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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):

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.

I
n 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 evidence 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.

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