A Quote by Leonardo da Vinci
Perspective is a most subtle discovery in mathematical studies, for by means of lines it causes to appear distant that which is near, and large that which is small.
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Of several bodies, all equally large and equally distant, that which is most brightly illuminated will appear to the eye nearest and largest.
How should all the apparatus of heaven and earth make poetry for a mind that had no movements of awe and tenderness, no sense of fellowship which thrills from the near to the distant, and back again from the distant to the near?
Do you, like a skilful weigher, put into the balance the pleasures and the pains, near and distant, and weigh them, and then say which outweighs the other? If you weigh pleasures against pleasures, you of course take the more and greater; or if you weigh pains against pains, then you choose that course of action in which the painful is exceeded by the pleasant, whether the distant by the near or the near by the distant; and you avoid that course of action in which the pleasant is exceeded by the painful.
Etching will suggest subtle variations of tone, the most delicate shadings, all with black lines, which, as far as lines go, are unsurpassed for sheer beauty.
In an atmosphere of uniform density the most distant things seen through it, such as the mountains, in consequence of the great quantity of atmosphere which is between your eye and them, will appear blue. Therefore you should make the building... wall which is more distant less defined and bluer... five times as far away, make five times as blue.
Since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear ... there is absolutely no doubt that every affect in the universe can be explained satisfactorily from final causes, by the aid of the method of maxima and minima, as it can be from the effective causes themselves ... Of course, when the effective causes are too obscure, but the final causes are readily ascertained, the problem is commonly solved by the indirect method.
The construction of extensive railways, however, and particularly the consolidation of small, experimental lines into large systems, dates from the days of the discovery of gold in California.
The construction of extensive railways, however, and particularly the consolidation of small, experimental lines into large systems, dates from the days of the discovery of gold in California
Wise men will apply their remedies to vices, not to names; to the causes of evil which are permanent, not the occasional organs by which they act, and the transitory modes in which they appear.
Since education is not a means to living, but is identical with the operation of living a life which is fruitful and inherently significant, the only ultimate value which can be set up is just the process of living itself. And this is not an end to which studies and activities are subordinate means; it is the whole of which they are ingredients.
The discovery I announce to the public is one of the small number which, by their principles, their results, and the beneficial influence which they exert upon the arts, are counted among the most useful and extraordinary inventions.
The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.
Perspective is nothing more than a rational demonstration applied to the consideration of how objects in front of the eye transmit their image to it, by means of a pyramid of lines. The Pyramid is the name I apply to the lines which, starting from the surface and edges of each object, converge from a distance and meet in a single point.
It is the thing that is most remote from the world in which we ourselves live that attracts us most. We are under the spell of what is distant from us. It is not our nature to desire passionately what is near at hand.
Dancing is just discovery, discovery, discovery - what it all means, the way the little bone near the ankle relates itself to the floor for a perfect stance, a perfect plie.
The safest and most suitable form of penance seems to be that which causes pain in the flesh but does not penetrate to the bones, that is, which causes suffering but not sickness.
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