JB/135/077/002

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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
instead of words
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
{adjectitious
or probative

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

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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

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

part line or

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

2. Being part of body,
Of a line <add>which <add>as</add> in the same the line is meant
figure does form the to be given as the
direct subject of the step,
is expressed by in contradistinctions
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 ,
are adapted to the
enuntiation of the
figure proposition
(understand the
word proposition here
in a logical or grammatical

sense)

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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 characterised 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 lessisly one such short crossng line. -mated by that step. — [+] added in the constructional and demonstrational party may be termed adjectitious or protrative.

Identifier: | JB/135/077/002"JB/" can not be assigned to a declared number type with value 135.
Date_1	1778	Marginal Summary Numbering
Box	135	Main Headings
Folio number	077	Info in main headings field	geometry graphical method of expression s & jb
Image	002	Titles
Category	rudiments sheet (brouillon)	Number of Pages	2
Recto/Verso	recto	Page Numbering
Penner	jeremy bentham	Watermarks
Marginals		Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	46195
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