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Online Geometry


Leonardo da Vinci. 1452-1519. Florentine artist, engineer, musician, and scientist.

Nothing can be found in nature that is not part of science, like continuous quantity, that is to say, geometry, which, commencing with the surfaces of bodies, is found to have its origins in lines, the boundary of these surfaces. Yet we do not remain satisfied with this, in that we know that line has its conclusion in a point, and nothing can be smaller than that which is a point. Therefore the point is the first principle of geometry, and no other thing can be found either in nature or in the human mind that can give rise to the point....
The principle of the science of painting is the point; second is the line; third is the surface; fourth is the body which is enclosed by these surfaces. And that is just what is to be represented...since in truth the scope of painting does not extend beyond the representation of the solid body or the shape of all the things that are visible.

Nessuna humana investigazione si pio dimandara vera scienzia s'essa non passa per le matematiche dimonstrazione.
No human investigation can be called real science if it cannot be demonstrated mathematically. Treatise on Painting.

While I thought I was learning how to live, I have been learning how to die.
Quoted in Des MacHale, Wisdom (London, 2002).





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