The Kangxi Emperor's Manchu-Language Elements of Geometry
The Kangxi Emperor's Manchu-Language Elements of Geometry A Rare Mathematical Manuscript Containing the Emperor's Own Corrections
MING YE
9/30/20266 min read
The Kangxi Emperor's Manchu-Language Elements of Geometry
A Rare Mathematical Manuscript Containing the Emperor's Own Corrections
By MING YE
The Manchu script of the Qing dynasty was used for far more than imperial edicts, memorials, official seals, and literary translation.
During the Kangxi period, Manchu also became one of the languages through which Western mathematics, astronomy, and medicine entered the Qing imperial court.
A remarkable example is the Manchu-language Elements of Geometry preserved in the Inner Mongolia Autonomous Region Library.
The manuscript is significant not only because it is a mathematical work written entirely in Manchu, but because its pages preserve numerous corrections, annotations, and revisions written by the Kangxi Emperor himself in red ink.
More than three centuries later, this manuscript allows us to observe not simply a finished mathematical text, but a historical process: the Kangxi Emperor learning European geometry through Manchu and actively participating in the refinement of the language used to explain it.
A Rare Manchu Mathematical Manuscript
The Manchu Elements of Geometry preserved in the Inner Mongolia Autonomous Region Library consists of two thread-bound volumes.
Each measures approximately 28.5 centimeters in height and 19 centimeters in width.
The entire work is handwritten in Manchu.
Numerous geometric diagrams appear in the upper margins and within the text, while the manuscript also contains red imperial annotations and several inserted slips carrying revisions.
According to the account associated with the collection, this manuscript was the actual working copy used by the Kangxi Emperor.
Three Manchu versions of the work are said to survive today.
The other two are preserved respectively in Russia and in the Palace Museum in Beijing. Those copies are clean versions prepared after the Kangxi Emperor's revisions had been incorporated.
The Inner Mongolia manuscript is particularly valuable because it preserves the earlier stages of translation and correction.
Hidden for More Than Half a Century
The manuscript remained largely unnoticed for decades.
It had been covered with a heavy printed wrapper associated with the Korean medical classic Donguibogam, which concealed the true nature of the book.
During the 1980s, Baoyin, a staff member of the Mongolian-language department of the Inner Mongolia Autonomous Region Library, encountered the manuscript while participating in the compilation of the National Union Catalogue of Manchu Books and Materials.
He catalogued it as a Manchu version of the Elements of Geometry.
At the time, however, its awkward-looking Manchu handwriting did not immediately suggest that it was an imperial working manuscript.
In retrospect, that very awkwardness became an important clue.
This was not a professionally copied final edition. It was closer to the working material used when European missionaries were explaining geometry to the emperor.
Identification of the Kangxi Working Copy
In November 2006, the French scholar Zhan Jialing, who had been searching for the location of the third surviving Manchu copy of the work, visited the Inner Mongolia Autonomous Region Library.
After examining the handwritten manuscript, she identified it as the original copy used by the Kangxi Emperor.
Its importance lies not merely in its age or rarity.
More importantly, it preserves the process of translation itself.
The manuscript contains missionary handwriting, geometric diagrams, textual revisions, and imperial corrections.
It is therefore not simply a finished book.
It is a record of a scientific conversation taking place across languages more than three hundred years ago.
Why Did the Kangxi Emperor Study Western Mathematics?
The Kangxi Emperor is well known for his interest in Western scientific knowledge.
According to accounts of his own recollections, one important motivation came from disputes over astronomical calculation.
When Chinese officials of the Astronomical Bureau and European missionaries disagreed over methods of calculation, practical observations were used to test their competing claims.
The results produced by European methods matched the observed phenomena closely.
The experience led Kangxi to a simple but important realization:
if he did not understand the knowledge involved, how could he judge who was correct?
He therefore began to study mathematics, astronomy, calendrical science, meteorology, and related subjects seriously under European missionaries such as Ferdinand Verbiest.
For Kangxi, mathematics was not merely a private intellectual hobby.
Astronomy, calendrical calculation, surveying, and mathematics also had practical connections with imperial administration.
Joachim Bouvet and Jean-François Gerbillon Teaching Geometry in Manchu
In 1689, two French Jesuits were selected to teach the Kangxi Emperor mathematics and astronomical knowledge.
Their Chinese names were Bai Jin and Zhang Cheng, better known in European sources as Joachim Bouvet and Jean-François Gerbillon.
Before teaching the emperor, they studied Manchu.
They then used the language to explain European geometry directly to Kangxi.
This point is particularly important.
Modern readers often assume that Western scientific knowledge entered China exclusively through Chinese translation.
The linguistic environment of the Kangxi court was more complex.
Manchu itself became one of the languages through which European science reached the emperor.
More Than a Simple Translation of Euclid
Although the manuscript is commonly called the Manchu Elements of Geometry, it was not simply a word-for-word translation of a single work by Euclid.
The missionaries compiled teaching material drawing on the geometrical tradition associated with Euclid, while also incorporating material connected with Archimedes, including discussions of circles, cylinders, spheres, conic sections, and related subjects.
The surviving manuscript is therefore better understood as a set of Manchu-language mathematical teaching notes prepared specifically for the Kangxi Emperor.
This makes the manuscript unusually significant.
It was, in effect, a textbook.
And its student was the emperor.
Seven Volumes of Geometrical Knowledge
The Manchu manuscript was organized into seven sections or volumes.
Its subjects included:
basic concepts such as points, lines, planes, and angles;
triangles;
quadrilaterals and polygons;
circles;
solid geometry;
the theory of proportion;
and geometrical construction.
This was not simply a collection of isolated mathematical terms.
It represented an attempt to construct a relatively systematic body of geometrical knowledge in Manchu.
For the language itself, this created a new challenge.
A language already widely used for government, military affairs, administration, and everyday communication now had to explain questions such as:
What is a point?
How should a line or angle be defined?
How should proportional relationships be expressed?
How should circles, spheres, cylinders, and complex geometrical relations be described?
New scientific knowledge therefore required new forms of linguistic expression.
Why Does the Handwriting Look So Unpolished?
One of the most interesting features of the manuscript is precisely the apparent awkwardness of its Manchu handwriting.
The European missionaries involved had only recently begun learning the language and script.
Their handwriting was therefore naturally less fluent than that of professional Qing Manchu scribes.
Some passages appear stiff, uncertain, or imperfectly formed.
The translation itself was also still being refined.
Yet this apparent imperfection is what makes the manuscript so valuable.
It preserves the scene of language learning itself.
We can observe:
Europeans learning to write Manchu,
Europeans attempting to explain Western geometry through Manchu,
and the Kangxi Emperor revising their language.
The Kangxi Emperor as Editor
Because the missionaries' command of Manchu was still developing, the Kangxi Emperor personally revised and polished parts of the manuscript.
Numerous corrections written in red remain visible in the surviving volumes.
This gives the manuscript an extraordinary characteristic:
Kangxi was not merely its reader.
To some extent, he was also its linguistic editor.
The imperial annotations allow us to see the emperor directly engaging with both mathematical ideas and Manchu expression.
For historians studying Kangxi's personal encounter with European science, such working materials are therefore even more revealing than polished copies produced later.
Why Is This Manchu Mathematical Work So Important?
He Yuanjing, a specialist in rare books at the Inner Mongolia Autonomous Region Library, has emphasized that books personally used by the Kangxi Emperor more than three centuries ago are already extremely rare.
A mathematical manuscript bearing the emperor's own corrections is even more exceptional.
From the perspective of Manchu studies, however, the work possesses another importance.
It demonstrates a fact that is often overlooked:
Manchu once functioned as a language of science.
It was used not only for:
imperial edicts,
memorials,
military archives,
court ritual,
Manchu literature,
and translations of traditional classics.
It could also be used to communicate European mathematics, geometry, medicine, and astronomy.
The history of the Manchu language therefore belongs not only to Manchu cultural history or Qing political history.
It is also part of the history of scientific transmission and intellectual exchange between China and Europe.
Conclusion: Scientific Exchange Preserved on a Page of Manchu
When we open the Kangxi Emperor's Manchu Elements of Geometry today, we encounter an extraordinary historical scene.
French Jesuits learned Manchu.
They then used Manchu to teach a Chinese emperor ancient Greek geometry.
The mathematical traditions of Euclid and Archimedes moved through European scholarship, missionary interpretation, and Manchu translation into the Qing imperial court.
The Kangxi Emperor learned the mathematics while simultaneously correcting the Manchu used to express it.
One manuscript thus connected several very different worlds:
ancient Greek mathematics,
European Jesuit science,
the Qing imperial court,
and the Manchu language and script.
More than three centuries later, its geometrical diagrams remain visible, as do the red corrections written by the emperor.
That is what makes historical manuscripts so remarkable.
Sometimes a book preserves far more than words.
It preserves the traces of how knowledge once moved between people, languages, and civilizations.
— MING YE