PREFATORIA (I)1What is Supposed
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.
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.
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.
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
PREFATORIA(I)What Parts have their
mathematical existences that have their Architypes
Of Quantity every considerable modification
may have its Architype in Nature.
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 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.
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
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jeremy bentham; samuel bentham; uk14
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