“Diego Velázquez was a master geometrician. He had an extensive library of geometry books, ranging from Euclid´s Elements to Vitruvius´s Ten Books on Architecture to Palladio´s Four Books on Architecture. Velázquez also had a wide assortment of geometry tools, which he used for his compositions. Velázquez had a great spontaneity about his work, yet his essential composition was very much based on his knowledge of harmonic design principles.
In Las Meninas, Velázquez contained all the figures within the horizontal one-half division of the picture plane; the artist´s own head and the frame of the mirror are precisely at that division line. The vertical one-half division runs along the edge of the open door in the background and also frames the right side of the central girl. The horizontal two-thirds division runs through the eyes of the two girls on the left side of the painting and also touches the bottom of the chin and top of the head of the two figures on the far right side of the canvas.
Velázquez made use of both major diagonals. The diagonal that runs from lower right to upper left frames the angle of the one of the main girls – her body and arm literally rest upon the line. This diagonal also sets the top-corner placement of the massive canvas within the paintings itself. The diagonal that runs from lower left to upper right sets the angle of the girl on the far left and also runs through the face of the figure in the mirror. In addition, the diagonal that runs from the lower middle to the upper left encloses the figure of the artist himself, while the adjoining diagonal, which runs from the lower middle to the upper right, sets the angle of the woman in the background. Many artists have been influenced by Velázquez´s compositions. John Singer Sargent bases his remarkable The Daughters of Edward Darley Boit on Las Meninas.”