1821. July 30 M
Proportions — mode of ascertaining
For conceiving distinction
as to extent no
clear ideas other than those
expressed in numbers.
For conceiving distinctions in respect of extent, the nature of things
admits of no clear ideas other than those which are expressed in numbers.
When two quantities
said to be incommensurable,
the truth is
that the mode of mensuration
employed is not
When two quantities are said to be in the relation to each other incommensurable,
the truth of the case is, not that the relation borne the
one to the other is not susceptible of being expressed by numbers, but
that the mode of numeration notation employed in the endeavour to give expression
to them, is not suited to the purpose.
In division the quotient
turns out to be not a
determinate portion of the
dividend without a remainder
but a portion with
an indeterminate remainder
indicated by a repetend or
In division, conducted according to the prevailing mode of numeration,
the quotient incidentally turns out to be instead of a determinate
portion of the dividend without a remainder, a portion with
an undeterminate remainder indicated by the form of a repetend or
by that of a circulate.
A circulate what
A circulate is a compound repitend: a quantity repeated being
expressed not by a single number but by divers numbers.
of arithmetic the
decimal — proposed
substitute the duodecimal;
The prevailing system of arithmetic is that which is styled decimal.
In lieu of it that which is styled duodecimal, has been proposed.
Saying usage out of the case some advantages there are & those very
considerable, which in comparison to the decimal there can be no
doubt of its affording. Whether to set against them there would be
any disadvantages & whether if any they would or would not be preponderant
could scarcely be obtained without recurrence to usage &
such recurrence seems not very likely ever to take place. Suppose the
duodecimal arithmetic established, it could never entirely supersede
the decimal: the burthen of the learning it the effect would be not the
substitution of a less burthen to a greater, but the addition of a new
burthen to the pre-existing one, for unless the decimal were also
learnt, all pre-existing accounts would be unintelligible.
Identifier: | JB/135/265/001
"JB/" can not be assigned to a declared number type with value 135.
copy/fair copy sheet
e2 / g78
c wilmott 1819