The study of algebra in China has often focused on the algebraic “procedure of the Celestial Source.” Its geometrical ancestors are less known. The Yigu yanduan, authored by Li Ye (1192-1279), presents the procedure alongside its two geometrical counterparts, the “Section of Pieces [of Areas]” and the “Old Procedure.” The three procedures are known to represent three generations of algorithms used to set up quadratic equations. A similar geometrical procedure appears in a treatise written by Yang Hui (second half of thirteenth century). Although the procedures look alike at first glance, the two treatises reveal different moments in their work on the relation between counting materials and geometrical representation. This study challenges their chronology trying to identify the meander of the geometrical roots of the Celestial Source. The construction of negative coefficients plays a pivotal role in this mutation and shows several layers of composition.
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Charlotte Victorine Pollet;
(2020)
The empty and the full: Li Ye and the way of mathematics : geometrical procedures by section of areas
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(2014)
The Influence of Qing Dynasty Editorial Work on the Modern Interpretation of Mathematical Sources: The Case of Li Rui's Edition of Li Ye's Mathematical Treatises
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Yassine Hachaichi;
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Note sur l'extraction de la racine carrée d'un entier chez ibn Al-Hayṯam et comparaison avec Al-Baġdādī
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Khalil, Roshdi;
Deeb, Waleed;
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An essay by the Uniquely Wise 'Abel Fath Omar Bin Al-Khayyam on Algebra and Equations: Algebra Wa Al-Muqabala
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Oaks, Jeffrey A.;
(2009)
Polynomials and Equations in Arabic Algebra
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Chemla, Karine;
(2012)
Reading Proofs in Chinese Commentaries: Algebraic Proofs in an Algorithmic Context
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Xu, Zelin;
Wei, Xia;
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Exploration on Yanduan---And on the Evolution of Algebraic Algorithm Mode in East Asia
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Ilana Wartenberg;
(2012)
The Place of Ibn al-Ahdab's Epistle of the Number in the Diffusion of Arabic Mathematics in Hebrew in Medieval Europe
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Guanglin William Liu;
(1825)
The Chinese Market Economy, 1000-1500
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Brown, Miranda;
(2015)
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Johansson, Bo Göran;
(2011)
Cube Root Extraction in Medieval Mathematics
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Explicit and Less Explicit Algorithmic Thinking, 1200-1500. Jordanus de Nemore, and the Contrast between Barthelemy de Romans et Chuquet
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Paul S. Sutter;
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The Technology of Orientation and Levelling in Yingzao Fashi
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Yuda Yang;
Nanny Kim;
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Texts and Technologies in Chinese Silver Metallurgy, Twelfth to Nineteenth Centuries
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Jinsong Guo;
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Sun, Xiaochun;
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Han, Jishao;
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