JB/135/007/002

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PREFATORIA (I)

1What is Supposed
and how far true.

Prefix an essay in the familiar popular stile stating the several
suppositions which Geometrical Arguments procede
on. What is supposed or is otherwards taken for
granted, and how far what is supposed or taken
for granted is conformable to physical existance.

2Examine
Marginal Contents

To find matter for Preface examine the marginal
contents of the several Heads and refer to those
parts which are thought to afford proper matter,
Refer to them from the Sheets entitled Prefatoria.

3Servility of
Editors.

The first and Fundamental Maxim Axiom
with all Euclid's Editors is that Euclid is
infallible; The perpetual consequence is that
if they find any thing they do not like, it is on
that account alone not Euclid's but somebody else's.
By men of this frame of Mind it is in vain to
expect that the Art of Teaching Geometry or
of any other Science should ever be brought to
its perfection. For They conceive it impossible
for Euclid's method to be improved.

whether the cause of this
partiality blindness service admiration be a
veneration humility servility for antiquity
& the works of the antients
or what else it is difficult
to guess.
4Bounds of the
Useful and the
Simply curious

Settle the Boundaries between what is useful in pure
Mathematics and what is simply curious. The
Doctrine that is useful is the doctrine of those Mathematical

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PREFATORIA(I)

What Parts have their
Architypes in
Nature.

mathematical existences that have their Architypes
in Nature.

Of Quantity every considerable modification
may have its Architype in Nature.

Quantity
Arch: of.

Of Figures many have already been proved
to have had their Architypes in Nature, many not yet.
If of any it were certain it neither has nor can have
its Architype, it would then appear clear certain
that the doctrine of that modification would be useless.

Of Figure.

Of modification of Figure some stand
exemplified in the Boundaries of material Substances,
others in the track described by Points of material
Substances moving through a Space.

5Mathematical
Suppositions
how far true.
Method of
Shewing this.

To prove how far Propositions in Mathematics are
conformable to the Truth of Things, take some
Proposition in mixed Mathematics (Mechanics for
example) in which some Proposition of pure
Mathematics is introduced; then observe in what
particular respect the Proposition of pure
Mathematics is true as applied to the material
Subject, that is, to that sort of Substance, of which
the given Proposition is asserted. For this purpose
see what is said of Infinite Quantities by
D'Alembert in his Melanges Tome

Identifier: | JB/135/007/002 "JB/" can not be assigned to a declared number type with value 135.
Date_1		Marginal Summary Numbering	1-5
Box	135	Main Headings
Folio number	007	Info in main headings field	prefatoria (i)
Image	002	Titles
Category	private material	Number of Pages	2
Recto/Verso	recto	Page Numbering
Penner	jeremy bentham; samuel bentham; uk14	Watermarks	[[watermarks::gr [with crown] [britannia emblem]]]
Marginals	jeremy bentham; samuel bentham	Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	46125
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