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JB/135/295/001

Completed

1821 Dec. 22 M 2
Posology — Arithmetic

134
Course of Instruction
Order for teaching.

3

8
Go next to square
and cube numbers
with ulterior powers.

9
Then to proportionality

6. From the four elementary operations proceed (to the if not to
this subject of square and cube numbers) to the idea of
proportionality.

10
To Rule of three
Uncharacteristic are
both locutions

7. The current language is here uncharacteristic and
incompleat. If, in respect of characteristicalness the
rule of three
is apt, the rule of f for compleatness the
rule of four should be added to it. The rule of three
is where one and the same number if in both pairs
of proportionable numbers

11
Shew relation of
proportionality to

8. To explain the idea of proportionality bring to view
the relation it bears to the ideas of addition and division.

12
From square numbers
and roots of
the squares shew
the relation between
arithmetical and
geometrical expression

9. When square numbers and the numbers that are the
roots of these square numbers come to be brought to
view then comes the occasion for explaining the relation
between arithmetical expression and geometrical
expression, between arithmetic and algebra on the one
hand and geometry on the other

13
Correspondent the
two modes as far
as square x2
and cube x3.

There the analogy ends
To x4 no figure
delineated figure
corresponds

10 It will then be seen that so far as square
numbers and cube numbers are in question the
arithmetical mode of designation corresponds with and
is illustrated by a material body of a particular figure
and a geometrical designation of its boundaries. But
that when from cube x3, you proceed to biquadratic
x4 the analogy fails. These relations (it is believed)
have never yet been explained with sufficient clearness: explained
ordinary language.

Identifier: | JB/135/295/001
"JB/" can not be assigned to a declared number type with value 135.

1821-12-22

8-13

135

posology

295

posology - arithmetic

001

text sheet

1

recto

c2 / d2 / e3 / g134

jeremy bentham

c wilmott 1819

andreas louriottis

1819

46413