One source (Etymology.com) states: "... The term "The whole is greater than the sum of its parts" originated with the Gestalt School of Psychology.The Gestalt concept was first introduced in contemporary philosophy and psychology by Christian von Ehrenfeis in the late 1800's although the idea has its roots in the theories of Johann Wolfgang von Goethe, Immanuel Kant and Ernst Mach. The Gestalt School theorists (Max Wertheimer Gestalt theory) saw objects as perceived within an environment according to all of their elements taken together as a global constuct. The 'whole form' approach sought to define principles of perception, sseemingly innate mental laws which determined the way in which objects were perceived.
"The sum of the whole is greater than its parts" is the idea behind this Gestalt principle. It's the perception of a composition as a whole. While each of the individual parts have meaning on their own, taken together, the meaning may change. Our perception of the piece is based on our understanding of all the bits and pieces working in unison. Approximately 1920..."