In classical architecture, the module was established as the radius of the lower axis of a classical column, with proportions expressed as fractions or simple multiples of that module.[4]​.

The study of proportion became a matter of great importance in Renaissance architecture, following different approaches:

In his “Four Books on Architecture”, Andrea Palladio establishes a hierarchy of spatial proportions that goes directly back to Plato.[5]​ "There are seven types of rooms that are most beautiful and best proportioned...":.

In his "Four Books" there are a series of designs for villas and palaces, such as the Antonini Palace shown as the first example, whose rooms are proportioned according to these categories. The height of the rooms corresponds to their width, the height of the mezzanine floor must be one sixth lower than that of the main floor below.

Daniele Barbaro and Andrea Palladio translated Vitruvius' treatise from Latin into Italian and supplemented it with mathematical and geometric methods, as well as geometric and architectural drawings. They also described the proportions of diagonals (square roots), which give architects additional proportions for a harmonious design. The procedure consists of starting from a square, whose diagonal is folded onto the opposite side with a compass, to create the proportion 1: (1:1.414...). The newly formed rectangle is lowered again along its diagonal, and a new triangle of proportion 1: (1:1,732..) is created. In this way, the proportions , ,... are obtained one after the other.

Since root proportions generally generate incommensurable numbers, approximations were used in the past that were precise enough for the builders of the time:.

Root proportions also became easier to handle through approximations:.

Palladio specified the dimensions 30:26:21:15 Vincentian feet (approximately 34.7 cm)[7]​ for his design of the famous Villa Capra.[8]​[9]​.

To harmonize the multitude of different proportions, Alberti and Palladio described the application of different means constructible with a ruler and compass. For example, the arithmetic mean (average) of the length and width of a floor plan is determined mathematically or geometrically to find the height of the room or the ratio of the next room. Both architects also describe the geometric mean and the harmonic mean to have a greater variety of relationships.[10]​.

In his work Le Modulor (1948), Le Corbusier presented a system of proportions that took the golden ratio and a man with a raised arm as the scalable modules of proportion.

In classical architecture, the module was established as the radius of the lower axis of a classical column, with proportions expressed as fractions or simple multiples of that module.[4]​.

The study of proportion became a matter of great importance in Renaissance architecture, following different approaches:

In his “Four Books on Architecture”, Andrea Palladio establishes a hierarchy of spatial proportions that goes directly back to Plato.[5]​ "There are seven types of rooms that are most beautiful and best proportioned...":.

In his "Four Books" there are a series of designs for villas and palaces, such as the Antonini Palace shown as the first example, whose rooms are proportioned according to these categories. The height of the rooms corresponds to their width, the height of the mezzanine floor must be one sixth lower than that of the main floor below.

Daniele Barbaro and Andrea Palladio translated Vitruvius' treatise from Latin into Italian and supplemented it with mathematical and geometric methods, as well as geometric and architectural drawings. They also described the proportions of diagonals (square roots), which give architects additional proportions for a harmonious design. The procedure consists of starting from a square, whose diagonal is folded onto the opposite side with a compass, to create the proportion 1: (1:1.414...). The newly formed rectangle is lowered again along its diagonal, and a new triangle of proportion 1: (1:1,732..) is created. In this way, the proportions , ,... are obtained one after the other.

Since root proportions generally generate incommensurable numbers, approximations were used in the past that were precise enough for the builders of the time:.

Root proportions also became easier to handle through approximations:.

Palladio specified the dimensions 30:26:21:15 Vincentian feet (approximately 34.7 cm)[7]​ for his design of the famous Villa Capra.[8]​[9]​.

To harmonize the multitude of different proportions, Alberti and Palladio described the application of different means constructible with a ruler and compass. For example, the arithmetic mean (average) of the length and width of a floor plan is determined mathematically or geometrically to find the height of the room or the ratio of the next room. Both architects also describe the geometric mean and the harmonic mean to have a greater variety of relationships.[10]​.

In his work Le Modulor (1948), Le Corbusier presented a system of proportions that took the golden ratio and a man with a raised arm as the scalable modules of proportion.