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# JB/135/077/002

Completed

Geometry Graphical method of expression S. & J.B. 1778 & 1794

Explanation of a
new mode, (stiled
the Graphical Mode)
of expression and
demonstration in relation
to Geometrical
Proportions

In the Graphical
mode of expression
each step in the proposition is expressed
by signs
For this purpose
The proposition
is divided in each
part of it, into as
many different
steps as are capable
of being
distinguished in
it.

Lines {Original
or else
or probative

Of the lines that
occurr in the
construction-al or the demonstrational
part
of a proposition
those which
occurr in the enantiative
part may
mid original
hich for the
of proof are

---page break---

Constituent parts of
a Geome
what is called a
Proposition in Geometry
are

1. The Enantiative
part or what may
be called the Enuntiaton

2. The Constructional
part as it mat be
called, or is
at present called,
the Construction.

3. The Demonstra
-tional-tive part as it may
be called, or as it is
at present called the
Demonstration.

The subject of a
proposition (from a geometrical
proposition) is
a figure.

The component parts of a simple
figure are either
lines and angles.

The component parts of a
compound figure
are simple figures
or a simple figure
or figures with a
part or parts of a
simple figure or figures.

In the graphical
mode of expression
in each step stands
expressed by a set
figure or set of figures
which by means of
laying signs previously

---page break---

Signs for the expression
of propositions
(logical) relative to Lines.

part line or

1. In each step every
which does not form the direct subject of that
step is drawn of characterised
by dots distinguished an extra thickness
by being composed of say a treble thickness
distinct dots, which as
everysuch line or part of

2. Being part of body,
figure does form the to be given as the
direct subject of the step,
unbroken line. to the other part or
parts, the part
has extra thickness
is confined to the
part so distinguished

.

3. Lines meant to be represented
as equal

3. Two or more lines
meant to be represented
as equal
to one another are
characterized for this
purpose by a spirals,
twisting as it
were round them
as thus {Four sketched diagrams}

4. Two or more lines
which, for the purpose of
the demonstration, are meant to be represented
as equal to one
another by supposition,
but though not so by supposit
in reality, the
supposition truth

-ously explained
enuntiation of the
figure proposition
(understand the
word proposition here
in a logical or grammatical
sense)

---page break---

truth of the supposition
being represented
as impossible,
are expressed
by an
incompleat spiral,
one side thereof
(i:e: the part on
one side the line
in question) being
wanting.

Otherwise thus
In lines supposed
equal contrary to
truth for the purpose
of the demonstration,
the impossibility
of the
dem supposition
is characterized
by the deficiency
of the spiral on
one side {Sketch diagram}

5. Of two lines
that which is meant
to be represented as
greater than another
is distinguished by
two short lines
crossing it; the lesser
by one such short crossng
line.

-mated by that step.

and demonstrational
parts
or protrative.

---page break---

Of two lines that
which is meant to
be represented as
much greater than
another minimal
or the greater as
being greater than
a third line which
is itself greater
than the aforesaid
lesser line, is characterized
by three
such short crossing lines

Lines which while
greater or less than
other lines are
meant to be represented
as equal
to one another are
characterised by
an equal number
of such crossing lines

In regard to
lines which, (for
the purpose of
demonstrating proving the
truth of a proposition
by the absurdity
of a the opposite
proposition
opposite to it) are
contrary to truth
supposed to be respectively
equal to
or greater or less
than one another
the falshood of the
and impossibility
of the supposition
is characterized denoted by
the deficiency of
the spiral or crossing

---page break---

Identifier: | JB/135/077/002
"JB/" can not be assigned to a declared number type with value 135.

1778

135

077

geometry graphical method of expression s & jb

002

rudiments sheet (brouillon)

2

recto

jeremy bentham

46195