Elementary arithmetic, with brief notices of its history... by Robert Potts.

25

12. The symbol - is assumed to denote the division of one number
by another; thus 18-3 means 18 divided by 3, and 18-3 =6 is read
18 divided by 3 is equal to 6.
A more convenient notation has been assumed to denote the
division of one number by another, by simply placing the dividend
above the divisor with a line of separation between them. Thus- = 6
denotes that 18 divided by 3 is equal to 6. By means of this notation
for representing the division of one number by another, the complete
quotients in all cases of division may be indicated. Thus, -la, and
-_-, indicate the respective quotients of 18 divided by 3, as well as 19
divided by 3, whether the dividend be exactly divisible by the divisor
-or not.
13. The following axioms will be found useful in arithmetical reasonings:1. Equal numbers multiplied by equal numbers are equal.
2. Equal numbers multiplied by unequal numbers, or unequal
numbers multiplied by equal numbers, are unequal.
3. Equal numbers divided by equal numbers are equal.
4. Equal numbers divided by unequal numbers, or unequal numbers divided by equal numbers, are unequal.
5. Any number multiplied and divided by the same number
remains unaltered.
6. When a dividend and a divisor are both multiplied or both
divided by the same number, the quotient is unaltered.'
ON OTHER SYSTEMS OF NUMERICAL CALCULATION.
14. In the preceding pages has been shewn the method of denoting
nunmbers by means of ten characters with device of place, and of
performing the processes of addition and subtraction, multiplication
and division with them as instruments of calculation. The local
value of this system of arithmetic being ten, is only one of the
possible systems of notation.
Any other number than ten might have been assumed for the local
value, and hence it follows that other systems of numerical notation can
be devised analogous to the denary system, and the character 0 will be
essential in every one of them, whatever may be the local value of the
-scale of notation.
In every system of notation the number of characters which have
*an intrinsic value as well as a local value cannot be greater nor less
than the number which denotes the local value of every two consecu

1 In the Lilavati, directions are given "to abridge the dividend and divisor by
equal numbers, whenever that is practicable," or, in other words, to divide the
dividend and divisor by any number by which they are divisible exactly.