The Day the Universe Changed - James Burke [64]
Before the end of the fifteenth century, however, Leonardo da Vinci had shown that a cannon-ball travelled in a curving path. With or without impetus this was supposed to be impossible because it violated Aristotle’s rule of two kinds of natural and forced movement. The straight line which the ball followed just after it came out of the cannon was feasible. It was earthly, degenerate movement. But the curve which followed was purely celestial and had no place on earth.
Leonardo da Vinci’s drawing of cannon-ball trajectories which, in following a curving path, apparently defy Aristotle. Leonardo, however, never analysed the matter beyond this artist’s impression.
The cannon shot a hole in Aristotle, because it was obvious to all who examined it that the trajectory was, in fact, curved. It was Archimedes who helped to explain things. In 1543, the year Copernicus published his theory, an Italian artillery expert known as Niccolo Tartaglia published a Latin version of Archimedes’ treatise on the behaviour of bodies in water, based on the famous ‘Eureka!’ incident in his bath, when he had discovered the principle of displacement. His treatise showed how the behaviour of objects in various media might be shown to follow rules of behaviour which could be measured by geometric means. Archimedes shifted the emphasis from the mysterious ‘qualities’ which objects were thought to possess, to quantifiable matters such as weight, centres of gravity, balance and so on.
His translator, Tartaglia, was Professor of Mathematics at the university of Venice. His real name was Fontana; Tartaglia was a nickname, meaning ‘stammerer’, given him because of a speech impediment he had developed after suffering head wounds at the battle of Brescia. Tartaglia’s major interest was military science, and his theories were much in demand by noble patrons who wanted to improve their cannon-firing ability.
Tartaglia had already published a book of his own about cannon-ball trajectories in 1537, called The New Science. It showed that the entire path of a cannon-ball was curved and that the best angle of fire to achieve maximum range was 45 degrees. An Italian version was published in 1551, which was probably when his pupil, Giovanni Benedetti, first read it.
Benedetti, a man almost forgotten by historians, was perhaps more directly responsible for the philosophical revolution that was about to overtake European thought than any other contemporary thinker. He was a mathematician who was more interested in dropping things than shooting them. Nobody had ever thought of testing Aristotle’s statement that the speed with which things fell related to their weight. Benedetti did so. If two bodies were joined by a thread of negligible weight, he reasoned, the combined object should weigh twice as much and, therefore, fall at twice the speed of each. This did not happen. Benedetti also thought that things fell as they did, not because they were heavy or light but because of their ability to get through the air resisting their fall. In other words, they behaved like the water-borne objects Archimedes had spoken about. In a vacuum, therefore, a feather should fall as fast as a heavy object. This observation had to wait for confirmation until the vacuum pumps of the next century.
Late sixteenth-century shipwrights at work. In spite of the apparent mathematical precision with which they are working here, the basic lack of understanding of displacement caused many unseaworthy vessels to be lost.
Tartaglia’s epoch-making treatise of 1551, in which he shows a cannon-ball breaking Aristotle’s law by following the curving path which only heavenly bodies were supposed to take. Tartaglia avoided persecution because he drew no philosophical conclusion from his findings.
All these theories and observations of Benedetti’s were explained in a letter he sent to a Spanish Dominican called Guzman. After this, throughout the years he spent in Parma as chapel-master and mathematician to