Diagonal Quotes
With regard to the diagonal, too, I am in complete agreement with you [with Theo van Doesburg ]. As soon as it appears together with straight [horizontal and vertical] lines, I believe it should be condemned... A while back I started a thing entirely in diamonds [diamond-shape] like this [his sketch in the letter of several diamond-forms]. I have to find out if it's possible: intellectually I'm inclined to say it is. There's something to be said for the idea, because perpendicular and flat lines can be seen everywhere in nature; by using a diagonal line I would be canceling that out. But I'm inclined to say that this cannot be combined with perpendicular and flat lines or with different kinds of slanting lines.
Piet Mondrian
But we're still left with structural or compositional elements. The problems aren't any different. I still have to compose a picture, and if you make an object [as Donald Judd does] you have to organize the structure. I don't think our work that radical in any sense because you don't find any really new compositional or structural element. I don't know if that exists. It's like the idea of the color you haven't seen before. Does something exist that's as radical as a diagonal that's not a diagonal? Or a straight line or a compositional element that you can't describe?
Frank Stella
The Pythagoreans discovered the existence of incommensurable lines, or of irrationals. This was, doubtless, first discovered with reference to the diagonal of a square which is incommensurable with the side, being in the ratio to it of √2 to 1. The Pythagorean proof of this particular case survives in Aristotle and in a proposition interpolated in Euclid's Book X.; it is by a reductio ad absurdum proving that, if the diagonal is commensurable with the side, the same number must be both odd and even. This discovery of the incommensurable... showed that the theory of proportion invented by Pythagoras was not of universal application and therefore that propositions proved by means of it were not really established.... The fatal flaw thus revealed in the body of geometry was not removed till Eudoxus discovered the great theory of proportion (expounded in Euclid's Book V.), which is applicable to incommensurable as well as to commensurable magnitudes.
Thomas Little Heath