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1831 May 21
II. Morphoscopics.
§. Mixture of Demonstration &

☞ Superseded this page, but consultable.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.

Identifier: | JB/135/105/001
"JB/" can not be assigned to a declared number type with value 135.



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c2 / d7


jeremy bentham



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"superseded this page but consultable"

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