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Skip to Content. Toggle navigation Carolina Digital Repository. Help Contact Us Login. You do not have access to any existing collections. You may create a new collection. Husson, Matthieu Multifaceted mathematical reasoning in Jean des Murs De moventibus et motis Reasoning is a central concern in many mathematical traditions and it is expressed in various sources reflecting different practices. When we address mathematical reasoning in mathematical sciences, taken broadly, the diversity of mathematical reasoning becomes greater in relation to the variety of contexts in which those reasonings were shaped.
Sometimes actors use the possibility of weaving different levels of reading of the same reasoning according to the rhetorical form chosen to express it. The first part of the fourth book of the Quadripartitum numerorum is a text known for several reasons in the historiography. Remarks in it about incommensurability and celestial motions were put in relation with similar arguments that Nicole Oresme made later. Our aim in this paper is to examine the mathematical reasoning expressed in the De moventibus et motis and to show how Jean des Murs uses the possibility of the specific form he chooses for his text to extend its core mathematical meaning in the direction of astronomy, cosmology and natural philosophy.
We thus analyze the background knowledge Liu Hui relied on when he commented on the Nine Chapters on Mathematical Procedures , and illuminate the concepts and methods he used to establish this procedure.
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Therefore, this article argues that the circles and the squares Liu Hui dealt with in the Geyuan procedure were empirical objects. Moreover, relying on the empirical finite method to cut a circle, Liu Hui proves the area formula of a circle, and writes the text in which the general argumentation theory works, instead of using deductive inference, which is based on the infinitesimal analysis.
Another approach is to extract argumentations in the Geyuan procedure within the framework of modern mathematics. By the comparison between the two approaches, this article suggests that to interpret ancient texts by modern mathematics is not a good approach to the study of ancient argumentations. However, to interpret ancient texts in its historical local context could avoid some problems caused by the second approach, and offer an open viewpoint about ancient argumentations.
The aim of this paper, beyond its study of a specific case, is to raise a certain number of questions which spring from the existence of reasonings and modes of justification in Sanskrit mathematical and astral sources. What reasonings are used to prove a rule? Do all reasonings have such an aim? Are modes of justification different in mathematics and astral science?
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In the following, a famous reasoning found in Sanskrit literature- the one used to both construct and justify tabulated values of Sines and associated chord portions- will be studied. In these verses, Brahmagupta returns to the values he had given earlier for Sines, to provide a derivation and an extension of this list. The transformation attested to in the astronomical terminologies that relate to different calendrical systems in China reveals changes in the perceptions of astronomical computations and of their relations to geometry.
The traditional Chinese astronomy had its own terminological system for different calendrical systems. When the Islamic astronomical tables were introduced and adopted in early modern China, some new terms were created. After Western astronomical tables were transmitted to China, some scholars tried to establish a connection and made an analogy between the traditional Chinese terms and the new Western terms. In addition, they sought to understand the obscure Islamic terms with the help of Western astronomical theories, when they obtained more grounding geometrical knowledge.
Middeke-Conlin, Robert Tabular administrative texts as a reflection of mathematical practice By the Old Babylonian period, that is, the early second millennium BCE in Southern Iraq, some administrations begin to produce texts in a tabular format, instead of a more common prosaic format.