JB/018/121/001

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8 May 1815
Chrest. Tab. II Conclusion

But the no where it is believed does is the explanation
so full as above, nor do in the giving it are the points
put together in such a manner as to present the idea
of a cube. Yet the cube being the of all the entities in question
of a cube the only one which in a separate state has in the nature
of things its exemplification, the ideas of a surface, a line, and a point,
having in the way by the process of abstraction, respectively been
deduced from the idea
of this solid in the
way of abstraction,
the consequence
seems to be, that when
images come to be exhibited,
the image of a
cube, ought no more
to have been omitted,
than the image of a
square.

8 May 1815

Neither is it very distinctly explained how a surface comes to why or how one of the surfaces
be considered as constitu by which a cube or die is
bounded comes to be considered as constituting representing the root of
it: nor how why or how one of the lines by which
the one of these surfaces is bounded comes to be considered
as constituting representing the root of that surface.

Supposing these matters to admit of explanation
the explanation, it is believed, will be to some such effect
as this. Take the a die and set it down upon a table
resting on any one of its faces or surfaces, suppose that which is
marked with one spot, then suppose the die to be a plant that surface may naturally
enough be considered as representing the root of the plant.
Of any figure approaching to that of a die, true it is that
no plant has ever yet been found. But, of a figure
approaching very nearly to that of a hemisphere, such as
that which might on all sides be contained exactly within the compass
of a die of correspondent dimensions, plants have
actually been found: witness a species of the genus cactus.

In like manner, in a vertical position, at right
angles to the table, set up a chess board, composed as above
the lower of the rows of squares, of which this square figure it is composed,
the lowest, i. e. that which is in contact with the
Table, represents that side boundary which in the language of geometry geometrical language
is frequently called stiled the base of the square, and whic
in the language of arithmetic, as above, may be termed
the root of it, the number of lines contained in it bearing, as it does, the same relation to the number of lines contained in the whole
solid, as surface, as the whole surface number of lines contained
in that surface bears to the number of lines contained in the whole
solid termed as above
a cube or die.

Identifier: | JB/018/121/001 "JB/" can not be assigned to a declared number type with value 18.
Date_1	1815-05-08	Marginal Summary Numbering	19 or 5 - 22 or 8
Box	018	Main Headings	chrestomathia
Folio number	121	Info in main headings field	chrest. tab. ii conclusion
Image	001	Titles
Category	text sheet	Number of Pages	1
Recto/Verso	recto	Page Numbering	e9
Penner	jeremy bentham	Watermarks
Marginals	jeremy bentham	Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	6530
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