Without giving it away - there are a couple of approaches I'd try. I'm leaving the details out on purpose so you still have work to do.
1) You can create a pair of similar triangles. One with two sides of 1 and X and the other with the corresponding sides of X and X-squared.
2) You can use the theorem that says two intersecting cords (AB and CD) of a circle cut each other (say at E) so that the product of the parts are the same (AE * EB = CE * ED). If you choose your cords to be perpendicular and the parts to be convenient values (AE=1, CE = ED = X) you can construct the circle and construct EB = X-squared).
At 4:54 PM -0500 11/11/97, Gilles G. Jobin wrote: >Please excuse my very poor English. > >My question might be trivial for many of you, but I really need to >know how to construct a segment measuring the square of the length of >a given segment, using only Euclid's tools. > >Thank you, > >Gilles Jobin