Let us start with the basic stages of Alberti’s work on perspective, the building blocks for his works De statua and De pictura.
As a first stage: Alberti draws a large rectangle like a window frame, through which he can see the subject he wishes to paint or create. For the second stage, he selects the largest human he wishes to paint seen through the picture frame. The height of this person is divided into three equal parts, which form the basic unit of measurement, called a braccia.
The Chinese, and later the Sienese engineers, used very similar methods for constructing towers and measuring their heights.
In the third stage, he makes the center point of the picture frame, which should be no higher than three braccia above the ground.
In the fourth stage, he divides the base line into braccia.
In the fifth stage: He draws straight lines from this center point to each of the braccia on the base line.
For illustrations of the above, please visit our website.
Now to compare where Alberti has gotten with the Chinese method illustrated in the Shu-shu Chiu-chang.
The first comparison is illustrated by the method for finding the height of a tower (as explained in Alberti’s Ludi matematici, ca. 1450):
Stick an arrow or a rod into the ground (c-d) so as to form a straight perpendicular line along which to take sightings to the tower (a-b). Mark the rod with wax where the line of sight to the top of the tower crosses it (f). The triangle formed by the arrow, ground and eye is the geometric counterpart of the triangle formed by the tower, ground and eye (abc) hence it can be used to find the height of the tower (ab). ab divided by bc equals fc divided by ce.
This is how Alberti “discovered” the rules of projection, which since then have formed the basis of perspective for sculptors and painters.
However, Alberti had not made an original discovery. The same explanation from Liu Hui in the third century is illustrated in the Shu-shu Chiu-chang. In this book the calculations are called “the method of double differences,” that is, the properties of right-angled triangles. There are illustrations depicting methods for calculating the heights of islands seen from the sea; the height of a tree on a hill; the size of a distant walled city; the depth of a ravine; the height of a tower; the breadth of a river mouth; the depth of a transparent pool. This trigonometry was invented by Euclid, and Alberti could have obtained his ideas from him as well as from the Chinese—he never acknowledged his sources.
However, the links between Chinese sources and Alberti go much further than trigonometry. Alberti used the same instruments as Toscanelli and adopted similar mathematics. Alberti’s method of perspective was brilliant. He realized that perspective was determined not only by the size of the object viewed and its distance from the beholder but also by the height of the observer relative to the viewed object and the angle from which the viewer was looking at the object. In short, each figure in a crowd when the crowd is viewed in depth would need a different rule of perspective.
By now I was beginning to feel uncomfortable about the amount of knowledge that it seemed Florentine mathematicians had copied from the Chinese—Taccola, Francesco di Giorgio, and Alberti from the Shu-shu Chiu-chang for mathematics, surveying, perspective cartography, and cryptography; Regiomontanus from Guo Shoujing’s work on spherical trigonometry, Toscanelli and Nicholas of Cusa for Guo Shoujing’s work on astronomy. I could explain one or two Chinese manuals coming into the hands of Venetians and Florentines—but this many, in so many different fields? It seemed too much of a coincidence—too good to be true! On the other hand, there was Toscanelli’s evidence about the transfer of knowledge that was unquestionably true—evidenced by maps, which do not lie.
It seemed sensible at this stage to see the original books in China, not only Needham’s accounts. Could these have been taken out of context in some way? Perhaps there were also many Chinese inventions that had never been copied by Europeans. Perhaps those that were was just a huge coincidence. Ian Hudson, who has been in charge of our research team and website for five years, volunteered to go to China to inspect the original books that I believed Europeans had copied—by visiting libraries in mainland China and Hong Kong.
He found there were, as far as we can see, no anomalies—first it seemed everything that Taccola, di Giorgio, Regiomontanus, Alberti, and Leonardo da Vinci had “invented” was already there in Chinese books, notably ephemeris tables, maps, mathematical treatises, and the production of civil and military machines. So how was the transfer effected? I had many sleepless nights of worry before the penny dropped—all of these books were reproduced in parts of the Yongle Dadian, which Zheng He would have carried. Zheng He’s representatives would have undoubtedly told the pope and Toscanelli about the Yongle Dadian—as evidenced by Toscanelli’s comment, China was indeed ruled by “astronomers and mathematicians of great learning.”
Alberti also applied his mathematical ability to surveying, and is cited by many as being the father of modern surveying. Here again, he makes a complete break with the past. His map of Rome bears almost no relation to Ptolemy’s system of mapping. He rejects Ptolemy’s rectangular coordinates and uses the astrolabe to find the relative positions of points on the ground, just as a navigator would—he takes sightings from more than one vantage point. As Joan Gadol says, “He first set forth these ideas in Descriptio urbis Romae, the brief Latin treatise written in the 1440s.” Gadol believes Alberti’s Descriptio urbis Romae and Ludi matematici were among the earliest works in surveying land areas by sightings and mapping by scale pictures. He believes Regiomontanus, Schöner, and Waldseemüller followed Alberti’s work.
Leonardo’s map of Pisa and the mouth of the Arno is thought to be the first modern map to show contours of land by using different shades of color. Leonardo followed Alberti in the principles used in surveying, as he did in rules of perspective.
15
LEONARDO DA VINCI AND CHINESE INVENTIONS
In my youth, Leonardo da Vinci seemed the greatest genius of all time. An extraordinary inventor of every sort of machine, a magnificent sculptor, one of the world’s greatest painters, and the finest illustrator and draftsman who ever lived. When our daughters were young, Marcella and I made a point of taking them to as many exhibitions of Leonardo’s work as we could—in London, Paris, Rome, Milan, Le Clos Lucé, and Amboise.
Then, as my knowledge of Chinese inventions slowly expanded, particularly with information provided by friends of our website, I began to wonder. More and more of Leonardo’s inventions appear to have been invented previously by the Chinese. I began to question whether there might be a connection—did Leonardo learn from the Chinese? The 1421 team and I examined the subject for years but came to no conclusions.
Leonardo drew all the essential components of machines with extraordinary clarity—showing how toothed wheels, gear wheels, and pinions were used in mills, lifting machines, and machine tools. He described how and why teeth could transfer power, the efficacy of antifriction teeth, the transmission of power from one plane to another, and continuous rotary motion. He drew and described ratchets, pins, axles, cams, and camshafts. Pulleys were an integral part of many of his mechanisms; he produced different systems and applications for them.
Some of the earliest known examples of gear wheels in China have been dated to ca. 50 B.C.
A toothed gear wheel, as drawn by Leonardo in the Madrid Codices.
All these devices had been used in China for a very long time. In the Tso Chuan are illustrations of bronze ratchets and gear wheels from as early as 200 B.C. that have been discovered in China.
Axles from the third and fourth centuries B.C. have been excavated from the royal tombs at Hui Hsien. By the second century B.C., in the Han dynasty, complex forms of cam-shaped rocking levers for the triggers of crossbows were in use. The Hsun I Hsiang Fa Yao, written in about A.D. 1090, illustrates a chain drive. By the eleventh century A.D. flywheels were used in China for grinding. The earliest archaeological evi
dence of a pulley is a draw well representing a pulley system of the Han dynasty.
One of Leonardo’s best-known inventions was the paddle-wheel boat. The paddle-wheel mechanism was fundamental to China’s early naval supremacy. The sight of a boat traveling forward at great speed seemingly without oars or sails was terrifying to those in its path. The first record of the existence of paddle-wheel boats occurs in a Chinese account of a naval action under the command of Wang Chen-o, an admiral of the Liu Sung dynasty in A.D. 418.1 “These vessels later reached enormous proportions: one monster from the Southern Sung dynasty was said to have been 300 feet long. It was crewed by 1000 men and powered by thirty-two paddle wheels.”2
The oldest known illustration of an endless power-transmitting chain drive from Su Sung’s Hsun I Hsiang Fa Yaoch drawn in A.D. 1090.
Leonardo da Vinci’s illustration of a chain drive (Madrid Codices).
Leonardo is renowned for his drawings of different forms of manned flight, notably his helicopter and parachutes and his attempts at wings. By Leonardo’s day, the kite had been in use for hundreds of years. “China is the homeland of the kite…the oldest heavier-than-air craft that gains lift from the wind. It is believed that the kite was invented some 3000 years ago by Lu Ban…c.507–444 bc a Chinese master carpenter of the Lu State in the Spring and Autumn period. It was said that Lu Ban made a magpie out of bamboo pieces, which could fly. The master carpenter was also the first to use the kite in military reconnaissance.”3
Drawing of a Sung paddle-wheel warship.
Along with the other Renaissance engineers Leonardo penned his own version of the paddleboat.
Parachutes were in use in China fifteen hundred years before Leonardo.
According to the historical records by Sima Qian of the Western Han dynasty, Shun, a legendary monarch in ancient China was deeply hated by his father, a blind old man. When Shun was working on top of a high granary, his father set fire to the granary from below, intending to kill Shun. Holding two cone-shaped bamboo hats in his hands, Shun flew down and landed safely. This book also describes how more recently (in 1214) a thief managed to steal the leg of a statue from the top of a mosque. When caught he admitted to using two umbrellas as a parachute to save himself from injury on his descent.4
The parachute is a small detail on a folio of the largest collection of da Vinci’s notebooks, the Codex Atlanticus.
Hot-air balloons were known in the second century A.D. in China. The contents of an egg were removed from the shell, then a little mug-wort tinder was ignited inside the hole so as to cause a strong air current. The egg rose up in the air and flew away.”5
The Chinese had made use of the essential principle of the helicopter rotor from the fourth century A.D., a fact noted by the philosopher and alchemist Ko Hung. By then, helicopter toys, like whirligigs, were popular in China, a common name being “bamboo dragonfly.” The toy was a bamboo with a cord wound around it and with blades sticking out from the bamboo at an angle. When the cord was pulled, the bamboo and blades rotated and the toy ascended as the air was pushed downwards. Needham describes a number of examples of rotating blades being used for flight, often in the form of flying cars.6
Leonardo devoted much time to the possibilities of manned flight. The earliest Chinese description of the concept occurred in the accounts of the short-lived and obscure Northern Chi dynasty (ninth century B.C.), when the emperor Kao Yang “caused many prisoners condemned to death to be brought forward, had them harnessed with great bamboo mats as wings, and ordered them to fly to the ground from the top of the tower…. All the prisoners died but the emperor contemplated the spectacle with enjoyment and much laughter.”7
A pictorial version of the aerial car, from the Shan Hai Ching Kuang Chu. “The skill of the Chi-Kung people is truly marvellous; by studying the winds they created and built flying wheels, with which they can ride along the paths of the whirlwinds….” “The artist here has drawn the aerial car with two wheels, but both seem to be intended to represent screw-bladed rotors….” (Text of the-2nd century, or earlier, plus 17th-century commentary).
A later description comes from Marco Polo in the Z manuscript.
And so we will tell you how when any ship must go on a voyage, they prove whether her business will go well or ill. The men of the ship will have a bundle or a grating of willow stem and at each corner and side of this framework will be tied a cord and they will all be tied at the end of a long rope. Next they will find some fool or drunkard and will bind him on the hurdle, since no-one in his right mind or with his wits about him would expose himself to that peril. And this is done when a strong wind prevails. Then the framework being set up opposite the wind, the wind lifts it and carries it up into the sky, while the men hold on by the long rope. And, if while this is in the air, the hurdle leans towards the way of the wind, they pull the rope to them a little so that it is set again upright, after which they let out some more rope and it rises higher. And if again it tips, once more they pull on the rope until the frame is upright and climbing, and then they yield rope again, so that in this manner it would rise so high that it could not be seen, if only the rope were long enough. The augury they interpret thus: if the hurdle going straight up makes for the sky they say the ship for which the test has been made will have a quick and prosperous voyage…. But if the hurdle has not been able to go up, no merchant will be willing to enter the ship.8
The idea of a man using wings for flight existed in Chinese legend hundreds of years before this fifteenth century Sienese flying man.
One of the many weapons mastered by China before Europe was the cannon.
The dismountable cannon appears in da Vinci’s notebook and in those of many other Renaissance engineers.
Leonardo drew an array of gunpowder weapons, including three variations of the machine gun, which can be seen in the fire lances used in China since A.D. 950.
The Genius of China states:
Fire lances with several barrels were frequently used and they were built so that when one fire-tube had exhausted itself, a fuse ignited the next, and so on. One triple barrelled fire lance was called the “triple resister” and another was called “the three eyed lance of the beginning of the dynasty…” One curious weapon was the “thunder fire whip” a fire lance in the shape of a sword, three feet two inches long tapering into a muzzle. It discharged three lead balls the size of coins…. There were also huge batteries of fire lances which could be fired simultaneously from mobile racks…a great frame with several wheels would hold many layers of sixteen fire lances one after the other…. When the enemy approaches the gate, all the weapons are fired in a single moment, giving the noise like a great peal of thunder, so that his men and horses are all blown to pieces. You can then open the city gates and relaxing, talk and laugh as if nothing had happened; this is the very best device for the guarding of cities.9
Leonardo’s multibarreled machine gun was essentially a reworking of a concept that had been used by the Chinese for centuries beforehand.
Leonardo also drew different types of cannons, mortars, and bombards. The Chinese use of bombards is well catalogued throughout the ages.10
Leonardo designed many different types of bridges, including suspension bridges. The first mention of a suspension bridge with cables and planking appears in 25 B.C. “Travellers go step by step here, clasping each other for safety and rope suspension bridges are stretched across the chasms from side to side.”11
By the seventh century China had segmental arch bridges. The Ponte Vecchio in Florence is a copy of a bridge in Quanzhou.
Leonardo was extremely curious about printing. He was eager to reproduce his drawings faithfully while saving time and labor through increased automation. The printing press by his time was in use all over China. Moveable type, however, was a relatively recent development; we shall return to this in later chapters.
Comparisons of the machines of Leonardo with earlier machines from China reveal close similarities in toothed
wheels and gear wheels, ratchets, pins, and axles, cams and cam-shaped rocking levers, flywheels, crankshaft systems, balls and chains, spoke wheels, well pulleys, chain devices, suspension bridges, segmented arch bridges, contour maps, parachutes, hot-air balloons, “helicopters,” multibarreled machine guns, dismountable cannons, armored cars, catapults, barrage cannons and bombards, paddle-wheel boats, swing bridges, printing presses, odometers, compasses and dividers, canals and locks.
Even the most devoted supporter of Leonardo (like my family and I!) must surely wonder whether his work’s amazing similarity to Chinese engineering could be the product of coincidence.
A revolving-type table printing press found in the Nung Shu, 1313. The Nung Shu was printed using a similar device.
Was there any connection between the Chinese visit of 1434 and Leonardo’s designs sixty years later? For many years I searched for clues in Leonardo’s life but could find none. He was extraordinarily observant and inquisitive and certainly was fascinated by Greek and Roman art and architecture, literature, and science, including the works of Aristotle and Ptolomy. He is said to have slept with copies of Vitruvius’s works beneath his pillow. But illustrated examples of the Greeks and Romans did not account for a quarter of Leonardo’s engineering devices shown on the 1434 website.
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