The Classical Orders of Greek and Roman antiquity represented their proportioning of elements that express perfect beauty and harmony.
The Colosseum in Rome, Italy is a great example of the classical Greek Orders because each tier was built with a different order.
Renaissance Theories include 'Ideal' room plan shapes as well as a harmonious proportion of height to the rooms width and length determined by Andrea Palladio. The Italian Renaissance architect's Villa Rotunda displays one of his seven ideal plans.
More recently in the 1940's, Le Corbusier developed his proportioning system, the Modulor, based on mathematics and the human scale. The French architect saw the Modular as a system of measurements that could govern length, surfaces, volumes, and maintain the human scale everywhere. An infinity of combinations ensuring unity with diversity.
Another theory of proportion comes from the Japanese Ken grid. The Ken is used as an aesthetic module that ordered the structure, materials, and space of Japanese architecture.
Anthropometry refers to the measurement of the size and proportions of the human body. These measurements affect the proportion of things we handle, the height and distance of our reach, and the dimensions of the furnishings we use. Below demonstrates the latter.
The last theory of proportion is scale. Scale refers to how we perceive or judge the size of something in relation to something else. The image of a large scale sculpture of a balloon animal towers over the house in the background, showing the disproportion of scale.