JB/135/266/001

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1821. July 30 M
Posology

79
Proportions — mode of working

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.
Lists made of square
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.
Date_1	1821-07-30	Marginal Summary Numbering	10-12
Box	135	Main Headings	posology
Folio number	266	Info in main headings field	posology
Image	001	Titles
Category	copy/fair copy sheet	Number of Pages	1
Recto/Verso	recto	Page Numbering	e3 / g79
Penner		Watermarks
Marginals	richard doane	Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	46384
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