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<p>(1)<lb/> | <p>(1)<lb/> | ||
Preface. Of the subject matter in question I had to <gap/><lb/> | |||
<gap/> | <gap/> before me that Euclid had; that from that scene<lb/> | ||
i saw elucidated to my own eyes.</p> | |||
<p>Euclids definition of an angle is a definition <foreign> | <p>Euclids definition of an angle is a definition <foreign>ignotum<lb/> | ||
per ignotius</foreign>. According to him an angle <hi rend="underline">γωνία</hi> <!-- Greek lettering --> is<lb/> | |||
a <hi rend="underline"> | a <hi rend="underline">κλίνω</hi>. <foreign>Κλίνω</foreign> has its <hi rend="underline">conjugate</hi> in the<lb/> | ||
Latin words <hi rend="underline"> | Latin words <hi rend="underline">inclino</hi> <hi rend="underline">declive</hi>—<del><gap/></del> according to which<lb/> | ||
it is a <hi rend="underline">bending</hi>. But what is a <hi rend="underline">bending</hi>? what b<gap/><lb/> | it is a <hi rend="underline">bending</hi>. But what is a <hi rend="underline">bending</hi>? what b<gap/><lb/> | ||
has it? It is a mere <hi rend="underline">fictitious entity</hi>. The idea<lb/> | has it? It is a mere <hi rend="underline">fictitious entity</hi>. The idea<lb/> | ||
it presents is rather of a curve than a straight line<lb/> | it presents is rather of a curve than a straight line<lb/> | ||
for when a straight line — a | for when a straight line — a curve for example or bend<lb/> | ||
what does it make but a curve? what at <gap/> so | what does it make but a curve? what at <gap/> so readily:<lb/> | ||
how can the line be made a <sic>strait</sic> one without a line<lb/> | how can the line be made a <sic>strait</sic> one without a line<lb/> | ||
<gap/> | and <gap/> manipulation. Curious it is that <sic>downe</sic><lb/> | ||
to this time <del><gap/></del> mathematicians all over<lb/> | to this time <del><gap/></del> mathematicians all over<lb/> | ||
the world should of been conte<hi rend="superscript">d</hi> to take up with<lb/> | the world should of been conte<hi rend="superscript">d</hi> to take up with<lb/> | ||
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<!-- Horizontal line --> | <!-- Horizontal line --> | ||
Thus confused is the conception which from<lb/> | Thus confused is the conception which from<lb/> | ||
the origin of the art and science | the origin of the art and science down to the present time<lb/> | ||
what for these two thousand years men have been<lb/> | what for these two thousand years men have been<lb/> | ||
content to <add>possess and</add> | content to <add>possess and</add> entertain of <del>this</del> <add>an effectual</add> subject matter belonging<lb/> | ||
to an art and science of which clearness is regarded<lb/> | to an art and science of which clearness is regarded<lb/> | ||
as the <add>essential and</add> distinctive character.</p> | as the <add>essential and</add> distinctive character.</p> | ||
| Line 48: | Line 48: | ||
it is bounded terminate, can the angle measured — can<lb/> | it is bounded terminate, can the angle measured — can<lb/> | ||
the size of it be determined and expressed: <add>and</add> whatsoever<lb/> | the size of it be determined and expressed: <add>and</add> whatsoever<lb/> | ||
be this circle it forms the third | be this circle it forms the third base a figure is completed,<lb/> | ||
<del>much of that figure</del> <add>a figure named a triangle, and of that | <del>much of that figure</del> <add>a figure named a triangle, and of that same triangle <gap/></add> it forms the third boundary, the<lb/> | ||
two others being the two right lines <del><gap/></del> between which<lb/> | two others being the two right lines <del><gap/></del> between which<lb/> | ||
the angle is contained: nor can this figure, with<lb/> | the angle is contained: nor can this figure, with<lb/> | ||
1831 Nov. 23
Posology.
Euclids Imperfect
Definitions
An angle continued
3
(1)
Preface. Of the subject matter in question I had to
before me that Euclid had; that from that scene
i saw elucidated to my own eyes.
Euclids definition of an angle is a definition ignotum
per ignotius. According to him an angle γωνία is
a κλίνω. Κλίνω has its conjugate in the
Latin words inclino declive— according to which
it is a bending. But what is a bending? what b
has it? It is a mere fictitious entity. The idea
it presents is rather of a curve than a straight line
for when a straight line — a curve for example or bend
what does it make but a curve? what at so readily:
how can the line be made a strait one without a line
and manipulation. Curious it is that downe
to this time mathematicians all over
the world should of been conted to take up with
such obscure conseptions.
(3)
Thus confused is the conception which from
the origin of the art and science down to the present time
what for these two thousand years men have been
content to possess and entertain of this an effectual subject matter belonging
to an art and science of which clearness is regarded
as the essential and distinctive character.
(2)
No otherwise than by reference made to the corresponding
circle — to the circle in which the lines by which
it is bounded terminate, can the angle measured — can
the size of it be determined and expressed: and whatsoever
be this circle it forms the third base a figure is completed,
much of that figure a figure named a triangle, and of that same triangle it forms the third boundary, the
two others being the two right lines between which
the angle is contained: nor can this figure, with
the angle in question belonging to it, be thus formed, without
forming, at the same time the two other sides boundaries of that same
triangle.
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Identifier: | JB/135/161/001"JB/" can not be assigned to a declared number type with value 135. |
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1831-11-23 |
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jeremy bentham |
street & co 1830 |
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antonio alcala galiano |
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1830 |
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