Construction (with only a ruler and compass)

Surprisingly  there is quite a few things that you can construct with just a ruler and a compass such as

1. A triangle of sides a,b,c
2. A square of side a
3. a perpendicular bisector
4. A square inside a circle
5. A regular hexagon inside a circle
6. An (equilateral) triangle inside a circle

For the first one note that a triangle can not be constructed if a+b>c

•  Starting at one end of the length of a, with the compass stretch out to the lenght of b, mark an arch. do a similar process for the length of a at the other end of a.
• The intersection of the two arcs will be the third point in the abc triangle. 

In drawing a perpendicular bisector to a line AB

• With the compass get the length of AB
• At both ends of AB, using the compass and keeping the length of AB, draw a large enough arc so that there is two intersection
• Align the ruler with the two intersection and draw a line (the resulting line is the perpendicular bisector)

 A square inside a circle
This construction is quite similar to the previous one. In a circle with diameter AB

• draw a perpendicular bisector like before and long enough that the bisector instersects the circle on both end
• Connect the 4 points on the circle which yields a square in the circle

Unanswered Question

1. Was there any practical application, back then,  of constructing with just a ruler and a compass?

Evaluation:
Complexity: 4
Interesting: 5
Quality: 8