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1830 June 29? or thereabouts
Posolog — Preached by J. B. to Colonel Thompson Quere whether Marginalia?
1.
Diffusion — or say Circulation,
— and Extension. Under To one or
other of these heads may perhaps
be found referable, whatsoever
can be done towards the advancement
of this or any other branch
of art and science.
In the case of Posology, Diffusion
presents itself as that one of the
two, by which the largest contribution
is in the present state
of things capable of being made
to the happiness of the community:
In this branch of art and science,
the progress, it is supposed, has
been made, as far, nearly if not
altogether, as the fruits of the discoveries
in what is called Pure
Mathematics are susceptible
of application to Physics: in these
abstractions, in so far as they
are applicable with advantage to
real entities. To the diffusion of
the matter of this art and science,
accordingly, will the endeavours
employed in this essay be
exclusively directed.
To the acquisition of an acquaintance
with the matter of it, one main
obstacle, it may perhaps be said
the most powerful if not the only
considerable one that has hitherto
opposed itself, consists in the repulsive
form of the language in and
by which all the ideas belonging
to it have as yet been expressed.
In Geometry and the other
branches in which figure is
taken into consideration, the
repulsive matter has for its
ingredients the diagrams or say
portraitures, by which the propositions
with the demonstrations
stand expressed, and the
figures letters of the alphabet in
Roman characters by which
they are surrounded. So much
for Geometry.
Now for Algebra, common
and transcendental included.
Algebra having nothing to do
with form or figure say figure
Here the Roman numerals no
longer obtrude themselves;
but the Arabic numerals
with their cortège of hieroglyphical pots
and hangers (Note, which are
Indian ) composed of
crosses, parallel lines, vs,
given as pictures of roots, and
these put together in two
stories divided by a horizontal
line, are not less appalling.
To obviate these difficulties,
the following are the contrivances
that have presented
themselves.
1. Whatsoever instruction
can be conveyed in ordinary
language without the use of
any of those appalling phantoms
to give expression to it accordingly,
in ordinary language.
2. In the next place, the
matter in question being in
every form that can be given to
it, pre-eminent in dryness,
do whatsoever can be done,
to confer upon it what may be soever
called the humectation, so to
speak, it is susceptible of.
1. As to the exclusive use
as far as may be, of the ordinary
language. This expedient is
productive of two distinguishable
advantages. —
In the first place comes,
the above-mentioned advantage
of rendering the comprehension
of the matter so much
more prompt & easy.
In the next place comes
the advantage of prodigious
importance, the nature of which
and thence the magnitude, present
themselves as having been
down to this time perhaps
universally overlooked. This
consists in the implanting
in the mind those general
ideas by which alone any
practical use and application
of this branch of art and
science can be made: Of
pure and abstract mathematics
to Physics, constituting
by the union of the two objects
that branch of art and science
which passes by the name of
mixed mathematics.
In the books of geometry,
in the way in which the truths
belonging to the science are
brought to view, — so long
as diagrams are employed,
the object that presents itself
to the view of the learner is, generally
speaking, not the general
idea but which it is wished to
implant, but only the particular
idea which is presented
to his view by the diagram:
insomuch that if the ideas meant
to be conveyed were to receive
expression in the ordinary language,
without the use of the
diagram, he would not recognise
them to be the same. A
consequence of which is that
a learner may have gone through
the whole of Euclid's Elements,
and have rendered himself
able to demonstrate every
proposition contained in that
work, without being, after
all, as the common phrase is,
much the better for it.
In relation to this matter,
what occurred to the author of
these pages some five-and-fifty
years ago, that it was no otherwise
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Identifier: | JB/135/173/002 "JB/" can not be assigned to a declared number type with value 135.
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1830-06-29 |
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135 |
posology |
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173 |
posology preached by jb to colonel thompson marginal abridgments |
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002 |
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rudiments sheet (brouillon) |
2 |
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recto |
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b&m 1829 |
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arthur moore; richard doane |
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1829 |
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46291 |
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