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# JB/135/296/001

Completed

1821 Decr. 22 M 2
Posology Arithmetic

135
Course of Instruction
Order for teaching

3 3

14
Thence shew — only
by arithmetic can
geometrical ideas be
clarified.

11. When the relation between arithmetic and geometry is shewn
then may be the time for shewing that it is only by means of
arithmetic that any clear ideas can be obtained in the
subject of geometry.

15
Analogous to arithmetical
repetends and
circulates are geometrical
rep incommensurables

12. Shew, on this occasion, the relation of incommensurable
quantities in geometrical language to repetends and
circulates in arithmetical

16
A circulate is a
compound repetend

13 A circulate is a compound repetend: a
continually repeated quantity, designated by a multitude
of figures instead of a single one.

17
Source of repetends
the decimal system
Would they be extirpated
by the duodecimal?

14 Repetends and circulates seem to have it is believed their origin
in the decimal form system of arithmetic. It would be curious
to see what would become of them in the duodecimal
system.

18
Fraction supposes
division: shew
relation of between vulgar
and decimal.

15 Fraction supposes division. Quere where would be the place
in which to insert the language of fractions — vulgar and decimal?

16 Would not the operation of called squaring
the circle
be effected by the substitution of the duodecimal system
to the decimal?

17 By the duodecimal system might not the mode of
designation be cleared of the obscurity involved in the idea
of mutually incommensurable quantities?

19
Arithmetic explains
geometry: number of atoms
constitute figures,
atom means indivible

18 Essential to clearness of conception in geometry is clearness
of conception in arithmetic. Essential to clearness of conception
in arithmetic is the idea of atoms or portions of matter
regarded as not susceptible of ulterior division. See Arnot.

20
In actual division
chemistry goes further
than mechanics; colour
than lines

19 In the case of actual division, chemistry goes much
further than — much lower down than mechanics. The
, divisions, the marks of which are shewn by coloured solutions
is vastly more minute, than any division which can be made
on the surface of a large body by the tracing of . lines.

Identifier: | JB/135/296/001
"JB/" can not be assigned to a declared number type with value 135.

1821-12-22

14-20

135

posology

296

posology - arithmetic

001

text sheet

1

recto

c3 / d2 / e3 / g135

jeremy bentham

c wilmott 1819

andreas louriottis

1819

46414