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Abstract.  Heron's Dioptra 35 is the unique witness of an ancient mathematical procedure for finding the great arc distance between two cities using methods of ancient spherical astronomy and simultaneous observations of a lunar eclipse. This paper provides a new study of the text, with mathematical and historical commentary. I argue that Heron's account is a summary of some longer work of mathematical astronomy or geography, which made extensive use of the analemma, an ancient model of the celestial sphere. Heron's text can be used to show the utility of the analemma model, both as a theoretical device and as a computational tool.