces of the Grecian figures, which were nothing more than letters of their alphabet.
A small comma, or dot, was their mark for units.
The letter β (b) if its two extremities are erased, produces the figure 2.
If we form the letter γ (g) with more inclination to the left than usual, shorten the foot, and give some rotundity to the left horns near the left side, we shall make the figure 3.
The letter Δ (D) is the figure 4, as we should find on giving the left leg a perpendicular form, and lengthening it below the base, which also should be enlarged towards the left.
From the ε (e short) is formed the 5, by only bringing towards the right side the demicircle which is beneath inclining to the left.
From the figure 5 they made the 6, by leaving out the foot, and rounding the body.
Of the Ζ (Z) they make the 7, by leaving out the base.
If we turn the four corners of the Η (e long) towards the inside, we shall make the figure 8.
The ϑ (th) was the figure 9 without any alteration.
The nought was only a point which they added to their figures, to make them ten times more; it was necessary that this point should be made very distinctly, to which end they formed it like a circle, and filled it up; this method we have neglected.
Theophanus, the Eastern chronologist, says in express terms, that the Arabians had retained the Grecian numbers, not having sufficient characters in their own language to mark them.
Menage says, they were first employed in Europe in 1240, in the Alphonsian Tables, made under the direction of Alphonso, son to king Ferdinand of Castile, by Isaac Hazan, a Jew of Toledo, and Abel Ragel, an Arabian. Dr. Wallis conceives they were generally used in England about the year 1130.
In the indexes of some old French books these figures are called Arabic ciphers, to distinguish them from Roman numerals.
NUMBER X, 10.
It is observed by Huet as a remarkable circumstance, that for calculation and numerical increase the number 10 is always used, and that decimal progression is preferred to every other. The cause of this preference arises from the number of our fingers, upon which men accustom themselves to reckon from their infancy. First, they count the units on their fingers, and when the units exceed that number, they have recourse to another ten. If the number of tens increase, they still reckon on their fingers; and if they surpass that number, they then commence a different species of calculation by the same agents; as thus—reckoning each finger for tens, then for hundreds, thousands, &c.
From this mode of reckoning by the fingers then, we have been led to prefer the number ten, though it is not so convenient and useful a number as twelve. Ten can only be divided by two and five, but twelve can be divided by two, three, four, and six.
The Roman numbers are adduced in proof of the origin of reckoning by the number ten, viz.—
The units are marked by the letter I, which represent a finger.
The number five is marked by the letter V, which represents the first and last finger of a hand.
Ten, by an X, which is two V’s joined at their points, and which two V’s represent the two hands.
Five tens are marked by an L; that is half the letter E, which is the same as C, the mark for a hundred.
Five hundred is marked by a D, half of the letter Φ, which is the same as M, the mark for a thousand.
According to this, the calculation of the Roman numbers was from five to five, that is, from one hand to the other. Ovid makes mention of this mode, as also of the number ten:—
“Hic numeris magno tunc in honore fuit.
Seu quia tot digiti per quos numerare solemnus,
Seu quia bis quino femina mense parit.
Seu quod ad usque decem numero crescente venitur:
Principium spatiis sumitur inde novis.”
Vitruvius also makes the same remark; he says, “Ex manibus denarius digitorum numerus.”
We have refined, however, upon the convenience which nature has furnished us with to assist us in our calculations; for we not only use our fingers, but likewise various figures, which we place in different situations, and combine in certain ways, to express our ideas.
Many unlettered nations, as the inhabitants of Guinea, Madagascar, and of the interior parts of America, know not how to count farther than ten. The Brasilians, and several others, cannot reckon beyond five; they multiply that number to express a greater, and in their calculations they use their fingers and toes. The natives of Peru use decimal progression; they count from one to ten; by tens to a hundred; and by hundreds to a thousand. Plutarch says, that decimal progression was not only used among the Grecians, but also by every uncivilized nation.