Science is the observation of things possible, whether present or past. Prescience is the knowledge of things that may come to pass, though but slowly.
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{a} Tempered spring.
{b} The pinion turning around may be of either cylindrical or conical shape. And the instrument depicted above shows how the said pinion is movable around its axle. And this axle lifts the pinion without turning around with it.
Instrumental or mechanical science is the noblest and above all others the most useful, seeing that by means of it all animated bodies that have movement perform all their actions; and the origin of these movements is at the center of their gravity, which is placed in the middle with unequal weights at the sides of it, and it has scarcity or abundance of muscles, and also the action of a lever and counter-lever.
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{a} Method by which a wheel always turning in the same direction will move a screw first to the right and then to the left.
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{a} This lifting device is based on a curved wedge forced down by a weight. You may say that it works like a screw, because it is put in motion by simple friction between the wedge and the tooth of the wheel. This is a good and simple lifting device.
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{a} Every body requires its members and every art its instruments. And the moment that the whole is created, its parts are also created.
{b} Method of contrariwise friction.
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{a} Of pinion and wheel.
{b} If the pinion must move the wheel, the spacings of the pinion’s teeth must be wider than those of the wheel’s teeth. And, if the wheel turns the pinion, the opposite should be made. However, if both were well constructed, having equal teeth and spacing would be satisfactory.
{c} If you turn one of these wheels, the other, meshing with it, will turn in the opposite direction.
{d} If you wish to have a wheel that turns in the same direction as does the movement of the first wheel, this wheel, by necessity, must have a motion of the third degree.
{e} If you have two wheels that turn each other with their teeth, if they touch at the outside, they will turn contrariwise to each other. But if one of the wheels turns the inside of the other wheel with its outside, both wheels will then turn in the same direction regardless of which wheel causes the motion.
{f} Regardless of the direction you turn wheel d, a and b shall turn in the same way. And wheel c will turn contrariwise. The same will happen when turning a and b. But if you turn wheel c, every other wheel will turn in the opposite direction.
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1. I have plans for bridges, very light and strong and suitable for carrying very easily, with which to pursue and at times defeat the enemy; and others solid and indestructible by fire or assault, easy and convenient to carry away and place in position. And plans for burning and destroying those of the enemy.
2. When a place is besieged I know how to cut off water from the trenches, and how to construct an infinite number of bridges, mantlets, scaling ladders, and other instruments that have to do with the same enterprise.
3. Also if a place cannot be reduced by the method of bombardment, either through the height of its glacis or the strength of its position, I have plans for destroying every fortress or other stronghold unless it has been founded upon rock.
4. I have also plans for making cannon, very convenient and easy of transport, with which to hurl small stones in the manner almost of hail, causing great terror to the enemy from their smoke, and great loss and confusion.
5. Also I have ways of arriving at a certain fixed spot by caverns and secret winding passages, made without any noise even though it may be necessary to pass underneath trenches or a river.
6. Also I can make armored cars, safe and unassailable, which will enter the serried ranks of the enemy with their artillery, and there is no company of men at arms so great that they will not break it. And behind these the infantry will be able to follow quite unharmed and without any opposition.
7. Also, if need shall arise, I can make cannon, mortars, and light ordnance, of very beautiful and useful shapes, quite different from those in common use.
8. Where it is not possible to employ cannon, I can supply catapults, mangonels, trabocchi, and other engines of wonderful efficacy not in general use. In short, as the variety of circumstances shall necessitate, I can supply an infinite number of different engines of attack and defense.
9. And if it should happen that the engagement was at sea, I have plans for constructing many engines most suitable either for attack or defense, and ships that can resist the fire of all the heaviest cannon, and powder and smoke.
10. In time of peace I believe that I can give you as complete satisfaction as anyone else in architecture in the construction of buildings both public and private, and in conducting water from one place to another.
Also I can execute sculpture in marble, bronze, or clay, and also painting, in which my work will stand comparison with that of anyone else whoever he may be.
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{a} The open arms of this crossbow—which is where the rope is secured—measure 42 braccia in width, while its broadest section measures one braccio and two thirds and, when it is fired, the rope-stretcher comes down and the crossbow straightens itself out along its whole length.
{b} Stretch the rope on the crossbow.
{c} This is how an instrument operated by a rope works. The rope is released by a blow of the mallet above the bolt knob.
{d} This one performs the same action.
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{a} The part of the carriage that is adjacent to the arquebus tails, and which is identified by a, should be lifted when the arquebus tails are to be moved outwards.
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{a} If a man have a tent made of linen of which the apertures have all been stopped up, and it be twelve braccia across and twelve in depth, he will be able to throw himself down from any great height without sustaining any injury.
An object offers as much resistance to the air as the air does to the object. You may see that the beating of its wings against the air supports a heavy eagle in the highest and rarest atmosphere, close to the sphere of elemental fire. Again you may see the air in motion over the sea, fill the swelling sails and drive heavily laden ships. From these instances, and the reasons given, a man with wings large enough and duly connected might learn to overcome the resistance of the air, and by conquering it, succeed in subjugating it and rising above it.
No impetus created by any movement whatever can be immediately consumed, but if it finds an object that has a great resistance it consumes itself in a reflex movement.
The impetus acquired by the beating of the wings in the slanting descent of birds is the reason for these birds descending for a long space without beating their wings and for the said slant.
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The first book deals with flying without motion of the wings. The bird that desires to descend lowers its wings from its middle down, at the side it wants to descend, and this steers it, along line a b. Afterwards, it turns round, in the face of site a b, and descends with the same obliquity, turning on itself until facing the place where it desires to land. When the north wind blows and the bird faces the east, with its tail leeward, this means that the bird desires to rise in circles, by the favor of the wind, which helps the bird’s motion by holding down its tail and aiding it above obliquely; the wind makes the bird partially rotate, as a result of the resistance of the wind’s streams breaking at the upper part of the tail. And this occurs until the bird turns facing the wind. Afterwards, when it turns towards the west the bird is struck from beneath by the wind and it is made to turn and to continue its circular motion. When the kite, in its circling motion, rises and returning presents the upper wing to the onrush of the wind, it would often be overturned were it not for the fact that it immediately changes the position of the upper wing, which was windward, by letting it down and placing it, from its middle on, leeward.
When the north wind blows, and the bird desires to fly south-east, that is, to sirocco, it will lower half of its southern wing receiving in it the percussion of the wind. On this account, it would approach the south, were it not that an oblique position towards the east is taken up, with the front part kept low, and for this, it moves towards the south-east.
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{a} Make the ladders curved to correspond with the body.
{b} When the foot of the ladder a touches the ground it cannot give a blow to cause injury to the instrument because it is a cone that buries itself and does not find any obstacle at its point, and this is perfect.
{c} Make trial of the actual machine over the water so that if you fall you do not do yourself any harm.
{d} These hooks that are underneath the feet of the ladder act in the same way as when one jumps on the points of one’s toes, for then one is not stunned as is the person who jumps upon his heels.
{e} This is the procedure when you wish to rise from an open plain: these ladders serve the same purpose as the legs and you can beat the wings while it is rising. Observe the swift, how when it has settled itself upon the ground it cannot rise flying because its legs are short. But when you have raised yourself, draw up the ladders as I show in the second figure above.
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{a} If you wish to see a real test of the wings make them of pasteboard covered by net, and make the rods of cane, the wing being at least twenty braccia in length and breadth, and fix it over a plank of a weight of two hundred pounds, and make in the manner represented above a force that is rapid; and if the plank of two hundred pounds is raised up before the wing is lowered the test is satisfactory, but see that the force works rapidly, and if the aforesaid result does not follow do not lose any more time.
{b} If by reason of its nature this wing ought to fall in four spaces of time and you by your mechanism cause it to fall in two, the result will be that the plank of two hundred pounds will be raised up.
{c} You know that if you find yourself standing in deep water holding your arms stretched out and then let them fall naturally, the arms will proceed to fall as far as the thighs and the man will remain in the first position.
{d} But if you make the arms, which would naturally fall in four spaces of time, fall in two then know that the man will quit his position and moving violently will take up a fresh position on the surface of the water.
{e} And know that if the above named plank weighs two hundred pounds a hundred of these will be borne by the man who holds the lever in his hand and a hundred will be carried upon the air by the medium of the wing.
You will perhaps say that the sinews and muscles of a bird are incomparably more powerful than those of man, because all the girth of so many muscles and of the fleshy parts of the breast goes to aid and increase the movement of the wings, while the bone in the breast is all in one piece and consequently affords the bird very great power, the wings also being all covered with a network of thick sinews and other very strong ligaments of gristle, and the skin being very thick with various muscles.
But the reply to this is that such great strength gives it a reserve of power beyond what it ordinarily uses to support itself on its wings, since it is necessary for it whenever it may so desire either to double or treble its rate of speed in order to escape from its pursuer or to follow its prey. Consequently in such a case it becomes necessary for it to put forth double or treble the amount of effort, and in addition to this to carry through the air in its talons a weight corresponding to its own weight. So one sees a falcon carrying a duck and an eagle carrying a hare; which circumstance shows clearly enough where the excess of strength is spent; for they need but little force in order to sustain themselves, and to balance themselves on their wings, and flap them in the pathway of the wind and so direct the course of their journeyings; and a slight movement of the wings is sufficient for this, and the movement will be slower in proportion as the bird is greater in size.
Man is also possessed of a greater amount of strength in his legs than is required by his weight. And in order to show the truth of this, place a man to stand upon the seashore, and observe how far the marks of his feet sink in; and then set another man on his back, and you will see how much deeper the marks of his feet will be.
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Remember that your bird should have no other model than the bat, because its membranes serve as an armor or rather as a means of binding together the pieces of its armor, that is the framework of the wings.
And if you take as your pattern the wings of feathered birds, these are more powerful in structure of bone and sinew, because they are penetrable, that is to say, the feathers are separated from one another and the air passes through them. But the bat is aided by its membrane, which binds the whole together and is not penetrated by the air.
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{a} Let the outer extremity of the screw be of steel wire as thick as a cord, and from the circumference to the center let it be eight braccia.
{b} I find that if this instrument made with a screw be well made, that is to say, made of linen of which the pores are stopped up with starch, and be turned swiftly, the said screw will make its spiral in the air and it will rise high. Take the example of a wide and thin ruler whirled very rapidly in the air, you will see that your arm will be guided by the line of the edge of the said flat surface.
{c} The framework of the above mentioned linen should be of long, stout cane. You may make a small model of pasteboard, of which the axis is formed of fine steel wire, bent by force, and as it is released it will turn the screw.
Under the body between the pit and the fork of the throat should be a chamois skin and put it there with the head and the feet.
Hold a windlass with the hands, and with feet and hands together you will exert a force equal to four hundred pounds, and it will be as rapid as the movement of the heels.
Every body that does not bend, although these are each in itself of different size and weight, will throw equal weights upon all the supports, which are equidistant from their center of gravity, this center being in the middle of the breadth of this body.
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{a} This can be made with one pair of wings and also with two.
{b} If you should wish to make it with one, the arms will raise it by means of a windlass, and two vigorous kicks with the heels will lower it, and this will be useful.
{c} And if you wish to make it with two pairs, when one leg is extended it will lower one pair of wings and at the same time the windlass worked by the hands will raise the others, helping also considerably those that fall, and by turning the hands first to the right and then to the left you will help first the one and then the other. This instrument resembles the large one on the opposite page except that in this the traction is twisted on the wheel M and goes to the feet.
{d} In place of the feet you should make a ladder in three parts of three poles of fir, light and slender, as is represented here in front, and it should be ten braccia in length.
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{a} This man exerts with his head a force that is equal to two hundred pounds, and with his hands a force of two hundred pounds; and this is what the man weighs.
{b} The movement of the wings will be crosswise after the manner of the gait of the horse.
{c} So for this reason I maintain that this method is better than any other.
{d} Ladder for ascending and descending; let it be twelve braccia high, and let the span of the wings be forty braccia, and their elevation eight braccia, and the body from stern to prow twenty braccia and its height five braccia and let the outside cover be all of cane and cloth.
Man when flying must stand free from the waist upwards so as to be able to balance himself, as he does in a boat, so that the center of gravity in himself and in the machine may counterbalance each other, and be shifted as necessity demands for the changes of its center of resistance.
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{a} a twists the wing, b turns it with a lever, c lowers it, d raises it up, and the man who controls the machine has his feet at f d; the foot f lowers the wings, and the foot d raises them. The pivot M should have its center of gravity out of the perpendicular so that the wings as they fall down also fall towards the man’s feet; for it is this that causes the bird to move forward.
{b} This machine should be tried over a lake, and you should carry a long wineskin as a girdle so that in case you fall you will not be drowned.
{c} It is also necessary that the action of lowering the wings should be done by the force of the two feet at the same time, so that you can regulate the movement and preserve your equilibrium by lowering one wing more rapidly than the other according to need, as you may see done by the kite and other birds. Also the downward movement of both the feet produces twice as much power as that of one: it is true that the movement is proportionately slower. The raising is by the force of a spring or if you wish by the hand, or by drawing the feet towards you, and this is best, for then you will have the hands more free.
The destruction of these machines may come about in two ways, the first of which is when the machine breaks, the second is when it turns edgewise or almost on its edge because it ought always to descend with a long slant and almost in a level line.
As regards the preventing of the machine from being broken, one may guard against this by making it as strong as possible in whatever line it may turn, that is either edgewise falling with head or tail in front, or with the point of the right or left wing, or along lines that bisect or are the quarterings of these lines.
As regards constructing the machine in such a way that in descending whatever may be the direction that it takes, it finds the remedy prepared; and this you will do by causing its center of gravity to be above that of the weight which it carries, always in a vertical line, and the one always at a sufficient distance from the other, that is that if the machine is thirty braccia in width the centers are four braccia apart, and as has been said one is beneath the other, and the heavier is below, because as it descends the heavier part always constitutes itself in part the guide of the movement. In addition to this, if the bird wishes to fall with its head downwards with a fraction of the slant that would cause it to turn over, this will not be able to happen, because the lighter part would be beneath the heavier and the light would be descending before the heavy, which is impossible in a descent of any length.
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{a} Spring with lock n o is a wire that holds the spring, and it is not straight. Spring of wing.
{b} The spring b should be strong, and the spring a feeble and bendable, so that it may easily be made to meet the spring b, and between a b let there be a small piece of leather, so that it is strong, and these springs should be of ox horn, and to make the model you will make it with quills.
{c} Take instead of the spring filings of thin and tempered steel, and these filings will be of uniform thickness and length between the ties, and you will have the springs equal in strength and power of resistance if the filings in each are equal in number.
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{a} The foundation of the movement.
