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1821 Dec 22 1831 March 11 May 3 M 1
Posology. Arithmetic
§. 8. Alegomorphics
133
Course of Instruction
Order for teaching
1 Alegomporphic
1
Posology Arithmetical Plan § Alegomorphics — Proposed course or say Order of Instruction
1
Mode of explaining
arithmetical operations
1 Shew their relations:
begin with
2 simplest, first:
3. Give Examples of all.
4. Shew the origin of
abstract, in material
ideas.
1 Explain the several operations of Arithmetic, by means of their
mutual relations, by a chain of definitions Expository propositions, beginning
with the most simple: for illustration elucidation give
on this occasion but one example to each: bearing keeping in view from
first to last the origin of these abstract ideas in material ones.
1 Note, in arithmetic equality is but synonymity. To say two and two are equal to four is
to say that by the
one and the same quantity
may with equal
correctness be designated
by the expression word
four, and by the phrase
two and two. This
applies to all the
operations of arithmetic,
and all the results
they give.
2 Instead of four rules say the four elementary operations
Commence with Addition of Arithmetic
3. Commence with addition. Addition is more simple than
Division. It is easier to be sure that one apple is
added to another apple than to be sure that either of
them is cut into two parts exactly equal
4 From addition proceed to Multiplication. Shew that
multiplication is but a particular and complicated mode
of addition: it is a sort of short hand an abridged mode of designating the
complicated addition that would be necessary. Words are
saved by it: as they are by cyphers substituted in arithmetic to
words and single letters substituted in Algebra to combinations
of cyphers or longwinded description designation, at length of the
relation borne by the unknown quantities to the known ones
5. From multiplication proceed to substraction. From
substraction to division. Division is to substraction what
multiplication is to Addition.
2
In arithmetic
equality is but synonymity
or say equivalence
3
Addition, first
4
Multiplication,
second.
5
Substraction, third
6
Division, fourth
7
As division multiplication
is to division
addition, so division
to substraction
Identifier:  JB/135/294/001 "JB/" can not be assigned to a declared number type with value 135.



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jeremy bentham 

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