7.1
Draw a circle with centre O and radius OA=1. Draw the
diameters AA' and BB', at right angles. With centres on
the diameter BB' draw two circles, each having radius
of half that of the original circle. From point A swing
an arc NM which is tangent to the circumferences of the
two inner circles. Repeat from point A'. Construct square
ACB'O from the radius of the original circle.
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7.2
The arc which lies tangent to the two inner circles cuts
the outer unity circle at exactly the point which gives
the side of a regular pentagon inscribed in the outer
circle, measured from the extreme upper end of the vertical
diameter to the left at J and to the right at F. In addition,
draw a circle centred at A' and tangential to the near
curve of the two inner circles, we obtain the exact length
of a third side of the pentagon, touching the outer circle
to the left at H and to the right at G. |
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7.3
Enclose the initial circle in a square. Then draw a circle
by using the centre of the initial circle as centre, and
the distance to the tip of the vesica as radius.
This circle will be equal in perimeter to the perimeter
of the square which is tangent to the initial circle. |
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