I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future.
Since geometry is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world (for what is there in God which is not God?), and he with his own image reached down to humanity.johannes kepler
"Some fool has put the head of this nail on the wrong end." "You idiot, it's for the opposite wall!" To be sure, if the space of physical objects allowed motions of translation only, and not also rotations. That space has such geometry is a fantasy; experience shows otherwise. It is only experience that makes this complaint and the rejoinder a dialogue of madmen.abraham kaplan
The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.john maynard keynes
Neither natural ability without instruction nor instruction without natural ability can make the perfect artist. Let him be educated, skilful with the pencil, instructed in geometry, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists, and be acquainted with astronomy and the theory of the heavens.vitruvius
Everything one invents is true, you may be perfectly sure of that. Poetry is as precise as geometry.Gustave Flaubert
Since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art.
Various relations being established in geometry between lines constituted under given conditions, as parts of geometrical figures, if we choose to adopt the idea of expressing these lines by numerical measures , we are then brought to the distinction of such lines being in some cases commensurable in their numerical values, in others not so. Their geometrical relations however are absolutely general, and do not refer to any such distinction.
The following are the other extant works generally attributed to Euclid: Phœnomena , a work on spherical geometry and astronomy; Optics , which develops the hypothesis that light proceeds from the eye, and not from the object seen; Catoptrica , containing propositions on reflections from mirrors; De Divisionibus , a treatise on the division of plane figures into parts having to one another a given ratio; Sectio Canonis , a work on musical intervals.
It is worthy of notice that Apollonius nowhere introduces the notion of directrix for a conic, and that, though he incidentally discovered the focus of an ellipse and hyperbola, he did not discover the focus of a parabola. Conspicuous in his geometry is also the absence of technical terms and symbols, which renders the proofs long and cumbrous.Florian Cajori
It is a remarkable fact in the history of geometry , that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences.
geometry is to sculpture what grammar is to the art of the writer.Kostrowitzki
geometry is that part of universal mechanics which accurately proposes and demonstrates the art of measuring.
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.
About the time of Anaxagoras, but isolated from the Ionic school, flourished Œnopides of Chios. Proclus ascribes to him the solution of the following problems: From a point without, to draw a perpendicular to a given line, and to draw an angle on a line equal to a given angle. That a man could gain a reputation by solving problems so elementary as these, indicates that geometry was still in its infancy, and that the Greeks had not yet gotten far beyond the Egyptian constructions.