JB/135/300/001

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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

---page break---

[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.

---page break---

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.
Date_1	1824-08	Marginal Summary Numbering
Box	135	Main Headings	posology
Folio number	300	Info in main headings field	posology rudiments
Image	001	Titles	euclid b. i prop. i
Category	rudiments sheet (brouillon)	Number of Pages	1
Recto/Verso	recto	Page Numbering	g146
Penner	jeremy bentham	Watermarks
Marginals		Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	46418
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