Except if we add something else : For instance some device to draw parallel lines etc.

To draw pairs of parallel lines, we may use the two parallel edges of a ruler, with width d.

The "axioms" are then :

- [C1] We may draw a line through two known points.
- [C2] We may draw a parallel line at distance d from a known line, d being the width of the ruler.
- [C3] We may draw, through two known points A and B, a line through A and a parallel line through B at distance d, if AB > d.
- Get new points by intersections of such together, or with known lines.

By using just these constructions [C1] [C2] [C3] above, to construct :

- A parallel through any given point to any given line Hint
- A perpendicular through any given point to any given line Hint

Can we discard axiom [C3] for these constructions ? Hint

More complicated : to construct an equilateral triangle ? an hexagon ? octogon ? dodecagon ?
Hint

A regular pentagon ? decagon ? etc ?
Hint

Same question : can we discard axiom [C3] ?
Hint