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<head>1831 May 21</ | <head>1831 May 21<lb/> | ||
Posology</head> | |||
II Morphoscopics<lb/> | <note>ult<hi rend="superscript">o</hi><lb/> | ||
II. Morphoscopics.<lb/> | |||
Euclid</note | §. Mixture of Demonstration &<lb/> | ||
Euclid</note> | |||
<p>Note | <p>☞ Superseded this page, but consultable.</p> | ||
has fallen | |||
yet brought to view, this is, in the | <p>Note here an impropriety of expression into which Euclid<lb/> | ||
has fallen, and which <del>I</del> as far as I can learn no man hath as<lb/> | |||
yet brought to view, this is, in the dispensation of the <add>sort of</add> figure in<lb/> | |||
question, the speaking not of its <hi rend="underline">sides</hi> but of its angles: an equilateral<lb/> | question, the speaking not of its <hi rend="underline">sides</hi> but of its angles: an equilateral<lb/> | ||
trilateral figure is what he should have | trilateral figure is what he should have said <add>called it</add>: not an<lb/> | ||
equilateral triangle, or say triangular figure. In other words, it<lb/> | equilateral triangle, or say triangular figure. In other words, it<lb/> | ||
is <del>by</del> the names of its sides <del>that</del> is what he should have called<lb/> | |||
it by | it by—not the names of its angles.</p> | ||
<p>The origin of the impropriety, and the | <p>The origin of the impropriety, and the imperfectness that<lb/> | ||
results from it in the point of the ideas planted <add>made to appear</add> in his own mind<lb/> | |||
other minds or this. | other minds, or this. Of angles it is that he speaks <add>treats</add> before he<lb/> | ||
<del>speaks of lines | <del>speaks of lines: whereas it is of lines that he should have</del><lb/> | ||
<del> | <del>spoken, before he spoke of lines</del><lb/> | ||
speaks of lines in number and | speaks of lines in number and quantity such as to comprehend<lb/> | ||
or say enclose | or say enclose and contain a space.</p> | ||
<p>The consequence is | <p>The consequence is—that the idea he gives <add>suggests</add> of an<lb/> | ||
angle is altogether | angle is altogether an indistinct one <del>It is a thing</del> <add>one</add> Is it a<lb/> | ||
Is it a line only? No it is more than a line. | Is it a line only? No it is more than a line. Is it a<lb/> | ||
surface? No | surface? No—it is not a surface: it is not <add>amounts not to</add> a <sic>compleat</sic> surface<lb/> | ||
be that surface ever so | be that surface ever so minute: <add>the least number</add> of the lines capable of <sic>inclosing</sic><lb/> | ||
a surface the least number is three: and to constitute an<lb/> | |||
angle <del>he</del> to constitute | angle <del>he</del> to constitute this same undefined and undefinable<lb/> | ||
something, <add>lines</add> he gives not — he allows not more than | something, <add>lines</add> he gives not—he allows not more than two—<lb/> | ||
his two lines may be of the same length | his two lines may be of the same length one as the other, is of two<lb/> | ||
different length they | different length: they may either of them or both be of any number of<lb/> | ||
millions of | millions of inches in length as in the case of the rags of Lytia,<lb/> | ||
or if no more than a fraction of the millionth of an inch in length<lb/> | or if no more than a fraction of the millionth of an inch in length<lb/> | ||
like the | like the leg of the one of one the this or the <add>this is the</add> of the <del>one</del> ephemeral animalcula.<lb/> | ||
rendered visible by M<hi rend="superscript">r</hi> Cartwright's | rendered visible by M<hi rend="superscript">r</hi> Cartwright's Solar microscope.</p> | ||
<p>In a word no otherwise than through the | <p>In a word no otherwise than through the medium by<lb/> | ||
the intervention of a | the intervention of a threesided figure or say surface can you<lb/> | ||
form any distinct and correct | form any distinct and correct conception of an angle.</p> | ||
<p>"A | <p>"A mechanical mechanism of two lines"...."touching one another". &c.<lb/> | ||
this will never do: in | this will never do: in regard to one angle this gives us to understand<lb/> | ||
that it is a species of | that it is a species of inclination a species of in relation <add>to</add> <note>to which an inclination<lb/> | ||
is a genus, its genus:<lb/> | is a genus, its genus:<lb/> | ||
<add> | <add>On this point</add> Could they having come in<lb/> | ||
contact | contact, seen countrymen,<lb/> | ||
Aristotle could have set him right</note></p> | Aristotle could have set him right.</note></p> | ||
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{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}}{{Completed}} | ||
1831 May 21
Posology
ulto
II. Morphoscopics.
§. Mixture of Demonstration &
Euclid
☞ Superseded this page, but consultable.
Note here an impropriety of expression into which Euclid
has fallen, and which I as far as I can learn no man hath as
yet brought to view, this is, in the dispensation of the sort of figure in
question, the speaking not of its sides but of its angles: an equilateral
trilateral figure is what he should have said called it: not an
equilateral triangle, or say triangular figure. In other words, it
is by the names of its sides that is what he should have called
it by—not the names of its angles.
The origin of the impropriety, and the imperfectness that
results from it in the point of the ideas planted made to appear in his own mind
other minds, or this. Of angles it is that he speaks treats before he
speaks of lines: whereas it is of lines that he should have
spoken, before he spoke of lines
speaks of lines in number and quantity such as to comprehend
or say enclose and contain a space.
The consequence is—that the idea he gives suggests of an
angle is altogether an indistinct one It is a thing one Is it a
Is it a line only? No it is more than a line. Is it a
surface? No—it is not a surface: it is not amounts not to a compleat surface
be that surface ever so minute: the least number of the lines capable of inclosing
a surface the least number is three: and to constitute an
angle he to constitute this same undefined and undefinable
something, lines he gives not—he allows not more than two—
his two lines may be of the same length one as the other, is of two
different length: they may either of them or both be of any number of
millions of inches in length as in the case of the rags of Lytia,
or if no more than a fraction of the millionth of an inch in length
like the leg of the one of one the this or the this is the of the one ephemeral animalcula.
rendered visible by Mr Cartwright's Solar microscope.
In a word no otherwise than through the medium by
the intervention of a threesided figure or say surface can you
form any distinct and correct conception of an angle.
"A mechanical mechanism of two lines"...."touching one another". &c.
this will never do: in regard to one angle this gives us to understand
that it is a species of inclination a species of in relation to to which an inclination
is a genus, its genus:
On this point Could they having come in
contact, seen countrymen,
Aristotle could have set him right.
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Identifier: | JB/135/105/001"JB/" can not be assigned to a declared number type with value 135. |
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jeremy bentham |
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"superseded this page but consultable" |
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