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# JB/135/229/001

Completed

1828 Sept. 21 4
Posology

Morphoscopic
27
Contrivance

4

Euclid's Elements Book I. Propositions 1
Contrivance

In

Problem. How to describe an Equilateral Triangle

Contrivance.

In this case the contrivance consists in marking
out by the turning about of the same rod, two circles, without any change
in the situation of the whole: one, by the rod first at one in its situation: only in the first turn keep to the point at one end
and, the other by the same rod first at the other end, first, in the other turn keeping the point at the other end fixt.
The two lines will Thus will be marked out two circles
cutting one another: and by at two points: and by drawing
from each of these two points a pair of lines one to each
end of the rod when restored to its first position you will
have delineated two three sided figures opposite to each other top to bottom, or back to back figures
the sides of which being formed by the same marks left
by one and the same instrument, in its course.

In D'Alembert's Mélanges de littérature et de
Philosophie
Tome — in speaking of morphoscopic
Posology (though not under that name) mentioned a need
of the principle of super-position, as being employed
by Euclid in the fourth Proposition of that same work

In this principle of super-position, may be seen another
of these Contrivances.

This is a means medium of demonstration only: demonstration
without effectuation

By In the case of The synthetic mode of generating a circle as
above the contrivance is a medium of effectuation
and demonstration at the same time.

Identifier: | JB/135/229/001
"JB/" can not be assigned to a declared number type with value 135.

1828-09-21

135

posology

229

posology

001

euclid's elements book i proposition 1 / problem how to describe an equilateral triangle / contrivance

text sheet

1

recto

d4 / e4 / g27

jeremy bentham

46347