In this article we trace the scientific and cultural history of the astrolabe, a mechanical instrument used in the past for astronomical measurements and navigational purposes. The story of the astrolabe is interesting from several points of view, since it intertwines mathematical developments, geographical explorations, changing worldviews, and different cultures and civilizations. In our explorations, we move from the early understanding of the world due to the Greeks, to the loss of their work, its rediscovery, the reception of Arab thinkers in Western natural philosophy, and, finally, to the new European culture that emerged with the end of the Middle Ages and the beginning of the early Renaissance. We present a mathematical analysis of how the Celestial Sphere can be represented on the plane through the stereographic projection: this is the consequence of some geometrical results of Apollonius, together with later refinements, whose first traces appear in the work of Al-Farghān̄ı.

中文翻译：

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星盘的数学及其历史

在本文中，我们追溯了星盘的科学和文化历史，该星盘是过去用于天文测量和导航目的的机械仪器。从多种角度来看，这个星盘的故事很有趣，因为它融合了数学发展，地理探索，不断变化的世界观以及不同的文化和文明。在我们的探索中，我们从对希腊人的早期了解开始，转向他们的工作流失，重新发现，阿拉伯思想家对西方自然哲学的接受，最后转向新的欧洲文化。中世纪末期和文艺复兴初期。我们将对如何通过立体投影在平面上表示天球的数学分析：