Symmetry and Proportion in Design

What Leonardo da Vinci Learned from Vitruvius

Architectural drawing of a future window with dimensions and focal point
Symmetry and Proportion in Architectural Drawing. Photo by Pierre Desrosiers/Photographer's Choice/Getty Images

How do you design and build the perfect building? Structures have parts, and those elements can be put together in many ways. Design, from the Latin word designare meaning "to mark out," is the overall process, but design outcomes depend on symmetry and proportion.

Says who? Vitruvius.

De Architectura

Roman architect Marcus Vitruvius Pollio wrote the first architecture textbook, called On Architecture (De Architectura).

Nobody knows when it was written, but it was at the dawn of human civilization—in the first century BC into the first decade AD. It's been translated a number of times throughout the years, but much of the theory and construction basics spelled out for the Roman Emperor is valid even in the 21st century.

So, what does Vitruvius say? Architecture depends on symmetry, the "proper agreement between the members of the work itself."

  • Symmetry, from the Greek word symmetros meaning "measured together."
  • Proportion, from the Latin word proportio meaning "for the part," or the relationship of the portions.

Did Vitruvius find the proper agreement?

Leonardo da Vinci Sketches Vitruvius

Leonardo da Vinci (1452-1519) is sure to have read Vitruvius. We know this because da Vinci's notebooks are filled with sketches based on the words in De Architectura. Da Vinci's famous drawing of The Vitruvian Man is a sketch directly from the words of Vitruvius.

These are some of the words Vitruvius uses in his book:

symmetry

  • in the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centered at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle
  • And just as the human body yields a circular outline, so too a square figure may be found from it.
  • For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.

Note that Vitruvius begins with a focal point, the navel, and the elements are measured from that point, forming the geometry of circles and squares. Even today's architects design this way.

proportion

Da Vinci's notebooks also show sketches of body proportions. These are some of the words Vitruvius uses to show relationships between elements of a human body:

  • the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part of the whole height
  • the open hand from the wrist to the tip of the middle finger is a tenth part of the whole body
  • the head from the chin to the crown is an eighth part
  • with the neck and shoulder from the top of the breast to the lowest roots of the hair is a sixth
  • from the middle of the breast to the summit of the crown is a fourth
  • the distance from the bottom of the chin to the under side of the nostrils is one third of it
  • the nose from the under side of the nostrils to a line between the eyebrows is a third
  • the forehead, from between the eyebrows to the lowest roots of the hair, is a third
  • the length of the foot is one sixth of the height of the body
  • the length of the forearm is one fourth the height of the body
  • the breadth of the breast is also one fourth the height of the body

Da Vinci saw that these relationships between elements were also the mathematical relationships found in other parts of nature. What we think of as the hidden codes in architecture, Leonardo da Vinci saw as divine. If God designed with these ratios, then man should design the built environment with the ratios of sacred geometry.

Designing with Symmetry and Proportion:

By examining the human body, both Vitruvius and da Vinci understood the importance of "symmetrical proportions" in design.

As Vitruvius writes, "in perfect buildings the different members must be in exact symmetrical relations to the whole general scheme." This is the same theory behind architectural design today. Our sense of what we consider beautiful comes from symmetry and proportion.

Source: On Symmetry: In Temples and in the Human Body, Book III, Chapter One, The Project Gutenberg EBook of Ten Books on Architecture, by Vitruvius, translated by Morris Hicky Morgan, 1914