# „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.“

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

Übernommen aus Wikiquote. Letzte Aktualisierung 3. Juni 2021. Geschichte
##### Nikolaus von Oresme
französischer Bischof, Naturwissenschaftler und Philosoph, … 1323 - 1382

## Ähnliche Zitate

### „Let us imagine that from any given point the system of shortest lines going out from it is constructed; the position of an arbitrary point may then be determined by the initial direction of the geodesic in which it lies, and by its distance measured along that line from the origin. It can therefore be expressed in terms of the ratios dx0 of the quantities dx in this geodesic, and of the length s of this line. …the square of the line-element is \sum (dx)^2 for infinitesimal values of the x, but the term of next order in it is equal to a homogeneous function of the second order… an infinitesimal, therefore, of the fourth order; so that we obtain a finite quantity on dividing this by the square of the infinitesimal triangle, whose vertices are (0,0,0,…), (x1, x2, x3,…), (dx1, dx2, dx3,…). This quantity retains the same value so long as… the two geodesics from 0 to x and from 0 to dx remain in the same surface-element; it depends therefore only on place and direction. It is obviously zero when the manifold represented is flat, i. e., when the squared line-element is reducible to \sum (dx)^2, and may therefore be regarded as the measure of the deviation of the manifoldness from flatness at the given point in the given surface-direction. Multiplied by -¾ it becomes equal to the quantity which Privy Councillor Gauss has called the total curvature of a surface. …The measure-relations of a manifoldness in which the line-element is the square root of a quadric differential may be expressed in a manner wholly independent of the choice of independent variables. A method entirely similar may for this purpose be applied also to the manifoldness in which the line-element has a less simple expression, e. g., the fourth root of a quartic differential. In this case the line-element, generally speaking, is no longer reducible to the form of the square root of a sum of squares, and therefore the deviation from flatness in the squared line-element is an infinitesimal of the second order, while in those manifoldnesses it was of the fourth order. This property of the last-named continua may thus be called flatness of the smallest parts. The most important property of these continua for our present purpose, for whose sake alone they are here investigated, is that the relations of the twofold ones may be geometrically represented by surfaces, and of the morefold ones may be reduced to those of the surfaces included in them…“

—  Bernhard Riemann German mathematician 1826 - 1866

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

### „Throughout, we shall be exemplifying the thesis of D. M. MacKay: that quantity of information, as measured here, always corresponds to some quantity, i. e. intensity, of selection, either actual or imaginable“

—  W. Ross Ashby British psychiatrist 1903 - 1972

Quelle: An Introduction to Cybernetics (1956), Part 3: Regulation and control, p. 252

### „For this, to draw a right line from every point, to every point, follows the definition, which says, that a line is the flux of a point, and a right line an indeclinable and inflexible flow.“

—  Proclus Greek philosopher 412 - 485

Book III. Concerning Petitions and Axioms.

### „There is but one question ultimately to be asked respecting every line you draw, Is it right or wrong? If right, it most assuredly is not a "free" line, but an intensely continent, restrained and considered line; and the action of the hand in laying it is just as decisive, and just as "free" as the hand of a first-rate surgeon in a critical incision.“

—  John Ruskin English writer and art critic 1819 - 1900

Cestus of Aglaia, chapter VI, section 72 (1865-66).

### „The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.“

—  Archimedes, buch The Method of Mechanical Theorems

Proposition 6.
The Method of Mechanical Theorems

### „The geometric line is an invisible thing. It is the track made by the moving point; that is, its product. It is created by movement – specifically through the destruction of the intense self-contained repose of the point. Here, the leap out of the static to the dynamic occurs. […] The forces coming from without which transform the point into a line, can be very diverse. The variation in lines depends upon the number of these forces and upon their combinations.“

—  Wassily Kandinsky Russian painter 1866 - 1944

1920 - 1930, Point and line to plane, 1926

### „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 English mathematican, astrologer and antiquary 1527 - 1608

Theorem II
Monas Hieroglyphica (1564)

### „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 French philosopher, Christian mystic, and social activist 1909 - 1943

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

### „As a Line, I say, is looked upon to be the Trace of a Point moving forward, being in some sort divisible by a Point, and may be divided by Motion one Way, viz. as to Length; so Time may be conceiv'd as the Trace of a Moment continually flowing, having some Kind of Divisibility from an Instant, and from a successive Flux, inasmuch as it can be divided some how or other. And like as the Quantity of a Line consists of but one Length following the Motion; so the Quantity of Time pursues but one Succession stretched out as it were in Length, which the Length of the Space moved over shews and determines. We therefore shall always express Time by a right Line; first, indeed, taken or laid down at Pleasure, but whose Parts will exactly answer to the proportionable Parts of Time, as its Points do to the respective Instants of Time, and will aptly serve to represent them. Thus much for Time.“

—  Isaac Barrow English Christian theologian, and mathematician 1630 - 1677

p, 125
Geometrical Lectures (1735)

### „There are two worlds: the world that we can measure with line and rule, and the world we feel with our hearts and imagination.“

—  Leigh Hunt English critic, essayist, poet and writer 1784 - 1859

As quoted in The Farmer's Wife, Vol. 36 (1933), p. 72

### „I imagine a line, a white line, painted on the sand and on the ocean, from me to you.“

—  Jonathan Safran Foer, buch Alles ist erleuchtet

Quelle: Everything Is Illuminated

### „As we all know, the singularity in the art of Bach is the fusion of both levels and lines, the horizontal and vertical line. It’s a real wonder to see that the creation and forming of the horizontal line, the polyphonic structure, also results in this perfect, beautiful vertical line, the harmonic line. As we also know, Bach already used the full harmonic range and radius as no composer before him. My artistic aim of course is to point out the horizontal line in soloistic manner in a dynamically elastic way, but in the same breath to form the harmonic line in a bright field of color (I would call it “harmonic articulation”), to achieve a particular atmosphere of emotions and moods, drama, velocity, vividness, and so on. As we can imagine, these are high demands …“

—  Burkard Schliessmann classical pianist

Talkings on Bach

### „Let the letters a b c denote the three angular points of a rectilineal triangle. If the point did move continuously over the lines ab, bc, ca, that is, over the perimeter of the figure, it would be necessary for it to move at the point b in the direction ab, and also at the same point b in the direction bc. These motions being diverse, they cannot be simultaneous. There-fore, the moment of presence of the movable point at vertex b, considered as moving in the direction ab, is different from the moment of presence of the movable point at the same vertex b, considered as moving in the same direction bc. But between two moments there is time; therefore, the movable point is present at point b for some time, that is, it rests. Therefore it does not move continuously, which is contrary to the assumption. The same demonstration is valid for motion over any right lines including an assignable angle. Hence a body does not change its direction in continuous motion except by following a line no part of which is straight, that is, a curve, as Leibnitz maintained.“

—  Immanuel Kant German philosopher 1724 - 1804

Section III On The Principles Of The Form Of The Sensible World

### „To a given right line to apply a parallelogram equal to a given triangle in an angle which is equal to a given right lined angle.According to the Familiars of Eudemus, the inventions respecting the application, excess, and defect of spaces, is ancient and belongs to the Pythagoric muse. But junior mathematicians receiving names from these, transferred them to the lines which are called conic, because one of these they denominate a parabola, but the other an hyperbola, and the third an ellipsis; since, indeed these ancient and divine men, in the plane description of spaces on a terminated right line, regarded the things indicated by these appellations. For when a right line being proposed, you adapt a given space to the whole right line, then that space is said to be applied, but when you make the longitude of the space greater than that of the right line, then the space is said to exceed; but when less, so that some part of the right line is external to the described space, then the space is said to be deficient.“

—  Proclus Greek philosopher 412 - 485

And after this manner, Euclid, in the sixth book, mentions both excess and defect. But in the present problem he requires application...

### „By reason of Arthur's position as its climax as well as of the long line of other traditional heroes, events and associations, and of its breadth of treatment, simplicity, intensity, enthusiasm, accord with the supernatural, vitality of imagination, elevation and sometimes nobility and religious feeling, the poem is the nearest thing we have to a traditional racial epic.“

—  Layamon English poet 1200

J. S. P. Tatlock The Legendary History of Britain (Berkeley: University of California Press, 1950) p. 485.
Criticism

### „[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 Peintre Néerlandais 1872 - 1944

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

### „Proposition 14. The straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the (circumference) within the earth's shadow a ratio greater than that which 675 has to 1.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

### „Although the classic theoretical foundation of distance measurement in physics is the 'rigid rod', nearly all distances in surveying, whether terrestrial or celestial, are made to depend on the properties of light. The two simplest properties so employed are the principle of propogation in straight lines and the principle that the intensity of light diminishes inversely as the square of the distance.“

—  Gerald James Whitrow British mathematician 1912 - 2000

p, 125
The Structure of the Universe: An Introduction to Cosmology (1949)

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

—  Fritz Houtermans German physicist 1903 - 1966

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

### „The quantity of civilization is measured by the quality of imagination.“

—  Victor Hugo, buch Die Elenden

Quelle: Les Misérables