JB/018/009/001

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10 April 1815

Chresta. Tab.II Inserenda branches
18
Geometry
9
3
Pt. 4 is the converse
of pt.1. It can not fully
be explained till after
pt.3. to which it is
subservient

Among the five abovementioned principles, ofOf the four principles applying that apply to Geometry, between the first and the fourth an intimate
relation will be seenat first
immediatelyglance be seen to have
place: they being
in fact the converse
of each other. But, of
the fourth, neither
the use nor consequently
the nature, can
be fully explained
till that of the third,
to which it is subservient has been brought to
view. | In the character of
fourth will the first glance the converse of each the In the character of
In the character of of Exercises, or mode of learning, the utility both of them, has, in
both instances, received, as will be seen, though, in respect of the
number of the learners, as yet on but or a person in whom experiment was
not even was such, the attestation of experience.

Of the first of these, the great case is - to serve as a
test, if and by that means an instrument of, and security

for, intellection. See Tab 11 above Exerc. No9: Princ. No 24. 4
As exercises both
have been attested by experience
on a small
scale, as below.

Mode of performing the Exercise. - Without the aid of any
The exercise consists in taking say A proposition,
diagram, and consequently without the use of any of those letters signs, such as the letters
of the alphabet, which,

as often as
a diagram
For bringing to
mind the figure in
question, a diagram
or delineation of it
is employed, are
necessary for designating,
and distinguishing
from each other
the parts of the
a proposition (in the geometrical
sense of the word
a proposition) and
consequently the sort of
which is the subject of of which
of subjectof it, is expressed
in words alone: which
Th Expr words will
of worse, be such, that
every proposition (taking
the word proposition in
the logical and grammatical
sense) which they
seem to constitute, will
be what is called a general
proposition, having
for its subject not
class merely and end residual thingobject but a class, a sort of things objects.
5
Of pt. 1, chief use
serving as an
of, and security for
intellation. See excercise
of the alphabet May in plain Geometry. taken any out of Euclids Elements
viz, the proposition, as followed by the demonstration, and by the demonstration directions
preceeded by the directions for the prepagatory additions, thereupon
for the addition to be used for the figure, for the purpose of
the demonstration, andin words alone without the aid of any diagram 6
Mode of performing
the corresponding decrease.
Without diagram
thence without
letters of reference
cause the whole matter
to be expressed in words
alone. These words
being necessarily
general, the relation
expressed with that
by relative as believed
the sorts of objects:
not merely the individual
objects presented by the
diagram and its letters
of reference.
giving to the whole in words when in descriptiona description of every thing is required to be given , in such
manner as to as shall be intelligible. It is only by a descriptionindication
given of the relation which they bearrespectively to each other that
the any in without the assistance of a diagram, and
any intelligible description of the componentand characteristic parts of the
species of figure in question can be given, and so in
regard to whatsoever parts come to be added for the purpose
of the demonstration. If Unless the whole be fully
and compleatly comprehended. By no person but by one
by whom the whole proposition is in all its parts as demonstration included
clearly and compleatly comprehended can any such
purely verbal description be given. In the instance of By every person by
whom that sort of description as given correctly and compleatly of it what is therefore certain
is that of that given proposition at the time at which it the descriptionis so given the proper a clear
correct and compleatly explic the proposition being at the same
and uned in all the generality it is formed and

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Identifier: | JB/018/009/001 "JB/" can not be assigned to a declared number type with value 18.
Date_1	1815-04-10	Marginal Summary Numbering	1-6
Box	018	Main Headings	chrestomathia
Folio number	009	Info in main headings field	chrest. tab. ii inserenda
Image	001	Titles
Category	text sheet	Number of Pages	1
Recto/Verso	recto	Page Numbering	c2 / e2
Penner	jeremy bentham	Watermarks
Marginals	jeremy bentham	Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	6418
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