Without symmetry and proportion there can be no principles in the design of any temple; that is, if there is no precise relation between its members, as in the case of those of well shaped man.
Symmetry is a proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme, in accordance with a certain part selected as a standard.
Therefore since nature has proportioned the human body so that its members are duly proportioned to the frame as a whole, ... in perfect buildings the different members must be in exact symmetrical relations to the whole general scheme.Note: Vitruvius (70?-25 B.C.E.) uses the phrase symmetrical relations to mean the same proportion rather than some other kind of symmetry. Roughly 1500 years later, Leon Battista Alberti would echo Vitruvius in his 10 books on architecture, de Re Aedificatoria, circa 1450 (which are largely his attempts at understanding Vitruvius' work). He defined beauty as
A harmony of all the parts, in whatsoever subject is appears fitted together with such proportion and connection that nothing could be added, diminished, or altered, but for the worse.The contemporary architect Herman Hertberger gives a related definition:
Building order is the unity that arises in a building when the parts taken together determine the whole, and conversely, when the separate parts derive from that whole in a n equally logical way.All three of these architects, from vastly different eras, are saying the same thing: buildings ought to be built in a way so that the size and shape of the whole is related in a logical way to the size and shape of the parts -- that is, that a system of proportions ought to be used in designing a building.