JB/135/078/002

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Geometry

1. Geometrical propositions
are all relative
to bodies

2 Are none of these
strictly true

3 Under what limitations
they may without
any prejudicial
error be considered
as true

4. They ought all
of them to be considered
in general terms:
and that throughout.

5 How the terms
employed in geometrical
propositions
may be made
general

6. Terms general
in themselves—as
triangle, parallelogram

7—2. General by
relation in reference:
where the name of
one object is taken
by from the relation it
bears to other objects.

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Mathematical has
science. The branch
of science termed Mathematical
has two
main divisions, Geometry
and Arithmetic.

Geometrical propositions
are general
propositions having
for their subject
either body (that is
bodies in general) or
space considered
as unoccupied by
body: both body
and space being
considered with reference
to their form
or configuration
solely without regard reference
to any other
properties they may
respectively possess:
Geometrical for
The proportions
termed geometrical
the proportions delivered
in books
termed books of
geometry are in
the first place all
of them relative to
figure which is
that is all of those
relative either to
body to a property
of body and thus
all of them relative
to body, [+] They are
therefore no farther true

[+] Space thus out of
the question.
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than in as far as
they are true of body,
that is of bodies
in general.
But of bodies in
general a geometrical
proposition
can no further be
true than in as
far as it is true
of every body whatsoever
possessed of
the figure to which
that proposition relates
the existence
of which is supposed
by the proposition.

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2. As Geometry
is the propositions
about which Geometry
is conversant
are without exception
general
names propositions
they ought without
exception to be conveyd
by expressed
in and convey'd
by general terms
the terms employ'd
for the expression
of them ought without
any exception
to be general terms
of a nature equally
general.

If in any instance
the expression
made use of
in any such occasion
fails of being
a general one, it
is pro tanto inadequate
to its object:
the idea it
excites of itself is
not a general one:
of itself therefore
it fails of exciting
the idea it is intended
to excite:
if that idea chances
notwithstanding
to present itself
to the reader,
it is owing to it
is an idea of his
own formation, it is not
the idea presented
to him by the author.

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That the
reader obtains
the instruction
meant to be convey'd
is owing
to his own sagacity
not to the
talent and skill
of the author. The
idea presented by
the author is
inadequate and
ill suited unadapted to the
purpose: and before
the purpose
can have been
answered that idea
must have been
changed: it must
have been set
aside, and an
idea the idea which
is adequate to the
purpose must
have by the sagacity
of the
reader have been
substituted in the
room of it. So
long as the reader
has an in his
mind no other
ideas than what
the writer has
words of the writer
present to it, so
long he fails of
understanding the
writer, so long the
writer fails of
having made himself
understood: of
ever

Identifier: | JB/135/078/002 "JB/" can not be assigned to a declared number type with value 135.
Date_1		Marginal Summary Numbering
Box	135	Main Headings
Folio number	078	Info in main headings field	geometry
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	46196
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