Luca Pacioli (ca. 1447–1517) is widely considered a central figure in the Italian Renaissance, particularly in the history of practical mathematics. The perspectival representations of geometrical bodies that Leonardo da Vinci drew for Pacioli’s Compendium de divina proportione are, in turn, often singled out to illustrate the relationships between the visual arts and mathematics in the late fifteenth century. Yet despite increasing scholarly attention, the philosophical framework of Pacioli’s works deserves to be further explored. This paper discusses how Pacioli ably developed his arguments on regular geometrical bodies by relying on a predominantly Aristotelian philosophical framework. In this way, Pacioli established correlations among the quantitative, material, and formal properties of regular geometrical bodies, concluding with the visualisation of their (geometrically defined) form at the level of the intellect.

中文翻译：

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卢卡·帕乔利 (Luca Pacioli) 的 Summa (1494) 和 Compendium de divina approxe (1498) 中规则几何体的形式和物质


卢卡·帕乔利（Luca Pacioli，约 1447-1517 年）被广泛认为是意大利文艺复兴时期的中心人物，特别是实用数学史上的中心人物。列奥纳多·达·芬奇为帕乔利画的几何体的透视表现神圣比例概要反过来，它们经常被挑选来说明十五世纪后期视觉艺术和数学之间的关系。然而，尽管帕乔利著作的哲学框架越来越受到学术界的关注，但仍值得进一步探讨。本文讨论了帕乔利如何依靠主要的亚里士多德哲学框架巧妙地发展了他关于规则几何体的论证。通过这种方式，帕乔利建立了规则几何体的数量、材料和形式属性之间的相关性，并最终在智力层面上可视化了它们（几何定义的）形式。