“The simultaneousness of states of mind in the work of art: that is the intoxicating aim of our art... In the pictorial description of the various states of mind of a leave-taking, perpendicular lines, undulating lines and as it were worn out, clinging here and there to silhouettes of empty bodies, may well express languidness and discouragement. Confused and trepidating lines, either straight or curved, mingled with the outlined hurried gestures of people calling to one another will express a sensation of chaotic excitement. On the other hand, horizontal lines, fleeting, rapid and jerky, brutally cutting in half lost profiles of faces or crumbling and rebounding fragments of landscape, will give the tumultuous feelings of the person going away.”

— Umberto Boccioni

Source: 1912, Les exposants au public', 1912, pp. 47, 49

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Umberto Boccioni 41

Italian painter and sculptor 1882–1916

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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 (1711–1787) Croat-Italian physicist

"Boscovich's mathematics", an article by J. F. Scott, in the book Roger Joseph Boscovich (1961) edited by Lancelot Law Whyte.
"Transient pressure analysis in composite reservoirs" (1982) by Raymond W. K. Tang and William E. Brigham.
"Non-Newtonian Calculus" (1972) by Michael Grossman and Robert Katz.

“Naturally man tended to lose his sense of scale and relation. A straight line, or a combination of straight lines, may have still a sort of artistic unity, but what can be done in art with a series of negative symbols? Even if the negative were continuous, the artist might express at least a negation; but supposing that Omar's kinetic analogy of the ball and the players turned out to be a scientific formula! supposing that the highest scientific authority, in order to obtain any unity at all, had to resort to the middle-ages for an imaginary demon to sort his atoms! how could art deal with such problems, and what wonder that art lost unity with philosophy and science! Art had to be confused in order to express confusion; but perhaps it was truest, so.”

Henry Adams (1838–1918) journalist, historian, academic, novelist

<p>Adams alludes to a well-known passage from the Rubaiyat of Omar Khayyam. In Edward FitzGerald's translation:</p><p>The Ball no Question makes of Ayes and Noes,
But Right and Left as strikes the Player goes;
And He that toss'd Thee down into the Field,
He knows about it all — HE knows — HE knows!</p>
Mont Saint Michel and Chartres (1904)

“On a Clear Day: Art work that is completely abstract - free from any expression of the environment is like music and can be responded to in the same way. Our response to line and tone and color is the same as our response to sounds... It holds meaning for us that is beyond expression in words.
These prints [title, 'On a Clear Day'] express innocence of mind. If you can go with them and hold your mind as empty and tranquil as they are and recognize your feelings at the same time you will realize your full response to this work.”

Agnes Martin (1912–2004) American artist

a passage Martin wrote in 1975 'On a Clear Day', 15 Oct. 1975. Printed in Agnes Martin, eds. Morris and Bell, p. 124
1970's

“The straight line belongs to Man. The curved line belongs to God.”

Antoni Gaudí (1852–1926) Catalan architect

The real author seems to be Pierre Albert-Birot https://books.google.com/books?id=3Ul51CwjUOcC&pg=PA290&dq=%22the+curved+line+that+belongs+let%27s+say+to+God+and+the+straight+line+that+belongs+to+man%22&hl=de&sa=X&redir_esc=y#v=onepage&q=%22the%20curved%20line%20that%20belongs%20let%27s%20say%20to%20God%20and%20the%20straight%20line%20that%20belongs%20to%20man%22&f=false.
Attributed

“I don't know what they call mysticism, it is in truth perhaps the interest of the spirit; that the work expresses the spirit, and not the formal aspect. While in the United States a lot of art production runs along the line of formalist art; what one could call the post-modernism, a kind of formalist intention like Don Judd, Carl Andre, Robert Morris, and these.”

Joseph Beuys (1921–1986) German visual artist

Source: 1970's, Interview with Louwrien Wijers, 1979, p. 243; Also cited in: Louwrien Wijers (1996). Writing as Sculpture: 1978 - 1987. p. 38

“"As the crow flies"—a popular and picturesque expression to denote a straight line.”

William Henry Maule (1788–1858) British politician

Stokes v. Grissell (1854), 23 L. J. Rep. Part 7 (N. S.), Com. PL 144.

“However, new plasticism is pure painting [in contrast with the opinion of Theo van Doesburg, then]: the means of expression still are form and color, though these are completely interiorized; the straight line and flat color remain purely pictorial means of expression.”

Piet Mondrian (1872–1944) Peintre Néerlandais

1910's, Natural Reality and Abstract Reality', 1919

“Our course of advance … is neither a straight line nor a curve. It is a series of dots and dashes.”

Benjamin N. Cardozo (1870–1938) United States federal judge

Other writings, The Paradoxes of Legal Science (1928)
Context: Our course of advance... is neither a straight line nor a curve. It is a series of dots and dashes. Progress comes per saltum, by successive compromises between extremes, compromises often … between "positivism and idealism". The notion that a jurist can dispense with any consideration as to what the law ought to be arises from the fiction that the law is a complete and closed system, and that judges and jurists are mere automata to record its will or phonographs to pronounce its provisions.

“Our minds are artists,
always drawing lines.

Making decisions, differentiating
One thing from another,
Calling it something.

This is the way we know.
This is how we think.

We define
by drawing the line.”

Alex Grey (1953) American artist

Art Psalms (2008), Let Love Draw the Line

“Instead of opposing comic and tragic characters [as Molière and Shakespeare] and contrary scenic states, I organize the opposition of contrasting values, lines, and curves. I oppose curves to straight lines, flat surfaces to molded forms, pure local colors to nuances of gray. These initial plastic forms are either superimposed on objective elements or not, it makes no difference to me. There is only a question of variety.”

Fernand Léger (1881–1955) French painter

Quote from 'Notes on Contemporary Plastic Life', 'Kunstblatt', Berlin 1923; as quoted in The documents of 20th century art – Functions of Painting by Fernand Léger, in Thames and Hudson Ltd, London 1973, p. 25
Quotes of Fernand Leger, 1920's

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Umberto Boccioni 41

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