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<head><foreign>PREFATORIA</foreign> (I)</head> | <head><foreign>PREFATORIA</foreign> (I)</head> | ||
<p>1 Prefix an essay in the familiar popular stile stating the several<lb/> suppositions which Geometrical Arguments <sic>procede</sic> on. What is supposed or is otherwards taken for<lb/> granted, and how far what is supposed or taken<lb/> for granted is conformable to physical <sic>existance | <p>1 Prefix an essay in the familiar popular stile stating the several<lb/> suppositions which Geometrical Arguments <sic>procede</sic> on. What is supposed or is otherwards taken for<lb/> granted, and how far what is supposed or taken<lb/> for granted is conformable to physical <sic>existance</sic>.</p> | ||
<p>2 To find matter for Preface examine the marginal<lb/> contents of the several Heads and refer to those<lb/> parts which are thought to afford proper matter,<lb/> Refer to them from the Sheets entitled <foreign>Prefatoria</foreign>.</p> | <p>2 To find matter for Preface examine the marginal<lb/> contents of the several Heads and refer to those<lb/> parts which are thought to afford proper matter,<lb/> Refer to them from the Sheets entitled <foreign>Prefatoria</foreign>.</p> | ||
<p>3 The first and Fundamental <del>Maxim</del> Axiom<lb/> with all Euclid's Editors is that Euclid is<lb/> <hi rend="underline">infallible</hi>; The perpetual consequence is that<lb/> if they find any thing they do not like, it is on<lb/> that account alone not Euclid's but somebody else's.<lb/> By men of this frame of Mind it is in vain to<lb/> expect that the Art of <hi rend="underline">Teaching Geometry</hi> or<lb/> of any other Science should ever be brought to<lb/> its perfection. For They conceive it impossible <lb/>for Euclid's method to be improved.</p> <note>whether the cause of this<lb/>blindness servile admiration<lb/> partiality humility servility be a<lb/> veneration for antiquity<lb/> or the works of the anticuts(?) or what else it is difficult<lb/> to guess.</note> | <p>3 The first and Fundamental <del>Maxim</del> Axiom<lb/> with all Euclid's Editors is that Euclid is<lb/> <hi rend="underline">infallible</hi>; The perpetual consequence is that<lb/> if they find any thing they do not like, it is on<lb/> that account alone not Euclid's but somebody else's.<lb/> By men of this frame of Mind it is in vain to<lb/> expect that the Art of <hi rend="underline">Teaching Geometry</hi> or<lb/> of any other Science should ever be brought to<lb/> its perfection. For They conceive it impossible <lb/>for Euclid's method to be improved.</p> <note>whether the cause of this<lb/>blindness servile admiration<lb/> partiality humility servility be a<lb/> veneration for antiquity<lb/> or the works of the anticuts(?) or what else it is difficult<lb/> to guess.</note> | ||
This Page Has Not Been Transcribed Yet PREFATORIA (I)
1 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.
2 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.
3 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
blindness servile admiration
partiality humility servility be a
veneration for antiquity
or the works of the anticuts(?) or what else it is difficult
to guess.
4 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
---page break---
mathematical existences that have their Architypes
in Nature.
Of Quantity every considerable modification
may have its Architypein Nature.
Of Figures many have already been proved
to have had their Architypes in Mature, 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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