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# JB/135/266/001

Completed

1821. July 30 M
Posology

79
Proportions — mode of ascertaining

3

10.
In duodecimal
arithmetic either
no repetends and
circulates or very
different from those
of decimal arithmetic.

As to repitends & circulates in duodecimal arithmetic, either
there would be none, or the list of them would be very different
from what it is in decimal arithmetic.

11.
and cube numbers —
might be useful to
make lists of repetends
and circulates —
too laborious to
be carried far.

Lists have been formed & published of square numbers &
cube numbers viz. in decimal arithmetic. Might it not be of use
if lists were framed of repitends & circulates. The framing of such
a list would in comparison of those others would be laborious in
the extreme, therefore would scarcely be worth while to carry it at
any rate in the first instance, to any very considerable length. But
to whatever length carried it would contribute to give clearness to
our ideas on the subject of quantity & number numbered quantity, & in this way be instructive.

12.
Does not the incommensurability
here
referred to the indivisibility
of certain
numbers, according
to the decimal
system: by substitution
of duodecimal
to decimal
remainders would
vanish.

The incommensurability ascribed by geometricians to certain
quantities does it not bear tacit reference to the indivisibility of certain
numbers (i.e. without a remainder) according to the decimal
system of arithmetic: the quantity expressed by the figures employed
in the designation of the one, being considered as divided by
the quantity expressed by the figures employed in the designation
of the other, there exists always a remainder. But
if, either for the designation of the remainder, or for the designation
of the entire dividend, the duodecimal or some other
system of numeration than the decimal were employed,
might not that remainder be, in every case, made to vanish?

Identifier: | JB/135/266/001
"JB/" can not be assigned to a declared number type with value 135.

1821-07-30

10-12

135

posology

266

posology

001

copy/fair copy sheet

1

recto

e3 / g79

46384