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1824 Aug.
Posology Rudiments
II Morphoscopics
146
Euclid. B.1. Prop. 1
Problem how to describe a
triangle having its three
sides equal. Description of the
Contrivance.
Draw two circles by
the same radius: all the
radii that can be drawn
whether in the one or in the
other will be equal. [1]
The first circle you
draw will give you two
radii that will form two
sides of your triangle: the
second will you the third circle will give you a
line which will make the third
side: the position of it
must be such, that its two
points join the one of them
the one, the others the other
of the two sides with
which you were furnished
by the first triangle
Of In these
two triangles one line namely
that which served as a
radius for drawing them
is common to both: and
to this line the two other
lines one being a radius
of the one circle the
other a radius of the
other can not but be equal
For drawing a three
sided figure with its
sides all equal to
one another, the contrivance
consists in the
drawing of two circles
by means of the same
right line the first
circle being drawn by
keeping the left end
fixt while the right
end is revolving: the
other circle by keeping
the right end
while the left end is
revolving
[2] Make each of the three
sides a radius either of
both circles, or what
comes to the same thing
of one of them, thus
will all the three sides
be equal to one another
The equality is constituted caused,
and demonstrated
to have place,
by identity: identity
of the instrument by
which the three boundaries
of the figure
are delineated.
These two circles will
now be seen cutting one
another at two points
the one above the line
resting on its first points;
call these the
the other
underneath it. Call
these the upper and
lower points of intersection.
From the left
end of the line
To the upper
point of intersection
draw one a second line from the
left end of the first
drawn line: then a
third line from the other
end of that same first
drawn line. You will
thus have one three
sided figure with
all its sides equal to
one another one being drawn
by
by one and the same right
line
page break
Morphoscopic
Medium of Demonstration
or
Contrivance
For an example
of it take in the case of
a Curve Section, whether
the result of the analytic
or the synthetic
method, the axis.
Shew how the figure of
the curve is measured
by perpendiculars drawn
from different parts of it
to the axis.
The physical archetype in
this case is the axis
of a wheel: of the
wheel for example
of a carriage.
The contrivance consists
in having the
three sides of the
figure constituted
by one and the same
right line. These
three lines meet at
three places which
are so many corners
or say angles. These
two circles are described
by one and the same
radius: namely the
same right line
Draw a line in the same
manner from each end
of the first drawn line
to the point of the intersection
of the two circles
which is underneath
it You will have now
three equilateral three
sided figures of the
the same form and size
with the first — call it
the lowermost of the
two contiguous triangles.
For — 3d, 4th &c
power put 3d 4th
multiplication
or multiplicate
of the 3d, 4th
Order.
Identifier:  JB/135/300/001 "JB/" can not be assigned to a declared number type with value 135.



182408 

135 
posology 

300 
posology rudiments 

001 
euclid b. i prop. i 

rudiments sheet (brouillon) 
1 

recto 
g146 

jeremy bentham 

46418 
