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

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tive characters. The local value of any system determines the number
of independent characters to be employed in that system; and the
notation of numbers will become confused when the number of
characters is greater in number than the local value, and impossible
when the number is less.
As in the denary system the number of characters must be ten,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, the number ten being represented by 10,
so in the septenary system, in which the local value is 7, the number
of characters must be seven, 0, 1, 2, 3, 4, 5, 6, the number seven
being denoted by 10.
The following characters are required in the first eleven systems:Binary system, localvalue 2, requires 2 characters, 0, 1.
Ternary,, 3,,, 3,, 0,1, 2.
Quaternary,, 4,,, 4,, 0,1, 2, 3.
Quinary,, 5,,, 5,, 0,1, 2,3,4.
Senary,, 6,,, 6,, 0,1,2,3,4,5.
Septenary,, 7,,, 7,, 0,1,2,3,4,5, 6.
Octenary,, 8,,, 8,, 0,1, 2, 3, 4, 5, 6, 7.
Nonary,, 9,,, 9,, 0, 1, 2, 3, 4, 5,6, 7, 8.
Denary,, 10,,, 10,, 0,1, 2,3,4,5,6,7,8,9.
Undenary,, 11,,, 11,, 0,1,2,3,4,5,6,7,8, 9, t.
Duodenary,, 12,,, 12,, 0,1, 2, 3, 4, 5, 6, 7, 8, 9, t, e.
The letters t, e, being taken to denote the numbers ten and eleven,
twelve being denoted by 10. And so for any other system of a larger
local value.
The operations of addition, subtraction, multiplication, and division
in any system may be performed in exactly the same manner as the
same operations are performed in the denary system of arithmetic.
A number expressed in one scale of notation can be transformed into
any other scale in which the local value is different. It will, however,
be found more easy in practice to transform the given number of any
scale into another in the denary scale, and this number into that of
the scale required.1
1 To transform 3542 from the septenary to the denary scale.
Here 3542 = 3.73 + 5.72 + 4.7 + 2 = 1304.
The operation may be exhibited thus:3542
7
26
7
186
1304
And 3542 in the septenary = 1304 in the denary scale.
Conversely. To transform 1304 from the denary to the septenary scale.
Since 1304 = 3.73 + 5.72 + 4.7 + 2 = 3542,