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For – to say a few words on technique – whereas the curved line was used predominantly for reasons of beauty, (Phidias, Michelangelo, Raphael, Rubens) it has been used more and more economically for reasons of truth (Millet, Monet, Paul Cézanne) until it will end as the straight line for reasons of Love. This will enable the art of the future to create an international form; a form understandable to all and vital enough to the expression of a general feeling of love in a monumental way. Such is the future.
--
'Onafhankelijke bespiegelingen over de kunst’, in De Avondpost 23 January 1916

 

Theo van Doesburg

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But if some mind very different from ours were to look upon some property of some curved line as we do on the evenness of a straight line, he would not recognize as such the evenness of a straight line; nor would he arrange the elements of his geometry according to that very different system, and would investigate quite other relationships as I have suggested in my notes.
We fashion our geometry on the properties of a straight line because that seems to us to be the simplest of all. But really all lines that are continuous and of a uniform nature are just as simple as one another. Another kind of mind which might form an equally clear mental perception of some property of any one of these curves, as we do of the congruence of a straight line, might believe these curves to be the simplest of all, and from that property of these curves build up the elements of a very different geometry, referring all other curves to that one, just as we compare them to a straight line. Indeed, these minds, if they noticed and formed an extremely clear perception of some property of, say, the parabola, would not seek, as our geometers do, to rectify the parabola, they would endeavor, if one may coin the expression, to parabolify the straight line.

 

Roger Joseph Boscovich

 

I don't want to know the reasons why,
Love keeps right on walking down the line.

 

Stevie Nicks

 

If you add something to a painting, never let it be for aesthetic reasons. Only let it be for reasons of expression.

 

Asger Jorn

 

This new plastic idea will ignore the particulars of appearance, that is to say, natural form and colour. On the contrary, it should find its expression in the abstraction of form and colour, that is to say, in the straight line and the clearly defined primary colour. (on neo-plasticism, fh)

 

Piet Mondrian

 

The new plastic idea cannot, therefore, take the form of concrete representation, although the latter does always indicate the universal to a degree, or at least conceal it within. This new plastic idea will ignore the particulars of appearance, that is to say, natural form and colour. On the contrary it should find its expression in the abstraction of form and colour, that is to say, in the straight line and the clearly defined primary colour.

 

Piet Mondrian