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JB/135/292/001

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Completed

1824 April 23. M

Alegomorphic
126

3.

6.
Equality of lines — the
idea founded on that of
identity. Euclid aware
of this when he proved
the equality of two
by a circle:
method of making
a circle on sand.

Of the idea we have of equality as applied to
lines the foundation is the idea of identity.

Of this truth it appears that Euclid had a conception
more or less explicit when for proof of equality as
between two lines he made use of the figure of a circle
He delineated suppose upon paper a figure which he
called a circle. Instead of paper, the production of
comparatively modern times, it wd. have been better to
have taken a small piece of ground covered with sand
which had existence in all times: in any rate in all times
we have any acquaintance with. Now then having occasion
to exhibit the figure of a circle on this sand, what
is the course he wd. take? Settling, upon a rough estimate,
the size of the circle he proposed to make, he wd. take
the first dry twig he happened to meet with, and reducing
it to its intended length, he wd. apply it to the
purpose of forming his intended circle. A circle then in
what way was it to be formed? One way there was, & in
the nature of the case there wd. be but one: this was
the fixing on some part of its length, no matter what,
& keeping that part pinned down constantly to the
same spot, making the other parts move round till they
came back to the same position they maintained at
first. if this point were any other than one of the two
extremities he wd. be making 2 circles one within the other,
but what he was in need of was one circle & no more; he
wd

Identifier: | JB/135/292/001
"JB/" can not be assigned to a declared number type with value 135.

1824-04-23

6

135

posology

292

posology

001

copy/fair copy sheet

1

recto

e3 / g126

richard doane

46410