JB/018/086/001

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10 May 1815
Chrest. Tab. II Conclusion

To Geometry – it seems pretty well agreed
among the learned – to Geometry, to the exclusion of in contradistinction to Algebra
(including Fluxions), is confined what may be called
the tonic or invigorative use of mathematics: the service
done to mental health and strength by a sort of
exercise, In which the by which the process of
close reasoning is carried on, and to the performance of which
close and unremitted attention is indispensable. It is
in consideration of this use it is that by some the Algebraic
form is held so cheap in a sort of contempt and that in the immense
class of occasions or that vast portion of the
mathematical field which belongs to Geometry and
Algebra in common, and in which the same conclusion
may be arrived at by either track the same problem
solved by the application of either set of instruments
whatsoever is done effected in the Algebraic mode is considered
as done in the way of makeshifts, and not productive
of use or advantage in any shape, over and above what may
happen to be attached to the solution of the particular problem for
the solution of which it is employed.

This being admitted, although by the solution of a
single problem in the algebraic mode, no such service could be
rendered to the mental frame, as in manner above mentioned
may be rendered to it by the solution of the same
single problem in the geometrical mode, yet by the
indication of this or that particular contrivance by means
of which this or that class of problems may be solved in the
algebraic mode, there seems little reason to doubt but that to
the same service mental frame a service might be rendered though not exactly of the same
sort, yet of a sort
not to be absolutely neglected,
may be rendered.
In the case of Geometrical
case, it is to the judgment
and the attention
that this service would be considered in the algebraical case it is to the conception and inventive faculty that the most immediate principal part of the service would will be rendered.

Identifier: | JB/018/086/001 "JB/" can not be assigned to a declared number type with value 18.
Date_1	1815-05-10	Marginal Summary Numbering	or 17
Box	018	Main Headings	chrestomathia
Folio number	086	Info in main headings field	chrest. tab. ii conclusion
Image	001	Titles
Category	text sheet	Number of Pages	1
Recto/Verso	recto	Page Numbering	d26 / e9
Penner	jeremy bentham	Watermarks
Marginals	jeremy bentham	Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	6495
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