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
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Nothing is that which fills no space. If one single point placed in a circle may be the starting point of an infinite number of lines, and the termination of an infinite number of lines, there must be an infinite number of points separable from this point, and these when reunited become one again; whence it follows that the part may be equal to the whole.
Leonardo da Vinci
Our workmen, in their hurry to finish, devote themselves only to the facings of the walls, setting them upright but filling the space between with a lot of broken stones and mortar thrown in anyhow. This makes three different sections in the same structure; two consisting of facing and one of filling between them. The Greeks, however, do not build so; but laying their stones level and building every other stone lengthwise into the thickness, they do not fill the space between, but construct the thickness of their walls in one solid and unbroken mass from the facings to the interior. Further, at intervals they lay single stones which run through the entire thickness of the wall. These stones... by their bonding powers... add very greatly to the solidity of the walls.
Vitruvius
Besotted Being! You think yourself the perfection of existence, while you are in reality the most imperfect and imbecile. You profess to see, whereas you can see nothing but a Point! You plume yourself on inferring the existence of a Straight Line; but I CAN SEE Straight Lines, and infer the existence of Angles, Triangles, Squares, Pentagons, Hexagons, and even Circles. Why waste more words? Suffice it that I am the completion of your incomplete self. You are a Line, but I am a Line of Lines, called in my country a Square: and even I, infinitely superior though I am to you, am of little account among the great nobles of Flatland, whence I have come to visit you, in the hope of enlightening your ignorance.
Edwin Abbot
How could one argue with a man who was always drawing lines and circles to explain the position; who, one day, drew a diagram [here Michael illustrated with pen and paper] saying 'take a point A, draw a straight line to point B, now three-fourths of the way up the line take a point C. The straight line AB is the road to the Republic; C is where we have got to along the road, we canot move any further along the straight road to our goal B; take a point out there, D [off the line AB]. Now if we bend the line a bit from C to D then we can bend it a little further, to another point E and if we can bend it to CE that will get us around Cathal Brugha which is what we want!' How could you talk to a man like that?
Eamon de Valera
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
Vinci, Leonardo da
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