Rudolf Wittkower's Architectural Principles in the Age of Humanism traces how the artists of Italian Renaissance, such as Alberti and Leonardo, found elaborate correlations between the visible and intelligible worlds. For Wittkower, the new scientific approach to nature "which is the glory of Italian fifteenth-century artists" had a notable share in consolidating and popularizing the mathematical interpretation of all matter. (p.29) They regarded architecture as a mathematical science which worked with spatial units: parts of that universal space for the scientific interpretation of which they had discovered the key in the laws of perspective. Thus they were made to believe that they could re-create the universally valid ratios and expose them pure and absolute, as close to abstract geometry as possible.
Alberti knew that the mathematical relations between plan and section cannot be correctly perceived when one walks about in a building. For Wittkower, "We must conclude that the harmonic perfection of the geometric scheme represents an absolute value, independent of our subjective and transitory perception." (P.8)