“[the double line in his paintings] is still one line, as in the case of your grooves [= the wide sunken lines in the relief's, the artist Gorin made then]... In my last things the double line widens to form a plane, and yet it remains a line. Be that as it may, I believe that this question is one of those which lie beyond the realm of theory, and which are of such subtlety that they are rooted in the mystery of 'art.”

— Piet Mondrian

But all that is not yet clear in my mind.
Quote in Mondrian's letter to artist Gorin, [who stated that the double line broke the necessary symmetry], 31 January, 1934; as quoted in Mondrian, - The Art of Destruction, Carel Blotkamp, Reaktion Books LTD. London 2001, p. 215
1930's

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Piet Mondrian 95

Peintre Néerlandais 1872–1944

Howard P. Robertson (1903–1961) American mathematician and physicist

Geometry as a Branch of Physics (1949)

“Every measurable thing except numbers is imagined in the manner of a continuous quantity. Therefore, for the mensuration of such a thing, it is necessary that points, lines, and surfaces, or their properties, be imagined. For in them… measure or ratio is initially found… Therefore, every intensity which can be acquired successively ought to be imagined by a straight line perpendicularly erected on some point of the space or subject of the intensible thing, e. g., a quality… And since the quantity or ratio of lines is better known and is more readily conceived by us—nay the line is in the first species of continua, therefore such intensity ought to be imagined by lines… Therefore, equal intensities are designated by equal lines, a double intensity by a double line, and always in the same way if one proceeds proportionally.”

Nicole Oresme (1323–1382) French philosopher

Tractatus de Configurationibus et Qualitatibus et Motuum (c. 1350)

“i still have no way to survive but to keep writing one line, one more line, one more line…”

Yukio Mishima (1925–1970) Japanese author

“On a double-log plot, my grandmother fits on a straight line.”

Fritz Houtermans (1903–1966) German physicist

as quoted in Herbert Kroemer's Autobiography http://nobelprize.org/nobel_prizes/physics/laureates/2000/kroemer-autobio.html, The Nobel Prize in Physics 2000.

“Still haunted by Haiku, and tried my hand at it, but I fall pitifully short of the Wordsworthian touch. But failure in this realm turned my mind to an old enthusiasm of mine, the Welsh englyn. This verse form was derived by the Welsh from the inscriptions which their Roman conquerors put on tombs … A good englym must have four lines, of ten, then six, syllables, the last two lines having seven syllables each. In the first line there must be a break after the seventh, eighth, or ninth syllable, and the rhyme with the second line comes at this break; but the tenth syllable of the first line must either rhyme or be in assonance with the middle of the second line. The last two lines must rhyme with the first rhyme in the first line, but the third or fourth line must rhyme on a weak syllable. Got that?”

Robertson Davies (1913–1995) Canadian journalist, playwright, professor, critic, and novelist

"Haiku and Englyn" in The Toronto Daily Star (4 April 1959), republished in The Enthusiasms of Robertson Davies (1979) edited by Judith Skelton Grant, p. 241.

“Always lines, never forms. Where do they find these lines in Nature? Personally I see only forms that are lit up and forms that are not, planes that advance and planes that recede, relief and depth. My eye never sees outlines or particular features or details… …My brush should not see better than I do.”

Francisco De Goya (1746–1828) Spanish painter and printmaker (1746–1828)

Goya, in a recall of an overheard conversation
conversation of c. 1808, in the earliest biography of Goya: Goya, by Laurent Matheron, Schulz et Thuillié, Paris 1858; as quoted by Robert Hughes, in: Goya. Borzoi Book - Alfred Knopf, New York, 2003, p. 176
probably not accurate word for word, but according to Robert Hughes it rings true in all essentials, of the old Goya, in exile
1800s

“But the Moderns advancing yet much farther, have receiv'd into Geometry all Lines that can be express'd by Æquations, and have distinguish'd, according to the Dimensions of the Æquations, those Lines into Kinds; and have made it a Law, that you are not to construct a Problem by a Line of a superior Kind, that may be constructed by one of an inferior one.”

Isaac Newton book Arithmetica Universalis

Arithmetica Universalis (1707)
Context: The Antients, as we learn from Pappus, in vain endeavour'd at the Trisection of an Angle, and the finding out of two mean Proportionals by a right line and a Circle. Afterwards they began to consider the Properties of several other Lines. as the Conchoid, the Cissoid, and the Conick Sections, and by some of these to solve these Problems. At length, having more throughly examin'd the Matter, and the Conick Sections being receiv'd into Geometry, they distinguish'd Problems into three Kinds: viz. (1.) Into Plane ones, which deriving their Original from Lines on a Plane, may be solv'd by a right Line and a Circle; (2.) Into Solid ones, which were solved by Lines deriving their Original from the Consideration of a Solid, that is, of a Cone; (3.) And Linear ones, to the Solution of which were requir'd Lines more compounded. And according to this Distinction, we are not to solve solid Problems by other Lines than the Conick Sections; especially if no other Lines but right ones, a Circle, and the Conick Sections, must be receiv'd into Geometry. But the Moderns advancing yet much farther, have receiv'd into Geometry all Lines that can be express'd by Æquations, and have distinguish'd, according to the Dimensions of the Æquations, those Lines into Kinds; and have made it a Law, that you are not to construct a Problem by a Line of a superior Kind, that may be constructed by one of an inferior one. In the Contemplation of Lines, and finding out their Properties, I like their Distinction of them into Kinds, according to the Dimensions thy Æquations by which they are defin'd. But it is not the Æquation, but the Description that makes the Curve to be a Geometrical one.<!--pp.227-228

“The glove has been thrown to the ground,
The last choice of weapons made.
A book for one thought.
A poem for one line.
A line for one word.”

Eugene McCarthy (1916–2005) American politician

"Courage After Sixty"
Poems

“For Space, when the position of points is expressed by rectilinear co-ordinates, ds = \sqrt{ \sum (dx)^2 }; Space is therefore included in this simplest case. The next case in simplicity includes those manifoldnesses in which the line-element may be expressed as the fourth root of a quartic differential expression…. I restrict myself… to those manifoldnesses in which the line element is expressed as the square root of a quadric differential expression…. Manifoldnesses in which, as in the Plane and in Space, the line-element may be reduced to the form \sqrt{ \sum (dx)^2 }, are… only a particular case of the manifoldnesses to be here investigated; they require a special name, and therefore these manifoldnesses… I will call flat. In order now to review the true varieties of all the continua which may be represented in the assumed form, it is necessary to get rid of difficulties arising from the mode of representation, which is accomplished by choosing the variables in accordance with a certain principle.”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

“Only now [1943] I become conscious that my work in black, white and little color planes has been merely 'drawing' in oil color. In drawing, the lines are the principal means of expressions... In painting, however, the lines are absorbed by the color planes; but the limitations of the planes show themselves as lines and conserve their great value.”

Piet Mondrian (1872–1944) Peintre Néerlandais

note from his postcard, late May 1943; as quoted in Mondrian, - The Art of Destruction, Carel Blotkamp, Reaktion Books LTD. London 2001, p. 240
1940's

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Piet Mondrian 95

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