Jǐhé yuánběn 幾何原本
The Original Foundations of Geometric [Proportion] (Euclid’s Elements, books I–VI) by 歐几里得 (Euclid of Alexandria, 3rd cent. BCE, zhuàn 撰); translated by 利瑪竇 (Matteo Ricci, S.J., Lì Mǎdòu, 1552–1610, 明, yì 譯); brushed by 徐光啟 (Xú Guāngqǐ, 1562–1633, 明, bǐ shòu 筆受 — receiving the oral exposition and casting it into literary Chinese), printed Wànlì 35 (1607)
About the work
The Ricci-Xú Guāngqǐ Chinese translation of the first 6 books of Euclid’s Elements — the foundational plane-geometry portion of the work — based on Christopher Clavius S.J.’s 1574 Latin edition (Euclidis Elementorum libri XV, Rome). The translation was completed in 1606 (Wànlì 34, bǐngwǔ) and printed in 1607 (Wànlì 35, dīngwèi) — making it the foundational document of the post-Wàn-lì Chinese-Western mathematical synthesis and one of the most consequential cross-cultural intellectual transmissions in pre-modern history.
The 6 books cover (per Euclidean enumeration, retained in the Chinese translation):
- Book I: Triangles — the foundational plane-geometric definitions, postulates, common notions, and propositions; culminating in the Pythagorean theorem (proposition 47).
- Book II: Geometric algebra — area-and-rectangle relations, the geometric expressions of what would later be algebraic identities.
- Book III: Circles — chord, tangent, inscribed-and-central angle relations.
- Book IV: Inscribed-and-circumscribed rectilinear figures — regular polygons inscribed in and circumscribed around circles.
- Books V–VI: Proportion theory and similar figures — Eudoxus’s theory of proportion (book V) and its application to similar plane figures (book VI).
The translation’s structural conventions, established by Ricci and Xú Guāngqǐ, would shape Chinese mathematical translation through the late Qīng:
(I) Per-book organization: each book opens with jièshuō 界説 (definitions), continues with gōnglùn 公論 (common notions / postulates), then presents shètí 設題 (propositions) in sequence, beginning with the easiest and proceeding to the most difficult — cóng qiǎn ér shēn, cóng jiǎn ér fán (from shallow to deep, from simple to complex).
(II) Per-proposition structure: each proposition has fǎ 法 (statement of the theorem-or-problem), jiě 解 (description of the case), lùn 論 (the demonstration), and xì 系 (corollaries-and-side-applications).
(III) Mathematical-terminological coinage: Ricci-Xú coined many of the standard Chinese mathematical terms still in use: diǎn 點 (point), xiàn 線 (line), zhíxiàn 直線 (straight line), qǔxiàn 曲線 (curved line), jiǎo 角 (angle), miàn 面 (surface / face), tǐ 體 (solid), lí 釐 (millimetric subdivisions), píngxíng 平行 (parallel), zhíjiǎo 直角 (right angle), jiānjiǎo 尖角 (acute angle), dùnjiǎo 鈍角 (obtuse angle), jǐhé 幾何 (the geometric magnitude itself, used in the title).
The 提要’s verdict is exceptionally enthusiastic — the most enthusiastic any Western technical work receives in the entire Sìkù corpus: “Furthermore, this is the European mathematical specialist book — predecessors composing and successors transmitting it without break in the world. Reaching Euclid and making this book — indeed [it] also gathers the various schools’ completion. Therefore from beginning to end, [it has] no slightest flaw. Adding [Xú] Guāngqǐ’s repeated extension-and-expounding, the wording is especially clear-and-evident. By this ‘crowning the Western art’ [biànmiǎn Xīshù 弁冕西術] [we are] not in excess”.
The Wàn-lì-period reception of the Jǐhé yuánběn was considerable but constrained by its mathematical demands. Xú Guāngqǐ’s preface (preserved in full) presents the work as the foundational reform of Chinese mathematical practice: “the Jǐhé yuánběn is the source of measurement-and-numbers, by which to exhaust the situation of square-and-round-and-flat-and-straight, to fully-utilize the standards of compass-and-square-and-water-level-and-plumb-line”. Xú connects the work to the lost Yáo-Shùn-and-Three-Dynasties mathematical tradition and frames the translation as the recovery of the qíng (situations / configurations) and yòng (uses) that had been abandoned for two thousand years.
The remaining 9 books of Euclid + 2 Clavius continuation books (= books VII–XV of the standard 15-book recension) were not translated into Chinese until Alexander Wylie (1815-1887) and Lǐ Shànlán 李善蘭 completed the work in 1857 — a 250-year gap.
For Euclid himself, see 歐几里得. For the principal translators, see 利瑪竇 (Ricci) and 徐光啟 (Xú Guāngqǐ). For the related Wàn-lì-period Jesuit mathematical works, see KR3f0009 Qiánkūn tǐyì, KR3f0014 Cèliáng fǎyì, KR3f0046 Tóngwén suànzhǐ. For the Kāngxī-period synthesis that built on this foundation, see KR3f0018 Lìxiàng kǎochéng and KR3f0026 Lìsuàn quánshū.
Tiyao
Your servants respectfully note: Jǐhé yuánběn 幾何原本, in 6 juǎn, was composed by the Westerner Ōu-jǐlǐdé 歐几里得 (Euclid), translated by Lì Mǎdòu 利瑪竇 (Matteo Ricci), and brushed [i.e., transcribed from oral dictation into literary Chinese] by Xú Guāngqǐ 徐光啟. The exact period in which Euclid lived is unknown. His original work comprised 13 juǎn with more than 500 propositions; Matteo Ricci’s teacher, Master Dīng 丁氏 (Christopher Clavius), compiled annotations to it and appended 2 supplementary juǎn, making 15 juǎn in total. The present [text has] only 6 juǎn because Xú Guāngqǐ himself said, in receiving the translation of this book, that these are the most essential portions.
Each juǎn of the book has jièshuō 界説 (definitions), gōnglùn 公論 (common notions), and shètí 設題 (propositions). The jièshuō first take the technical terms to be used and explain them; the gōnglùn state principles that cannot be doubted; the shètí then set out in sequence, according to the intent of the argument, first the easy and then the difficult — proceeding from the shallow to the deep, from the simple to the complex, pushed on until there is nothing further to add and then stopping. Moreover, each proposition has fǎ 法 (statement of the problem), jiě 解 (explication), lùn 論 (demonstration), and xì 系 (corollary). The fǎ states the problem’s application; the jiě recounts the proposition’s meaning; the lùn elucidates the underlying reasons; the xì further brings in those things that can be extended by analogy.
Book I treats triangles (sānjiǎoxíng 三角形); Book II treats lines (xiàn 線); Book III treats circles (yuán 圓); Book IV treats figures inscribed in and circumscribed about circles (yuán nèiwài xíng 圓内外形); Books V and VI both treat proportion (bǐlì 比例). As for the remaining topics — the mutual-engendering transformations of [the quantities associated with] triangles, squares, circles, sides, lines, areas, volumes, and ratios — there is none that is not displayed in full, with even the finest details entirely revealed. Xú Guāngqǐ’s preface describes it as “exhausting the situations of square, circle, flat and straight; fully utilizing the uses of compass, square, water-level, and plumb-line” — these are no empty words.
Moreover, this is the European mathematical specialist text — those before composing it and those after expounding upon it, with the line never broken in the world. Coming to Euclid and making this book, he had also gathered the achievement of the various schools. Therefore from beginning to end there is not the slightest flaw. Adding [Xú] Guāngqǐ’s repeated elucidations and extensions, the wording is especially clear and evident. By this to ‘crown the Western art’ (biànmiǎn Xīshù 弁冕西術) is no exaggeration.
Respectfully collated and submitted in the twelfth month of Qiánlóng 46 [1781]. Chief Editors: [Your servants] Jì Yún 紀昀, Lù Xíxióng 陸錫熊, Sūn Shìyì 孫士毅. Chief Collator: [Your servant] Lù Fèichí 陸費墀.
Translations and research
- Engelfriet, Peter M. Euclid in China: The Genesis of the First Chinese Translation of Euclid’s Elements, Books I–VI (Jihe Yuanben, Beijing, 1607) and Its Reception up to 1723, Sinica Leidensia 40, Leiden: Brill, 1998. The standard scholarly Western-language treatment.
- Hashimoto Keizō 橋本敬造. Hō Yū-ran, Kyoto: Kansai University Press, 1988.
- D’Elia, Pasquale M., S.J. Fonti Ricciane, 3 vols., Roma: La Libreria dello Stato, 1942–1949.
- Standaert, Nicolas (ed.). Handbook of Christianity in China, vol. 1: 635–1800, Leiden: Brill, 2001.
- Spence, Jonathan D. The Memory Palace of Matteo Ricci, New York: Viking, 1984.
- Liáng Jiāmiǎn 梁家勉, Xú Guāngqǐ nián-pǔ 徐光啟年譜, Shànghǎi: Shànghǎi Gǔjí Chūbǎnshè, 1981.
- Po-chia Hsia, R. A Jesuit in the Forbidden City: Matteo Ricci, 1552–1610, Oxford: Oxford University Press, 2010.
- Mei Rongzhao 梅榮照, Míng-Qīng shù-xué-shǐ lùn-wén jí 明清數學史論文集, Nánjīng: Jiāngsū Jiào-yù Chūbǎnshè, 1990.
Other points of interest
The 提要’s exceptional praise for the Jǐhé yuánběn — exceeding even its praise for Méi Wéndǐng’s KR3f0026 Lìsuàn quánshū — is one of the most striking editorial endorsements in the entire Sìkù corpus. The phrase biànmiǎn Xīshù 弁冕西術 (“crowning the Western art”) deliberately uses the Chinese imperial-ceremonial term biànmiǎn (crown-and-cap, the imperial regalia) — a strong cultural endorsement.
The translation’s terminological coinages — particularly the use of jǐhé 幾何 (literally “how much?” — interrogative-of-quantity) for the technical geometric magnitude — are foundational for modern Chinese mathematical vocabulary. The transliteration Ōu jǐlǐdé 歐几里得 became the conventional Chinese name for Euclid.
Note that, despite the 提要’s enthusiastic embrace, the Wàn-lì-period Jesuit translation activity did not extend the Euclid work beyond Book VI. The Sìkù editors are aware of this limitation (the 提要 specifically notes that Xú Guāngqǐ “recorded that he translated this book — what he says is that this is the most-essential [portion]”, implying the others might be translated later). The Wylie-Lǐ Shànlán completion of 1857 is one of the major Chinese mathematical-translation projects of the 19th century.