Let it be granted:

i. That a straight line may be drawn from any point to any other point.

ii. That a terminated line may be produced to any length in a straight line.

iii. That a circle may be described from any centre, at any distance from that centre.

Euclid's first 3 Postulates

A new point is determined in Euclidian geometry exclusively in one of the following ways:

Having given four points A,B,C,D, not all incident on the same straight line, then:

Whenever a point P exists which is incident on both (A,B) and on (C,D) that point is regarded as determinate.

1. Whenever a point P exists which is incident both on the straight line (A,B) and on the circle C(D) that point is regarded as determinate.

2. Whenever a point P exists which is incident on both the circles A(B), C(D), that point is regarded as determinate. The cardinal points of any figure determined by a Euclidian construction are always found by means of a finite number of successive applications of some or all of these rules 1, 2, 3.

E.W. Hobson Squaring the Circle. History of the Problem(1913, 7-8)

The term Euclidean construction is used for any construction, whether contained within his works or not, which can be carried out with Euclid’s two operations repeated any finite number of times (Hudson 1915, 1ff.). -These two operations are the drawing of straight lines and circles according to his postulates