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the case is <lb/> | the case is <lb/> | ||
not that he has <lb/> | not that he has <lb/> | ||
been taught | been taught Geometry<lb/><pb/> | ||
try, but that he has invented it. So far as a book is composed of such propositions no man who reads it understands Geometry any further than he has invented it. Which the <gap/> <del><gap/></del> is in this state, that is while books of instruction in it are thus imperfect no man really understands Geometry who has not invented Geometry. So far If a book of Geometry were composed wholly of general propositions had no propositions in it that were not but general propositions every man would be able to understand and would accordingly would understand geometry by who was whom able to comprehend to those propositions had been were comprehended of which the book consisted whereas at present no man understands geometry but he who besides being comprehending the propositions given to him has been capable of inventing them. | |||
if ever the reader
comes to understand the
proposition it is by
means of having in
his mind ideas of
his own formation,
ideas which the words
of the writer did not
present to him. It is
in a word by having possessing
contrive to form to himself a general proposition
which the
writer ought to have
formed for him but
did not.
For conveying affectually
that is to every
body and at all times
a general idea no
proposition can serve
that is not a general
proposition. A general
proposition that
is really a general
one conveys, the idea
the general idea to
every one who by whom
the import of it is understood,
and to that time
at all times. Of A proposition
that is not a
general one may be
const a man may
understand the import
and that most perfectly
without having
a general idea
in his head mind, without
having in his head
that sort of prop idea which
---page break---
which the proposition
was intended
to convey. In a
word of propositions
that are not general
a man may
understand as many
as would fill a
book that should
have the appearance
of a book
of geometry, without
understanding
a syllable of Geomtery.
All books of Geometry
hitherto extant
have with
propositions that
are not general.
There is not a book
extant Euclid not
excepted which a
move in which
are not to be found
propositions in abundance
every
one of which a
man may understand,
and that
most perfectly,
without understanding
any thing of
Geometry. Suppose
a book of Geometry
composed wholly of
such propositions, if
a man by reading
it has learntunderstands Geometry,
the case is
not that he has
been taught Geometry
---page break---
try, but that he has invented it. So far as a book is composed of such propositions no man who reads it understands Geometry any further than he has invented it. Which the is in this state, that is while books of instruction in it are thus imperfect no man really understands Geometry who has not invented Geometry. So far If a book of Geometry were composed wholly of general propositions had no propositions in it that were not but general propositions every man would be able to understand and would accordingly would understand geometry by who was whom able to comprehend to those propositions had been were comprehended of which the book consisted whereas at present no man understands geometry but he who besides being comprehending the propositions given to him has been capable of inventing them.
Identifier: | JB/135/078/003"JB/" can not be assigned to a declared number type with value 135. |
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135 |
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078 |
geometry |
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003 |
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rudiments sheet (brouillon) |
2 |
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recto |
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jeremy bentham |
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46196 |
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