“The line has in itself neither matter nor substance and may rather be called an imaginary idea than a real object; and this being its nature it occupies no space. Therefore an infinite number of lines may be conceived of as intersecting each other at a point, which has no dimensions and is only of the thickness (if thickness it may be called) of one single line.”

—  Leonardo Da Vinci

The Notebooks of Leonardo da Vinci (1883), II Linear Perspective

Adopted from Wikiquote. Last update Sept. 27, 2023. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The line has in itself neither matter nor substance and may rather be called an imaginary idea than a real object; and …" by Leonardo Da Vinci?
Leonardo Da Vinci photo
Leonardo Da Vinci 363
Italian Renaissance polymath 1452–1519

Related quotes

John Wallis photo

“[W]hereas Nature, in propriety of Speech, doth not admit more than Three (Local) Dimensions, (Length, Breadth and Thickness, in Lines, Surfaces and Solids;) it may justly seem improper to talk of a Solid (of three Dimensions) drawn into a Fourth, Fifth, Sixth, or further Dimension.
A Line drawn into a Line, shall make a Plane or Surface; this drawn into a Line, shall make a Solid. But if this Solid be drawn into a Line, or this Plane into a Plane, what shall it make? A Plano-plane? This is a Monster in Nature, and less possible than a Chimera or a Centaure. For Length, Breadth and Thickness, take up the whole of Space.”

John Wallis (1616–1703) English mathematician

Nor can our Fansie imagine how there should be a Fourth Local Dimension beyond these Three.
Treatise of Algebra (1685)

John Dee photo

“Neither the circle without the line, nor the line without the point, can be artificially produced. It is, therefore, by virtue of the point and the Monad that all things commence to emerge in principle.
That which is affected at the periphery, however large it may be, cannot in any way lack the support of the central point.”

John Dee (1527–1608) English mathematican, astrologer and antiquary

Theorem II
Monas Hieroglyphica (1564)

“These formulae [in (1) and (2) above] may be shown to be valid for a circle or a triangle in the hyperbolic plane… for which K < 0. Accordingly here the perimeter and area of a circle are greater, and the sum of the three angles of a triangle are less, than the corresponding quantities in the Euclidean plane. It can also be shown that each full line is of infinite length, that through a given point outside a given line an infinity of full lines may be drawn which do not meet the given line (the two lines bounding the family are said to be "parallel" to the given line), and that two full lines which meet do so in but one point.”

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

Geometry as a Branch of Physics (1949)

William Burges photo

“Use a good strong thick bold line so that we may get into the habit of leaving out those prettinesses which only cost money and spoil our design.”

William Burges (1827–1881) English architect

Attributed to William Burges (1860) paper on architectural drawing in: Sir Reginald Theodore Blomfield (1912) Architectural drawing and draughtsmen https://archive.org/stream/cu31924015419991#page/n25/mode/2up, Cassell & company, limited, 1912. p. 6-7

Simone Weil photo

“The materialists say, it is by means of a series of straight lines more or less perfect that one imagines the perfect straight line as an ideal limit. That is right, but the progression in itself necessarily contains what is infinite; it is in relation to the perfect straight line that one can say that such and such a straight line is less twisted than some other. … Either one conceives the infinite or one does not conceive at all.”

Simone Weil (1909–1943) French philosopher, Christian mystic, and social activist

Source: Lectures on Philosophy (1959), p. 87

James Jeans photo

“Minkowski… supposed that this fourth dimension of time was not detached from and independent of the three dimensions of space. He introduced a new four-dimensional space to which ordinary space contributed three dimensions, and time one; we may call it 'space-time'…. The succession of positions which a particle occupied in ordinary space at a succession of instants of time would be represented by a line in space-time; this he called the 'world-line' of the particle…. Newton's absolute space and absolute time fell out of science, and they carried much with them in their fall. First to go was the concept of simultaneity…. It now became necessary to find a way of treating gravitation which should not involve simultaneity. Einstein found through the medium of his 'Principle of Equivalence'.”

James Jeans (1877–1946) British mathematician and astronomer

The Growth of Physical Science (1947)

Girard Desargues photo

“When no point of a line is at a finite distance, the line itself is at an infinite distance.”

Girard Desargues (1591–1661) French mathematician and engineer

Brouillion project (1639) as quoted by Harold Scott MacDonald Coxeter, Projective Geometry (1987)

Willem de Sitter photo

“The sequence of different positions of the same particle at different times forms a one-dimensional continuum in the four-dimensional space-time, which is called the world-line of the particle. All that physical experiments or observations can teach us refers to intersections of world-lines of different material particles, light-pulsations, etc., and how the course of the world-line is between these points of intersection is entirely irrelevant and outside the domain of physics. The system of intersecting world-lines can thus be twisted about at will, so long as no points of intersection are destroyed or created, and their order is not changed. It follows that the equations expressing the physical laws must be invariant for arbitrary transformations.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

Nicole Oresme photo

“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)

Bernhard Riemann photo

“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)

Related topics