The paper analyses the proportional relationships in the plans of Palladio’s buildings presented in the second book of his I quattro libri dell’architettura. In 1949 Rudolf Wittkower suggested that harmonic proportions were the underlying principle of Palladio’s designs, but he analysed only 8 out of 44 buildings that Palladio presented in the book. Subsequently, in 1982, Deborah Howard and Malcolm Longair attempted a comprehensive statistical and quantitative analysis of all 44 buildings. Their results were only partly satisfactory: although Palladio’s ratios in about two-thirds of plans fitted Wittkower’s interpretation, proportions of some of Palladio’s best known buildings, such as the villa Rotonda remained unexplained. Further, neither Wittkower nor Howard and Longair took into consideration the heights of the rooms–they studied only ground-plan (room length/width) ratios.

This paper increased the number of explainable length/width ratios, introduced the consideration of triangulation in Palladio’s designs, analysed data pertaining to rooms’ heights, and offered a theory about the way Palladio coordinated of proportions between rooms.