The Greek historian Herodotus writes of the origins of geometry in Egypt:

They say that that king [Sesostri, ca. 2000 a. C.] distributed the land among all of the Egyptians, each one having an equal lot in the a square shape, and from these subdivisions obtained tribute, having imposed an annual payment. If the river bore away a part, the owner announced the loss, and officials were sent to observe the extent to which the plot had been diminished for the purpose of adjusting the tribute payment. It is my feeling that this indicates the invention of geometry here, prior to its passing to Greece.

Geometry - literally earth measurement, was the responsibility of the "arpedonapti", those who knot ropes.

It is by tightening ropes that they drew the two simplest and most important lines in geometry: the straight line and the circle. The first, simply tightening a rope between two points, a kind of operation which image is still present in the expressions "to draw a line", "to draw a perpendicular"; the second, making one of the two points turn around the other which is held fixed.

So the suggestion is that the "earth measuring arpedonapti" of ancient used only lines and circles and this was the art inherited by the Greeks. (I'm not entirely convinced.)

Euclid makes no reference to the edge and compass in his axioms.

Source : The Garden of Archimedes.

The Greek historian Herodotus writes of the origins of geometry in Egypt:

They say that that king [Sesostri, ca. 2000 a. C.] distributed the land among all of the Egyptians, each one having an equal lot in the a square shape, and from these subdivisions obtained tribute, having imposed an annual payment. If the river bore away a part, the owner announced the loss, and officials were sent to observe the extent to which the plot had been diminished for the purpose of adjusting the tribute payment. It is my feeling that this indicates the invention of geometry here, prior to its passing to Greece.

Geometry - literally earth measurement - was the responsibility of the "arpedonapti", those who knot ropes.

It is by tightening ropes that they drew the two simplest and most important lines in geometry: the straight line and the circle. The first, simply tightening a rope between two points, a kind of operation which image is still present in the expressions "to draw a line", "to draw a perpendicular"; the second, making one of the two points turn around the other which is held fixed.

So the suggestion is that the "earth measuring arpedonapti" of ancient Egypt used only lines and circles and this was the art inherited by the Greeks. (I'm not entirely convinced.)

Euclid makes no reference to the edge and compass in his axioms.

Source : The Garden of Archimedes.