In examining the roles of the shadow (umbra) in medieval science, this paper analyses a hitherto unstudied early fourteenth-century optical treatise with the incipit Perspectiva cum sit una (PCSU), which, on the basis of medieval evidence, may arguably be attributed to Thomas Bradwardine. The third part of this treatise, on shadows, presents the doctrine of three shadow shapes – a doctrine which was popular in pre-modern optics and astronomy and was important in explaining eclipses – as well as the theory of umbra recta and versa, parallels of (co)tangent functions, which were essential for (instrumental) measurements. While the bulk of the treatise draws on John Peckham’s Perspectiva communis, an extensive analysis of medieval canons to astronomical tables, manuals of practical geometry and texts on instruments leads us to Campanus of Novara’s Practica quadrantis as the chief source of the last chapter of PCSU. Finally, the paper reflects on whether the light-centred conception of optics embodied in the PCSU may echo an alternative current to the otherwise predominantly sight-centred approach in pre-modern optics.

中文翻译：

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中世纪光学、实用几何和天文学中的阴影：关于托马斯·布拉德沃丁 (Thomas Bradwardine) 的视角

在检查阴影的作用时（本影) 在中世纪科学中，这篇论文分析了一篇迄今未被研究的 14 世纪早期光学论文，并从Perspectiva 暨坐 una(PCSU)，根据中世纪的证据，可以说是托马斯·布拉德沃丁 (Thomas Bradwardine) 的作品。这篇论文的第三部分，关于阴影，介绍了三种阴影形状的学说——这一学说在前现代光学和天文学中很流行，对解释日食很重要——以及直本影和相反，平行于（共）切函数，这对于（仪器）测量是必不可少的。虽然该论文的大部分内容借鉴了 John Peckham 的观点, 对中世纪教规到天文表、实用几何手册和仪器文本的广泛分析将我们引向诺瓦拉的坎帕努斯象限练习作为最后一章的主要来源PCSU. 最后，论文反思了光学的光心概念是否体现在PCSU可能与前现代光学中以视觉为中心的方法相呼应。