I have truly found the Royal way of treating in their natural order all of matheamatics. And having begun with the Ratios and Proportions, Common Properties of Quantities, the univrsal subject of all Mathematics, and seeming to me that I have not only treated them, as I said, in their natural order, but have also amplified and pared them down where necessary, and with such facility have I explained them that they have become clear and easy, difficult though they were.
Silvio Belli, "To the Readers"

With these words, Silvio Belli, known as a "friend of Palladio's" and "Palladio's mathematical companion", summed up his achievements in On Ratio and Proportion. Belli lived at almost exactly the same time as the architect Andrea Palladio; they were both founding members of Vicenza's Accademia Olimpica. Palladio himself referred to Belli in a letter as "the most excellent geometer in our area". Published in Venice in 1573, On Ratio and Proportion is the second of Belli's two publications, following his very successful Libro del misurar con la vista (Book on Measuring by Sight). Regarding Belli's achievements in On Ratio and Proportion, Lionel March writes in his Foreword, "The tract does not make any original contribution to mathematics, and that may be its value from an art historical viewpoint. It records the ordinary understanding of ratio and proportion as would be appreciated by contemporaries of Palladio." The present translation and commentary makes the "ordinary understanding" of the cinquecento accessible to English-speaking scholars for the first time.

Stephen R. Wassell is a professor of mathematics in the Department of Mathematical Sciences at Sweet Briar College, Sweet Briar, Virginia (USA).

Kim Williams is the director of the conference series Nexus: Architecture and Mathematics and editor of the Nexus Network Journal.