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Keywords = Euclid’s Elements

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16 pages, 420 KB  
Article
Translating Euclid’s Elements into Chinese: Western Missionaries and the Enlightenment for Modern Chinese Mathematics During the Late Ming and Early Qing Dynasties
by Jiyun Huang, Shangqing Hu and Yafeng Li
Religions 2025, 16(7), 921; https://doi.org/10.3390/rel16070921 - 17 Jul 2025
Viewed by 1342
Abstract
During the late Ming and early Qing Dynasties, China underwent a period of broad-based economic and societal transformation. Among the cultural forces at play, the Christian culture has significantly impacted the trajectory of Chinese history. At the time, responding to a distinct socio-political [...] Read more.
During the late Ming and early Qing Dynasties, China underwent a period of broad-based economic and societal transformation. Among the cultural forces at play, the Christian culture has significantly impacted the trajectory of Chinese history. At the time, responding to a distinct socio-political environment, Western missionaries employed a variety of religious methodologies to pursue the goal of proselytizing. As part of missionary efforts, they introduced Western scientific and cultural knowledge into China alongside Christian doctrines, coinciding with a period of political and cultural transformation and development in China. Accordingly, this influx of new ideas from the West had a far-reaching impact on Chinese society. This paper focuses on the Chinese translation of Euclid’s Elements, examining the intercultural dissemination of Western mathematical knowledge through missionary activities. Furthermore, the study also elucidates the positive impact of Western mathematics carried with religious efforts on the Chinese traditional mathematical system via presenting a comparison of paradigms in mathematics. Finally, this study argues that the translation practice by Christian emissaries from the West in the natural sciences during the Ming and Qing Dynasties engendered novel intellectual currents, thereby facilitating the development of a contemporary Chinese knowledge framework and a shift in religious research toward comprehensive perspectives. Full article
(This article belongs to the Special Issue Chinese Christianity and Knowledge Development)
20 pages, 3100 KB  
Article
SDGs-Based River Health Assessment for Small- and Medium-Sized Watersheds
by Chenyang Xue, Chaofeng Shao and Sihan Chen
Sustainability 2020, 12(5), 1846; https://doi.org/10.3390/su12051846 - 1 Mar 2020
Cited by 23 | Viewed by 3622
Abstract
A river health assessment index system was established, focusing on the realistic needs of county sustainable development and the refined management of small- and medium-sized watersheds. The index system takes into consideration the United Nations’ Sustainable Development Goals (SDGs) and the vulnerability characteristics [...] Read more.
A river health assessment index system was established, focusing on the realistic needs of county sustainable development and the refined management of small- and medium-sized watersheds. The index system takes into consideration the United Nations’ Sustainable Development Goals (SDGs) and the vulnerability characteristics of small- and medium-sized watershed ecosystems and consists of 15 indicators in four areas: clean water, sanitation, the present status of biodiversity and threats to biodiversity. This paper uses the minimum discrimination information principle to construct a dynamic combination-weighting technology composed of a subjective weighting method (document frequency method) and an objective weighting method (entropy weight method). Using the fuzzy matter-element analysis theory, a comprehensive river health assessment technology system was constructed. Baoxing County was chosen as the research area and the results reveal that: (1) Key indicators are the biodiversity index of fish, water use intensity, endemic or indicative species retention, and chemical oxygen demand (COD) emissions. (2) The Euclid approach degree of Baoxing County indicates that the entire river is in a moderate state of health. In the future, towns must take targeted measures to coordinate the relationship between the ecological environment and socio-economic development, and enhancement and releasing must be prioritised. Full article
(This article belongs to the Special Issue Sustainable Water, Economic Management and Governance Issues)
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13 pages, 2279 KB  
Article
The Two Supreme Principles of Plato’s Cosmos—the One and the Indefinite Dyad—the Division of a Straight Line into Extreme and Mean Ratio, and Pingala’s Mātrāmeru
by Maria Antonietta Salamone
Symmetry 2019, 11(1), 98; https://doi.org/10.3390/sym11010098 - 16 Jan 2019
Cited by 2 | Viewed by 8865
Abstract
The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos—Fire and Earth—through the Mean Ratio. [...] Read more.
The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos—Fire and Earth—through the Mean Ratio. As we know, from the algebraic point of view, it is possible to compose a continuous geometric proportion just starting from two different quantities a (Fire) and b (Earth); their sum would be the third term, so that we would obtain the continuous geometric proportion par excellence, which carries out the agreement of opposites most perfectly: (a + b)/a = a/b. This equal proportion, applied to linear geometry, corresponds to what Euclid called the Division into Extreme and Mean Ratio (DEMR) or The Golden Proportion. In fact, according to my mathematical interpretation, in the Timaeus 32b and in the Epinomis 991 a–b, Plato uses Pingala’s Mātrāmeru or The First Analogy of the Double to mould the body of the Cosmos as a whole, to the point of identifying the two supreme principles of the Cosmos—the One (1) and the Indefinite Dyad (Φ and1/Φ)—with the DEMR. In effect, Fire and Earth are joined not by a single Mean Ratio but by two (namely, Air and Water). Moreover, using the Platonic approach to analyse the geometric properties of the shape of the Cosmos as a whole, I think that Timaeus constructed the 12 pentagonal faces of Dodecahedron by means of elementary Golden Triangles (a/b = Φ) and the Mātrāmeru sequence. And, this would prove that my mathematical interpretation of the platonic texts is at least plausible. Full article
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21 pages, 1917 KB  
Article
Study on the Comprehensive Benefit Evaluation of Transnational Power Networking Projects Based on Multi-Project Stakeholder Perspectives
by Yunqi Zhao, Jing Xiang, Jiaming Xu, Jinying Li and Ning Zhang
Energies 2019, 12(2), 249; https://doi.org/10.3390/en12020249 - 15 Jan 2019
Cited by 10 | Viewed by 2985
Abstract
Interconnection of transnational power grids plays an important role in realizing the optimal allocation of energy resources. It can also deepen regional economic cooperation, achieve energy conservation and emission reduction, and improve people’s livelihood. This paper constructs a comprehensive benefit evaluation index system [...] Read more.
Interconnection of transnational power grids plays an important role in realizing the optimal allocation of energy resources. It can also deepen regional economic cooperation, achieve energy conservation and emission reduction, and improve people’s livelihood. This paper constructs a comprehensive benefit evaluation index system for transnational power networking projects which is suitable for the four stakeholders of investors, international lending institutions, sending-oriented states, and receiving-oriented states. Therefore, on the basis of this index system, this paper adopted the weight determination method based on the order relation method and Gini coefficient method to synthesize subjective and objective information. Then the comprehensive benefit evaluation of such projects was carried out by matter-element extension model with grey relational projection value. Therefore, the problem with the Euclid approach degree leading to a low discrimination of many samples to be evaluated was effectively solved. The final empirical analysis results showed that the focus and evaluation results of the comprehensive benefits of such projects from the perspective of different stakeholders were quite different. The results of comprehensive benefit evaluation will improve the accuracy of decision-making and the objectivity of evaluation, so as to provide decision-making references for different stakeholders. Full article
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12 pages, 4042 KB  
Proceeding Paper
Ad Oculos. Images, Imagination and Abstract Thinking
by Alessandra Cirafici
Proceedings 2017, 1(9), 945; https://doi.org/10.3390/proceedings1090945 - 14 Mar 2018
Cited by 1 | Viewed by 2560
Abstract
The unusual edition of Elements of Euclid released for publishing in 1847 by Oliver Byrne offers the occasion to suggest a few elements for discussion on the uniqueness of the ‘representation’ of geometric-mathematical thinking—and more in general of the abstract thinking—enshrined in its [...] Read more.
The unusual edition of Elements of Euclid released for publishing in 1847 by Oliver Byrne offers the occasion to suggest a few elements for discussion on the uniqueness of the ‘representation’ of geometric-mathematical thinking—and more in general of the abstract thinking—enshrined in its ‘nature of a pure imaginative vision able to connect the intelligible with the tangible’. The purpose is, thus, a reasoning on images and communicative artefacts, that, when articulated, provide different variations of the idea of ‘transcription’ of complex theoretical structures from one language (that of abstract logic) to another (that of sensory experience), with a view to facilitate, ease and make more accurate the noetic process. Images able over time to facilitate the understanding of complex and abstract theoretical principles—since able to show them in an extremely concrete way, ad oculos,—and which at some points could reveal the horizons of art interpretation to inscrutable and figurative meaningless formulas. Full article
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