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1831 Nov. 22


Euclids Imperfections

If, to give expression to your angle, you take any
greater number of those parts, you have then indeed a wedge wedge
but your wedge has a different boundary, a boundary constituted by the remainder
of the circle: the
area of it having
for its boundaries the
two other sides of
the lines which formed
the boundaries of
your first wedge.

The circle being thus divided into 360 parts; the
number of these parts contained in that the circle that
bounds your angle is the number of degrees spoken of as contained
in that same angle: for example an angle of 45 degrees
is an angle the two constituent sides of which
terminate respectively in 45 out of the 360 degrees into
which your circle is considered as divided

Note here that for conveying a clear and correct
conception of an angle, a right line will be better
adapted than a curve line: for by the idea a curve line, the mind
is led to a complicated description on the subject of the relation
borne by the different species of curves, to one another,
and to a right line: and, for this, the wedge, the
base of which is a correspondent portion of the inscribed polygon,
or the wedge which is the basis of the correspondent portion of a circumscribed
polygon may, either of them, serve. This done, you
have a right lined triangle, of which [in the case, the this case the of the inscribed
wedge or say sector,] the base is the secant of the circle,
and the two sides the line by the meeting of which at the ends
a triangle — an isosceles triangle species of triangle — namely that called an isosceles triangle — is formed.

Note however that though the section is thus inappropriately,
denominated, the secant is appropriately
denominated: for by it the circle is actually cut,
[+] Take a Chester cheese
[+] The form of a
Chester cheese
is the an exemplification
of that of
solid species of solid called a cylinder.
Take one of these
cylinders &

apply a knife to it at right
angles to the upper circular surface of the cylinder, in such manner
as to cut through the cheese in that same direction with
the line which the knife has drawn on that same surface
is a secant of that circle: and is likewise the line
described at the bottom of the cylinder
in the place at which that same bottom has been cut through.

Of To this same isosceles triangle gives legs
as long as those which would terminate in a fixt stay
you give increase to your triangle — increase
in exact proportion to their length; but you give an increase
to your angle

Identifier: | JB/135/160/001
"JB/" can not be assigned to a declared number type with value 135.



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