I think it would help if you told us what a "mira" was. I've never heard this term and a quick search of Wikipedia didn't help me. You don't mean mirror I suppose?
It's not a mirror, actually. It does kind of work like one. Here is a picture of one: http://www.enasco.com/prod/images/pr.../VC121881t.jpg
Thanks for that. Since I've never seen anything like it before it's a bit hard to advise you,
but I'd do something like this.
Draw a straight line that will be one side of the square.
Use the Mira to draw a perpendicular to the first line. You can do that by using the Mira to bisect the "angle" of the straight line which is two right angles.
Then you can do the same thing twice more to get a rectangle.
Then bisect the angle at one of the corners to find out and draw that line. It will meet the opposite side where the other corner of the square should have been.
There are other ways do it though. For example you could draw a straight line, bisect it,
draw the perpendicular there. Then construct a right angle at one end of the first line, bisect that again. That would give you an isosceles triangle with a right angle. The two short sides of the triangle are two half diagonals of the square, the long side is one side of the square, or if you prefer the long side is a diagonal and the short sides two sides of the square.