MATTEO RICCI, JESUIT PRIEST, MATHEMATICIAN & CARTOGRAPHER. HIS 1602 WORLD MAP, “KUNYU WANGUO QUANTU” DISCUSSED FOR ITS FORTUITOUS & SERENDIPITOUS LAYOUT GRATICULE.

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INTRODUCTION

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Matteo Ricci was born in Italy, 1552, and after his early studies entered the “Society of Jesus” in April 1571. He studied Mathematics, Cosmology and Astronomy under the direction of Christopher Clavius and afterwards departed Rome c1577 and travelled to Lisbon, a particular centre for the Jesuits, where he studied for a short while. In 1578 he sailed on a missionary expedition to the Far East, arriving first in Goa where he stayed until 1582. He then departed for Macau China and in 1583 settled in Zhaoqing, China. In 1584 he completed a map called “Da Ying Quan Tu”, a “Complete Map of the World”, which unfortunately now does not exist. A second map was produced at Nanking in 1600, but in 1602 he produced the third, “Kunyu Wanguo Quantu”, which was then produced as a wood cut on six large blocks and printed on Bamboo paper at the behest of the Wanli Emperor of Ming China.
This chart is some 12 feet long and in a rather dark format which does not allow it to be used easily as a diagram. Hence, I have chosen to use the coloured copy as the background for my diagrams which is a 1604 copy.

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The texts appended to the map has information to the reason it exists as follows; “Certain scholars of Kwangtung requested me to make a map of the various countries I had passed through, so that the memory of my journey might endure. At that time I was not yet thoroughly conversant with the Chinese Language: nevertheless, I made a series of selections from the maps and books which I had brought with me , as well as from the notes and dairies of several years , and had them engraved on blocks in 1584, which is the map named DA YING QUANTU. The translation, however, made by an official interpreter could not in the nature of things be free from mistakes; so in “keng-tzii” (1600) when I went to Nanking and received the instructions of Mr Wu Tso-hai, I prepared a second edition of the map for him”.

He continues; “In 1601 I came to Peking where several gentlemen saw this map and were impressed by it.” “A new edition of my work on a larger scale was suggested.”
“For the greater convenience of the spectator, I made the map in the form of a large screen with six leaves thus enabling him to travel about, as it was , while reclining in his own study.” “Respectfully indited by Matteo Ricci, a native of Europe, on a lucky day in the first month of autumn in the year 1602 in the reign of Wan-Li.”

That information immediately provides us with a “Terminus ad quem”, the aim or terminal point for the maps and books he carried from Lisbon in 1578 he could have used to produce the 1584 map and subsequent maps until the revised 1602 map which it is thought also contains Chinese information unknown to the Europeans of the age to create the final map.

The John Ford Bell Library, University of Minnesota, has the following note;
“Kunyu Wanguo Quantu”, or “complete geographical map of ten thousand countries” is the oldest surviving map in Chinese to show the Americas. It is a xylograph (wood block print) on six panels of fine native paper ( made with bamboo fibre), each panel measuring 608.33mm x 1820mm. Li Zhizao (1565-1630), a Chinese mathematician, astronomer and geographer who worked on the project with Ricci may have engraved the map. It was printed by Zhang Wentao of Hangzhon, possibly an official printer of the Ming Court.”

Thus there were many maps and atlases and texts printed in the 1540’s to 1570’s which could have been used by Matteo Ricci and many are the same elliptical/rectangular format, such as P Forlani, 1562, which has a geographical S America. The maps by Munster, 1544 and Ortelius 1570 have a decidedly bizarre non-geographical S America.

But the atlas by Battista Agnese , 1544 is quite easily a basis for M Ricci’s map. Others are S Munster and B Bordone published in 1544 and 1547, with Antonio Flotiano in the 1550’s and Girolamo Ruscelli, “Orbis Descriptio” was published by G Ziletti, 1561 in Venice. There are of course many more that could be candidates.

However, the geographical S America is the key to the maps and texts Matteo Ricci carried with him to China and they are very few prior to his departure date of 1578. Africa and the Far East were well illustrated from the early 1500’s as was the Caribbean Sea and gradually the east coast of the America’s. Hence if Matteo Ricci had a copy of the Paolo Forlani 1562 World map published in Venice or the works of Battista Agnese he had a reasonably good basis for his own map even to the fact that the Caspian Sea was the Ptolemaic version.
His problem was that he produced what is one of the largest World maps, 12 feet long, and the distortion of the curvature of the meridians at that size unless properly constructed would be very noticeable and the projection of the America’s onto the largest curves a problem.

THE PROBLEMS FACING MATTEO RICCI IN PRODUCING THIS LARGE MAP

1) Until a European started producing maps in China the centre of the world was the Atlantic Ocean with its dividing line, the Line of Demarcation with Portugal and Spain trying to “own” a half of the world sphere. Thus if he was viewing a rectangular elliptical format with horizontal latitudes the conversion from one set of curves to the opposite set would present a major challenge. Thus to counter this a plain or square world chart would enable him to draw onto these reversed curves of the meridians. These were available prior to his leaving Lisbon but actually were under the strictest usage and even as a Jesuit may not have been allowed.

2) Although the Roman Foot was 11.64706 statute inches or 295.8353mm, it was divided into 16 digitus or 12 unciae, being either 18.49 or 24.653mm. The height of the woodcut block is given as 1820mm or 71.6535 inches, which does not equate to the 5.75 feet (1752mm) also quoted, and unfortunately the two panels held in the Museo della Specola, Bologna are given as 1800 x 700. So much for rounding out measurements!

Thus logically Matteo Ricci would have used measurements he was accustomed to, that is the Pes/Digitus/Unciae. Using the 1752mm or 29 inch height it equates to c95 digitus or c71 unciae and we can thus see that a very simple measurement of 90 digitus for the latitudinal chart inner circumference would be a boon and each degree would be ½ digitus or 18 1/2mm with thus a central equatorial measurement of 180 digitus or 131 inches (c11 feet). Whether he had a scale with him marked in digitus and unciae is another unknown.

But the Ming Dynasty in China, 1358-1644, had a variety of measures in that time and latterly had a chi/foot of 300.8 to 319mm. Thus an amalgam of Chinese and Roman divisions of a foot, bearing in mind the work is by Matteo Rici and Li Zhizao an easy compromise was available. Thus 1/16th of a CHI is either 18.8 or 19.9375mm with 90 being 1692 or 1795mm and hence we have the measurement of the printed map. The Roman Pes/foot = 295.835 and the CHI/foot = 319mm. The length would therefore be 3585.73 or 11.77 feet giving the overall length of the map at 12 feet and an easy degree measurement when used as 10 degrees each segment.

Thus Li Zhizao probably set out on a Bamboo Paper with a dimension for 6 blocks, the two centre lines and subdivided each into either 90 or 180 degrees of 1/16th CHI and subdivided it into degrees giving 180 latitude and 360 longitude. Each 10 degree section would be 199.375mm and thus the 608.33 x 1820 sheet was derived as a wood block.

3) The elliptical setting out.

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Basically it is a rectangle, side ratio 2:1, with the east and west ends transformed into curves, semicircles, with the radius half the latitudinal height. That radius is then used for the first 90 degrees at the extreme east or west with the middle 180 degrees formed by two sets of ever increasing radii as meridians.

The expansion of the radius from the 90° longitude point is dependent upon the size of the map as drawn. Thus the P Forlani and A Ortelius maps range from base radius of 900 to 5000 for the 1700 meridian adjacent to the vertical centre line.

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Battista Agnese uses a 15° spacing for his meridians and thus uses the same radius of 90° up to the 105 meridian from each extremity and has a maximum radius of c128° for the 170 meridians. Given the small size of the World map on the page as printed that radius will just fit on the actual page centre line.

The Matteo Ricci engraving would therefore have required monstrous radii for the map size and a careful study of the meridians indicates many wobbles in them and also a setting out which may actually be segmented in places. In the Pacific Ocean the meridians appear to be one curve from tropic to tropic and a definite change north and south of those lines.

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It is possible they are hand drawn curves which skilled engravers are quite adept at drawing, but, given the size of the map and its segments these type of anomalies must be expected.

There is also an error in the latitudinal lines in the N Pacific across N America with mis-alignments,
The southern portion has latitudes set out correctly.
The error appears to be in the setting out of the double lines of the Equator which steps one degree from the precise centre line and would normally indicate the top of the line if doubled. But the switch of position causes confusion.
The same can be said for the central longitude marker which is actually correct side to side. Again, given the size of the map and its segmental form these are minor aberrations to be accepted on such a fantastic achievement as this 1602 map surely is.

THE 1602 WORLD MAP AS PRINTED AND JOINED INTO ONE UNIT

1) Overlay to original as drawn.

Noted on various points of the chart are the geographical latitude/longitudes for comparison with the setting out shown on the map.
Firstly, the outer bordure is Zero or 360 degrees with the 180 degree centre line mimicking the International Date Line through the far eastern peninsular of the Eurasian Continent. But, with this setting out Europe is overlarge from Cape St Vincent to the Gulf of Issus and then the Caspian Sea is drawn as per Ptolemy. Africa is accurate with the west coast basically at 20 (17W) with the Bight of Benin correctly set out to the 40 (37) degrees east to the coast. The Horn of Africa is set at 12N but 81East when it should be 12N and 51East, hence the overall longitude is perfect. Then the entrance to the Persian Gulf is at 90E, with the tip of India at 105E and the Ganges at 120E.

Remove the 30 degrees setting out from the bordure to the “London” longitude and they are all geographically correct. Even the Cape of Good Hope is thus correct at 35S/20E.

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2) THE PLOT IS CORRECTED.

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The two diagrams form a geographic plot based upon the 30East Meridian of Matteo Ricci, which passes through London, the Mediterranean Sea and Africa in the geographically correct position. Thus when the graticular points on the first pair of diagrams are correctly positioned to the new Longitudinal Setting Out ( the latitudes are basically correct), the movement of coast lines can be clearly seen and the “accuracy” of Matteo Ricci’s original world map appreciated.

The basic movement is that the Far Eastern mainland extends 30 degrees to the east and the America’s move 10 degrees east to match.

The Magellanican continent has Australia, Papua New Guinea and New Zealand plotted as curiously Matte Ricci writes with respect to Magellanica;
“With regard to the latter (Magellanica), “its boundaries cannot yet be exactly determined, but its northern side extends up to Greater and Lesser Java and the Straits of Magellan.” Note the Straits of Magellan are at 52S and those tow land masses basically are at 10 degrees south and he has shown a very large land mass towards them which can only represent Australia and Papua New Guinea. Thus hinting at Australia and Tierra Del Fuego which he appears to know nothing about even though it is shown on many preceding maps as forming the southern coast line of the Strait Of Magellan.

This possibility of Australia could be from the Chinese and emanating from the world cruises of 1421/1423 by Admirals Hong Bao and Zhou Wen.

THE TECHNICAL DATA THAT APPEARS ON THE MAP

On the continent of Magellanica near S America is a table thus explained by M Ricci;
“Every degree of latitude, south and north of the Equator, equals 250 LI on the Earth’s surface. With regard to the degrees of longitude running east and west, only on the Equator is a degree equal to this. In calculating the rest, the further you go north or south, the smaller the degree; so that these degrees of longitude are all less than 250 LI in length. An arithmetical table showing the diminishing number of Minutes and Seconds is appended on the left; for, knowing the breadth of a degree in Minutes and Seconds, we can find the corresponding number of LI.”

The table appended is surprisingly accurate and mimic’s the Cosine of the latitude commonly used to find the longitude length. After the table M Ricci states ; “In the table on the right, 60 minutes make 1 degree and 60 seconds make 1 minute. Applied to the surface of the Earth, every degree of Latitude equals 250 LI, and every minute 4 1/6th I; so that 1 LI works out at 14 2/3rds LI , 10 LI at 2’ 24”, 100 LI at 24’. 1000 Li at 4° and 10,000 Li at 40°.

This table however is a curious addition for a rectangular elliptical map which has meridians set out along the Equator at their correct measurement, but thence it is a semi-circular geometrical construct having no relationship to the change of distance between meridians. In fact it is a basic square chart drawn with semi-circular meridians. Thus, the question must be asked, why Matteo Ricci gave himself the associated problems with the projection when he could have produced a square chart? Thus with Latitudes and Longitudes equal, or even a pseudo square chart similar to the projection of Gerardus Mercator with all lines parallel and at 90 degrees the production problems would have been obviated. This question is particularly pertinent given the size of the map produced and from (?) a small rectangular elliptical map the errors/differences would be magnified.

Matteo Ricci also appends on the left hand side of the map the following distances;
Circumference of the Earth; 90,000 LI
Distance from the centre of the Earth
To the surface of the Earth; 14,318.9 LI. ( note Ricci is using 22/7 for PI)
To 1st or Moon Sphere; 482,522 LI
To 2nd sphere (Mercury); 718, 750 Li
To 3rd sphere (Venus); 2,400,681 Li.
To 4th sphere (Sun); 16,055,690 Li.
To 5th sphere (Mars); 27,412,100 Li.
To 6th sphere (Jupiter); 126, 769, 584 Li.
To 7th sphere (Saturn); 205, 770,564 Li
To 8th sphere (fixed stars) 322,769,845 Li.
To 9th sphere (Primum mobile); 647, 338,690 Li.

These spheres enclose one another like the coats on an onion. All are hard, transparent, colourless like crystal, and sun, moon and stars ‘inhere’ in their substance like knots in a plank of wood.

There then follows a table of magnitudes. He concludes, “Hence it can be proved that if there are men on the 4th sphere and those above it, they cannot see the Earth. The Earth, then, is a mere speck compared with the immensity of the heaven.”

COMMENT

I my text MS7: Curious Additions to two Atlases dated 1550 and 1565, Notes and Planetary Circuits, Distances and Diameters, the works of Diego Homen and Baptista Agnese in Atlas form were discussed. That this indicates M Ricci being an Astronomer and probably knew the works of Companus of Navarra, he may well have obtained a copy of one or both of these Atlases from Venice or Lisbon along with the maps by Paolo Forlani produced in Venice. To avoid lengthy comparison I attach the text MS7 as an appendix.

THE MAPS OF MATTEO RICCI AND POSSIBLE FORE-RUNNERS

Quoting first from HOC Volume 2, Book 2 Chapter 7, Traditional Chinese Cartography; “On the wall of the mission room at Zhaoqing, according to Ricci’s journal, “”there was a cosmographical chart of the universe, done with European lettering. The more learned among the Chinese admired it very much and, when they were told that it was both a view and a description of the entire world, they became greatly interested in seeing the same thing done in Chinese””. At the request of the prefect of Zhaoqing, Ricci made the map “”speak Chinese””, drawing a new version: “”The new map was printed in 1584 as the YUDI SHANHAI QUANTU ( complete geographic map of the mountains and streams). No examples of this edition are extant, but a rendition of it survives in the TUSHU BIAN (compilation of illustrations and writings), compiled by Zhang Huang (1527-1608), who met Ricci in 1595.”

“If Zhang Huang’s rendition (fig 7.1) can serve as an indication, Ricci’s map was based on a map of the Ortelius type, oriented with north at the top.”
The engraving of the “Typus Orbis Terrarum by A Ortelius is 14 ½ x 20 inches and just under our A2 size of 16 ½ x 23 1/3rd inches.

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In 1564 he produced an 8 leaved wall map, some 34 2/3rds x 59 inches drawn in the cordiform projection which if available would certainly have been something to admire, but the smaller map is hardly a wall map.
However studying the Zhang Huang copy of the “Yudi Shanhai Quantu” in the book certainly does not look like a map of the world as Europeans would know it and it appears the only similarity is the rectangular elliptical projection which is not based upon semi-circles but on a slightly larger radii of +16% or 1/6th larger.

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Thus I am sceptical that it was a copy of the A Ortelius map, and bearing in mind it was first published in May 1570 with M Ricci departing for Lisbon in 1577 would a Flemish map have arrived in Rome prior to the departure or even in Lisbon in 1578.

It is estimated that from the end of the 16th century the market for voluminous map works began to grow as examples such as Sebastian Munster’s “Cosmographia” printed in Basle, 1544.

WHAT WAS AVAILABLE FOR MATTEO RICCI TO CARRY WITH HIM 1577 AD

B. Agnese was a very prolific Atlas producer and many contained the Polar Projections and world maps drawn on the rectangular elliptical format between 1536 and 1564.
P Forlani who engraved for many publishers in Venice and even copied/up-dated Giacomo Gastaldi’s world map of 1546, size 532 x 365mm, doing this several times from 1560 to 1576 and gradually enlarging it to 760 x 420mm in 1565. The work by P Forlani included many maps of parts of the world which could have enabled Matteo Ricci to produce such a large engraving as they included N America, Africa and the Far East.

Thus when the original translators and researchers of the 1602 map indicated that Pietro Plancius, 1552-1622, was probably one of the cartographers utilized by Matteo Ricci, it should be borne in mind and clearly noted that it is considered the earliest cartographical output by Plancius was after 1590.

Glancing through the World Maps produced in 1550/1570 there are at least five cartographers/publishers in Venice which Matteo Ricci may well have had access to in Rome and thus I believe given the number available the search for one is perhaps a lost cause.

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In 1623, Giulio Alenio (1582-1649) drew his own version of the 1602 map, Diagram ChMR/1/D14. He altered the original setting out and certain profiles as the map illustrates.. That he arrived in China 1610AD, the year that Matteo Ricci died, 11 May, and actually wrote a text, “Life of Matteo Ricci, Xitai of the west” when he never met him, shows the greatness of the man and his works.

CONCLUSION

We are aware from the texts that Matteo Ricci has carried with him to China such a variety of Charts/Atlases that he is able to cherry pick the geographical by virtue of the majority indicating one profile for S America and a consensus on the others.

However, he states that the zero longitude is the Canary Isles, then ignores it but keeps the meridian such that the Canary Isles are near correct to the west coast of Africa and thence the geographical meridian of Longitude through London is correct.

Individual sections of the 1602 map are basically correct, but slightly mis-placed longitudinally, mostly because the length of the Eurasian Continent is 30 degrees short.

Again, the positioning of the map centre line on the International Date Line, 1800, passing through the last portion of Eurasia is no doubt serendipitous, but also surprising!

Even the Chinese influence on the map is unknown, but considering the “Chinese Treasure Fleets” 1421-1423 and their ability to determine latitudes and from solar, polar and lunar sights taken similar to the Arab system a form of longitude no doubt existed. They also produced their maps of China based upon a square grid and hence a square graticule world map would not have surprised them.

Thus in 1602 wee see a map of the world which to all intents and purposes is applicable today as a visual guide equal to any produced in Europe.

MICHAEL J FERRAR MARCH 2024