Rectification of a circumference by the method of Archimedes
In the first place, we are going to divide the diametre of the circumference that we are going to rectify into seven equal parts
to then place three times the diameter of the circumference plus a seventh
We have the circumference they give us with radius 'r',
we are going to take a diametre
and we are going to divide into seven parts equals
To do it,
we are going to use the Tales Theorem
we are going to take a any auxiliar line which forms an angle with the diameter
we are going to put seven units
the last we will join it with the extreme of the diameter of the circumference
We are going to do the parallels lines and we already have to the diametre divides into seven parts equals
Now, we are going to draw a any line
and we are going to take the diametre measure
and we are going to take
from the beginning, the diameter three times
Once the three marks are drawn
we are going to take the measure of the a seventh of the circumference
There is! And we will put it below
As we said at the beginning
on a line, the measurement of the diameter of the circumference is placed three times plus one seventh of the same
This length is the rectification that have it a value of 2ℼr
that is to say,
rectification of the given circumference
