JB/018/123/001

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9 May 1815
Chrest. Tab. II

A plan A principle of nomenclature so inadequate –
a principle by which neither multiplication nor division
could be carried to on more than two stages, how came it in what source instance is will the course source of it to be found? to be adopted to what cause shall it be ascribed? – Obviously
enough as this viz. in the continual interconversion conversion of
as between of the algebraical and the geometrical forms into each other.
In geometry when from your point you laid down a line
when from in your line you had erected your surface in the form of a square, and on your
square you had erected your solid in the form of a cube
there you found yourself at a stand: no other ulterior dimensions
did the nature of things afford: so much as to the line scale of encrease.
So, on the other hand in regard to roots. In the square you
possessed a figure, of which the imaginary metaphorical root represented by
any of its boundaries, might be found: from in the cube
you possessed another figure, for which a still deeper root,
viz. the same this by which the root of the square had
been represented, might be found. But, the nature of things not affording there being nothing
more substantial or solid or substantial than a cube,
there ended also the corresponding line of roots: so much as to
the line scale of decrease
for in the number called a square number, in other words in the 2d power of the number representing one boundary of of that the correspondent number, or in the first branch of that same number considered in the character of a branch, geometry affords
an image capable of in some sort of representing it: so likewise for in the
number called a cube number. But there at that point the
representation and consequently the interconvertibility ends: at that
next point you come to the 3d power of it or the 2d branch of the number
in question, and to that the stores of Geometry afford not any correspondent image.

Here then may perhaps may be seen the cause of
this obscure and imperfect portion of nomenclature. But
by the statement indication thus given of the cause, be it ever
of the imperfection, the mass of inconvenience resulting from it is not
by any means diminished: nor, therefore the demand for
the application of such remedy as the nature of the case
admitts of.

Identifier: | JB/018/123/001 "JB/" can not be assigned to a declared number type with value 18.
Date_1	1815-05-09	Marginal Summary Numbering	26 or 12 - 27 or 13
Box	018	Main Headings	chrestomathia
Folio number	123	Info in main headings field	chrest. tab. ii
Image	001	Titles
Category	text sheet	Number of Pages	1
Recto/Verso	recto	Page Numbering	e11
Penner	jeremy bentham	Watermarks
Marginals	jeremy bentham	Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	6532
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