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# JB/135/193/001

Completed

1831 May 11 M 16
Posology

ult
Introduction
1. Alegomorphics
Elucidation continued
§5 Nomenclature amended
Equivalents
1. Ascendendo.

? 2

16
One above another
rise all these equivalents:
and at every step are
more distant from the
originally known
Thus they rise in the
ascending direction: and
descend lower than one
another in the converse
direction

Relation had to the contents of this aggregate, those of all
others other aggregates may be said to be unknown: in comparison had with this
aggregate, those the contents of all other aggregates may be said to be unknown
As they advance higher and higher above this basis
they are less and less known — less and less clearly and readily promptly
known: require more and more explanation, the every one of them
by another some other

17
explanation does this
than what is given by
indication of its relation
to the original and standard
size

Thus 1. next to what is known — first of the relations, unknown
operation stands addition. This requires not — this
admitts not explanation by any other medium than the relation
which it bears to the abovementioned standard sizes

18
2. Multiplication
Explained is this by its
relation to the addition — the
intermediate operation between
that and operation and
the original standard

2. Next in the ascending line, comes stands multiplication

19
3. Squaring.
Explained is this by its
relation to the two preceding
operations intermediate
between the results of
this operation and the
original standard

3. Next comes consideration of the 2d power: or say squaring. This admitts — this requires —
this receives explanation by the medium of the relation
it bears to multiplication, and thence to addition

20
4. Cubing or say
cubation. Explained
in like manner, by the
three intermediate operations.

4. Next comes squ cubing involution to the 3d power: or say
cubing: or say though as yet the term is thought to be scarcely in use. As to this matter
see further in § conjugates. If we have not cubation, we have at
any rate incubation: but here, analogy fails us altogether: the image — the material
image is an altogether different one

21.
5. Involution to the
Explained in
like manner: intermediate
operations, four.

5. Next comes involution to the fourth power or say
biquadration: though as yet the term is thought to be scarcely in use

22.
Higher than this goes
not the scale of different
independently denominated
equivalences:
the word power are the
5th, 6th power
&c in an infinite series
(a)

Note 22(a) series or say scales of addition in any number may be formed, by adding continually to the standard number any number other than itself.

6. Next After these, come or comes involution to the 5th, 6th
and so other powers in number actually indefinite, encreasing
and ascending and encreasing in serieses of correspondent length
produced by multiplication (a)

Note (a)

(a) Another species of series is that which is produced by addition
In the Numeration Table, the subject matter of the addition is no other
than No 1. Number one. But any other number may be added either
to itself to to any other number or numbers; and thus in infinite
variety altogether infinite may be formed all in the way produced of simple addition serieses in number altogether
infinite.

Identifier: | JB/135/193/001
"JB/" can not be assigned to a declared number type with value 135.

1831-05-11

16-22

135

posology

193

posology

001

note (a)

text sheet

1

recto

d16 / e2

jeremy bentham

46311