J.L. Heilbron’s book “The Sun in the Church” addresses a basic problem: how is time measured? Since the time period of the Earth’s orbit around the Sun is not neatly divisible into a whole number of days, it is hard to construct a calendar that will mark a moment in time back at the exact same point after the Earth makes a complete orbit around the Sun. In the book, Heilbron gives a comprehensive overview of the various approaches that have been proposed and implemented by the Catholic Church to fix the calendar. As the Church wanted to have a systematic way to determine when Easter should be celebrated, the calendar had to be made as accurate and reliable as possible. In consequence, the Church became deeply involved in improving the quality of observational data on which calendars were based. Huge cathedrals were considered to be ideal solar observatories: by making a hole in the ceiling and fixing a mark on the floor where the sun's shadow fell along a meridiana, or a line laid out on the cathedral floor, exact measurements could be made regarding the position of the sun.

Many historical and technical facts on how the cathedrals came to be used as an instrument of measurement have been recorded in this book. Heilbron has succeeded in providing the readers with a most enriching and interesting experience as they read the historical account. Nonetheless, most readers would probably find it hard to appreciate the technical sections of this book because these sections call for a certain level of understanding in some mathematical concepts. This paper has been specially written as a mathematical supplement to enable readers to have a clearer comprehension of how certain conclusions have been drawn or how certain values have been obtained. Due to the sheer volume of this book, the supplement provides explanations for only a few sections of it; similar supplements for the rest of the book are expected to appear in the near future.

The structure of this supplement is broadly categorized into two parts. Firstly, a collection of preliminary information used in later explanations is given. This includes some mathematical tools and the models created by Hipparchus, Ptolemy and Kepler to explain the motions of the Sun and the planets. Secondly, detailed explanations of selected sections of Heilbron’s book are provided. These concern the steps in calculation involved in working out certain values and the comparison of models. The use of a meridiana to justify the superiority of one model over another is also discussed.