Notebooks (16 page)
Authors: Leonardo da Vinci,Irma Anne Richter,Thereza Wells
Tags: #History, #Fiction, #General, #European, #Art, #Renaissance, #Leonardo;, #Leonardo, #da Vinci;, #1452-1519, #Individual artists, #Art Monographs, #Drawing By Individual Artists, #Notebooks; sketchbooks; etc, #Individual Artist, #History - Renaissance, #Renaissance art, #Individual Painters - Renaissance, #Drawing & drawings, #Drawing, #Techniques - Drawing, #Individual Artists - General, #Individual artists; art monographs, #Art & Art Instruction, #Techniques
No movement can ever be so slow that a moment of stability is found in it.
That movement is slower which covers less distance in the same time.
And that movement is swifter which covers more distance in the same time.
Movement can acquire infinite degrees of slowness.
It is in the power of movement to extend to infinite slowness and likewise to infinite velocity.
Movement has the power to extend to infinite velocity.
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4. MOVEMENT AND WEIGHT98
Of Movement and Weight
In equal movements made in equal time the mover will always have more power than the thing which is moved; and the mover will be so much the more powerful than the thing moved in proportion as the movement of this moved thing exceeds the length of movement of its mover; and the difference of the power of the mover over that of the thing moved will be so much less in proportion as the length of the movement made by the thing moved is less than the movement of this mover. . . .
And this we see with an arrow from a bow, when its point is resting on the wood; for though the cord drive it with all the force of the bow it only penetrates the wood very little, but does the contrary if it has some movement.
Some say that the arrow in moving propels a wave of air in front of itself, and that this wave by means of its movement prevents the course of the arrow from being impeded. This is incorrect, however, because everything which is moved exhausts and impedes its mover. The air therefore which passes in waves in front of the arrow does so because of the movement of this arrow, and it lends little or no help of movement to its mover, which has to be moved by the same mover, but rather checks and shortens the movement of the thing moved.
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Every heavy substance moves on the side where it weighs most. And the movement of the heavy substances is made where it encounters least resistance.
The heaviest part of bodies that move in the air becomes guide of the movements.
That heavy substance descends more slowly through the air which has greater width.
It follows that that heavy substance will descend more swiftly which has the least width.
The free descent of every substance is made along the line of its greatest diameter.
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The movements of weight are of three kinds, of which two are contrary and the third participates in one and the other.
The reason is that the movement made from below upwards becomes feebler the more it rises; the other on the contrary grows stronger the further it descends. While the first leaves its highest contact unharmed the second, on the contrary, inflicts great damage to itself and to others; the third movement is transverse and half of it resembles the weight that descends and the other half is like the weight that rises.
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Proof of the proportion of the time and movement together with the speed made in the descent of heavy bodies in the shape of pyramids, because the aforesaid powers are all pyramidal seeing that they commence in nothing and proceed to increase in degrees of arithmetical proportion.
If you cut the pyramid at any stage of its height by a line equidistant to its base, you will find that the proportion of the height of this section from its base to the total height of the pyramid will be the same as the proportion between the breadth of this section and the breadth of the whole base.
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101
Now we have found that the discontinuous quantity when moving acquires at each stage of its movement a degree of speed; and so in each stage of harmonic time they acquire a length of space from each other and this acquisition is in arithmetical proportion.
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102
Of movement
The weight which descends freely acquires a degree of movement with every degree of time, and with every degree of movement it acquires a degree of velocity.
Although the equal division of the movement of time cannot be stated by degrees as is the movement made by bodies, nevertheless I must in this case make the degrees after the manner in which they are made among musicians.
Let us say that in the first degree of time the weight acquires a degree of movement and a degree of velocity, then it will acquire two degrees of movement and two of velocity in the second degree of time and so it continues in succession. . . .
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The wave of the air that is produced by a body moving through the air will be much swifter than the body that moves it.
This happens because the air is very volatile and when a body moves through it, it makes the first wave in its first movement, and that first wave cannot be made without at the same time causing another after it and that causing another. And so this body moving through the air creates beneath it in each stage of time multiplications of waves which in their flight prepare the path for the movement of their mover.
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If two bodies of equal weight and shape fall one after another from an equal altitude one will be a degree more distant than the other in each degree of time.
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The weight which has a free descent acquires a degree of weight with every degree of movement. . . .
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The weight which descends freely gains a degree of speed with every stage of movement.
And the part of the movement which is made in each degree of time grows longer successively.
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If many bodies of equal weight and shape are allowed to fall one after the other at equal times the excesses of their intervals will be equal to each other.
The experiment of the aforesaid conclusion as to movement ought to be made in this way: One takes two balls of equal weight and shape and lets them drop from a great height in such a way that at the beginning of their movement they touch one another; and the experimenter should station himself on the ground below in order to watch whether in their fall they have maintained contact with each other or not. And this experiment should be made repeatedly so that no accident may occur to hinder or falsify the proof—for the experiment may go wrong and may or may not deceive the experimenter.
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Of the descent of weight
Every natural action is made by the shortest way; and this is why the free descent of the weight is made towards the centre of the world; because it is the shortest distance between the movable thing and the ultimate depth of the universe.
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Every weight desires to descend to the centre by the shortest way; and where there is greater weight there is greater desire, and that thing which weighs the most if left free falls most rapidly. The less the slant of the opposing substance the greater its resistance. The weight passes by nature into whatever supports it and thus penetrating from support to support it grows heavier as it passes from body to body until it realizes its desire. . . .
In its action of pressing and weighting it is like force. Weight is subdued by force as force is by weight. One can see weight without force, but not force without weight. If weight has no neighbour it seeks one with fury, while force drives it away with fury.
If weight desires a permanent position, force readily flies from it.
If weight desires stability, force always desires flight; weight of itself is without fatigue, while force is never exempt from it. The more weight falls the more it increases and the more force falls the more it diminishes. If one is eternal the other is mortal. Weight is natural and force is accidental. Weight desires stability and permanence, and force is desirous of flight and death.
Weight, force, and a blow resemble each other as regards pressure.
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5. MOVEMENT AND FORCE109
First. If a power move a body a certain distance in a certain time, the same power will move half of this body in the same time twice this distance.
Second. If any force move any movable thing a certain distance in a certain time the same force will move half this movable thing the whole distance in half this time.
Third. If a force move a body in a certain time a certain distance the same force will move half of this body half the distance in the same time.
Fourth. If a power move a body in a certain time a certain distance, half the force will move in the same time half the body half the distance.
Fifth. If a force move a body in a certain time a certain distance it is not necessary that such power move twice this weight in twice the time twice this distance, because it might be that this force could not move this body.
Sixth. If a force move a body in a certain time a certain distance, it is not necessary that half of this force move this same body in the same time half this distance, for perhaps it would not be able to move it.
Seventh. If two separate forces move two separate bodies the same forces united will move in the same time the two movable things joined together for the same distance, because the proportion remains the same.
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Nothing that can be moved is more powerful in its simple movement than its mover.
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111
Of the mover or the movable thing
The power of the mover is always greater than the resistance of the thing moved.
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112
Of the movement made by things proportionately
to the power which drives them
to the power which drives them
One ought to make the experiment with a crossbow or other power which does not grow weaker, and also with balls of equal shape and of different substances and weight to test which goes furthest away from its motive power, and to test with various shapes of various sizes, breadths and lengths and to make a general rule. I wish to know what weight the power will have which shall drive to a greatest distance from itself a weight of a pound spherical in shape.
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Of the power of the crossbow
The weight that charges the crossbow has the same proportion to the weight of the arrow as the movement of the arrow of this crossbow has to the movement of its cord.
Here one ought to deduct three resistances made by the air, that is the percussion of the bow of the crossbow made upon the air, and that of the cord; the third is that made against the arrow.
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If the cord of the crossbow draws four hundred pounds weight upon its notch with the movement of a third of a braccio, as it discharges itself, it will draw two hundred pounds with two-thirds of a braccio distance from its notch; and one hundred pounds will be removed from its position by such power for a space of one braccio and a third.
And as much as you diminish the weight of the movable thing so the power will cause it to make a greater movement, so that you will always find that the movement of the cord and the movement of the thing propelled will be in the same proportion as the weight that drew the cord to the notch was to the weight that was driven by the cord (if the air did not restrain it).
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A man who wants to make a bow carry a very long way must be standing entirely on one foot and raising the other so far from the foot he stands on as to afford the requisite counterpoise to his body which is thrown forward on the first foot. And he must not hold his arm fully extended, and in order that he may be more able to bear the strain he must hold a piece of wood which as used in crossbows extends from the hand to the breast, and when he wishes to shoot he should suddenly leap forward and at the same instant extend his arm with the bow and release the cord. And if by dexterity he does everything at once it will go a very long way.
The reason given for this is as follows: know that as the leap forward is swift it lends one degree of fury to the arrow, and the extending of the arm because swifter lends a second; the push of the cord being also swifter gives a third. Therefore, if other arrows are driven by three degrees of fury and this by dexterity is driven by six it should travel double the distance. And I must remind you to leave the bow relaxed so that it will spring forward and remain taut.
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