Geometry... is of much assistance in architecture, and in particular it teaches us the use of the rule and compasses, by which especially we acquire readiness in making plans for buildings in their grounds, and rightly apply the square, the level, and the plummet. By means of optics... the light in buildings can be drawn from fixed quarters of the sky. ...Difficult questions involving symmetry are solved by means of geometrical theories and methods.
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Chapter I, Sec. 4Vitruvius
To find the directions and quarters of the winds your method of procedure should be as follows. In the middle of the city place a marble amussium, laying it true by the level, or else let the spot be made so true by means of rule and level that no amussium is necessary. In the very center of that spot set up a bronze gnomon or "shadow tracker." At about the fifth hour in the morning, take the end of the shadow cast by this gnomon, and mark it with a point. Then, opening your compasses to this point which marks the length of the gnomon's shadow, describe a circle from the center. In the afternoon watch the shadow of your gnomon as it lengthens, and when it once more touches the circumference of this circle and the shadow in the afternoon is equal in length to that of the morning, mark it with a point. From these two points describe with your compasses intersecting arcs and through their intersection and the centre let a line be drawn to the circumference of the circle to give us the quarters of south and north. ...and thus we have designed a figure equally apportioned among the eight winds.
Vitruvius
The Aga Khan Awards for Architecture seeks to make a better place in physical terms. This means trying to bring values into environments, buildings, and contexts that improve the quality of life for future generations."
Aga Khan IV
There is no greater fallacy than the belief that aims and purposes are one thing, while methods and tactics are another, This conception is a potent menace to social regeneration. All human experience teaches that methods and means cannot be separated from the ultimate aim. The means employed become, through individual habit and social practice, part and parcel of the final purpose; they influence it, modify it, and presently the aims and means become identical.
Emma Goldman
The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.
Isaac Newton
This absence of similarity among military questions naturally brings out the inability of memory to solve them; also the sterility of invariable forms, such as figures, geometrical drawings (épures), plans (schémas), etc. One only right solution imposes itself : namely, the application, varying according to circumstances, of fixed principles.
Ferdinand Foch
Vitruvius
Vitter, David
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