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<p>Note how an impropriety of expression into which Euclid<lb/> | <p>Note how an impropriety of expression into which Euclid<lb/> | ||
has fallen, and which <del>I</del> as far as I can learn no more < | has fallen, and which <del>I</del> as far as I can learn no more <unclear>hath</unclear> as<lb/> | ||
yet brought to view, this is, in the disposition of the <add>sort of</add> figure in<lb/> | yet brought to view, this is, in the disposition 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 said<add>called it</add>. not an<lb/> | 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 <unclear>masses</unclear> of its sides <del>that</del> is what he should have called<lb/> | |||
it by - not the names of its angles.</p> | it by - not the names of its angles.</p> | ||
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or say enclose, and embrace a space.</p> | or say enclose, and embrace a space.</p> | ||
<p>The consequence is - that the he gives<add>suggests</add> | <p>The consequence is - that the idea he gives<add>suggests</add> of an<lb/> | ||
angle is altogether one instruction one <del>It is a thing</del><add>one</add> Is it a<lb/> | angle is altogether one instruction 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<lb/> | Is it a line only? No it is more than a line. Is it a<lb/> | ||
surface? No - it is not a surface: it is <add>amounts not to</add>not a <sic>compleat</sic> surface<lb/> | surface? No - it is not a surface: it is <add>amounts not to</add>not a <sic>compleat</sic> surface<lb/> | ||
be that surface ever so | be that surface ever so <unclear>minute</unclear>: <add>the least number</add>of the line capable of <unclear>inclosing</unclear><lb/> | ||
a surface the least number is three: and to constitute an<lb/> | a surface the least number is three: and to constitute an<lb/> | ||
angle <del>he</del> to constitute the same < | angle <del>he</del> to constitute the same <unclear>undefined</unclear> and undefinable<lb/> | ||
something, <add>lines</add> he gives not — he allows not more than two<lb/> | something, <add>lines</add> he gives not — he allows not more than two<lb/> | ||
his two lines may be of the same length one as the other, is of two<lb/> | his two lines may be of the same length one as the other, is of two<lb/> | ||
different length they may either of them or both be of any number of<lb/> | different length: they may either of them or both be of any number of<lb/> | ||
millions of inchs in length as in the case of the rags if higher,<lb/> | millions of inchs in length as in the case of the <unclear>rags</unclear> if higher,<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 <gap/> of the one of one <add>this is the</add> of the <del><gap/></del> <unclear>ephemerial animalcule</unclear><lb/> | like the <gap/> of the one of one <add>this is the</add> of the <del><gap/></del> <unclear>ephemerial animalcule</unclear><lb/> | ||
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<p>In a word no otherwise than through the machine by<lb/> | <p>In a word no otherwise than through the machine by<lb/> | ||
the intervention of a <unclear> | the intervention of a <unclear>threesided</unclear> figure or say surface can you<lb/> | ||
form any distinct and correct <gap/>place of an angle</p> | form any distinct and correct <gap/>place of an angle</p> | ||
<p>"A <gap/> < | <p>"A <gap/> <unclear>inclination</unclear> of two lines"...."touching one another".<gap/><lb/> | ||
this will never do: in reg<gap/> to an angle this gives us to understand<lb/> | this will never do: in reg<gap/> to an angle this gives us to understand<lb/> | ||
that it is a species of <unclear> | that it is a species of <unclear>inclination</unclear> a species of in relation <add>to</add> <note>to which an <unclear>inclination</unclear><lb/> | ||
is a genus, its genus:<lb/> | is a genus, its genus:<lb/> | ||
<add>an th<gap/>v<gap/></add> Could they <gap/> <gap/><lb/> | <add>an th<gap/>v<gap/></add> Could they <gap/> <gap/><lb/> | ||
1831 May 21
Posology ult
II Morphoscopics
S M of Demonstration
Euclid
Superseded this page, but consultable
Note how an impropriety of expression into which Euclid
has fallen, and which I as far as I can learn no more hath as
yet brought to view, this is, in the disposition 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 saidcalled it. not an
equilateral triangle, or say triangular figure. In other words, it
is by the masses 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 speakstrials before he
speaks of linesin: hra of lines that he should have
spoke, before he spoke of lines
speaks of lines in number and such as to comprehend
or say enclose, and embrace a space.
The consequence is - that the idea he givessuggests of an
angle is altogether one instruction one It is a thingone 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 amounts not tonot a compleat surface
be that surface ever so minute: the least numberof the line capable of inclosing
a surface the least number is three: and to constitute an
angle he to constitute the 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 inchs in length as in the case of the rags if higher,
or if no more than a fraction of the millionth of an inch in length
like the of the one of one this is the of the ephemerial animalcule
rendered visible by Mr Cartwright's Solus microscope.
In a word no otherwise than through the machine by
the intervention of a threesided figure or say surface can you
form any distinct and correct place of an angle
"A inclination of two lines"...."touching one another".
this will never do: in reg to an 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:
an thv Could they
contact his countrymen
Aristotle could have set him right
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