The Grail Geometry used to compose paintings is explained:
STEP 1. The artist starts with a convenient square ABCD and marks the midpoints of each side. Then he draws the smaller square EFGH: Note that the artist will do this geometry work on a preliminary drawing sheet, often bigger than the final canvas. Vermeer often uses only part of the total geometry – i.e. the complete Grail Geometry often extends beyond the confines of Vermeer’s canvases. This is governed by the artist’s compositional ideas.[]This diagram comes from an ancient proof of Plato's Theorem:
STEP 1. The artist starts with a convenient square ABCD and marks the midpoints of each side. Then he draws the smaller square EFGH: Note that the artist will do this geometry work on a preliminary drawing sheet, often bigger than the final canvas. Vermeer often uses only part of the total geometry – i.e. the complete Grail Geometry often extends beyond the confines of Vermeer’s canvases. This is governed by the artist’s compositional ideas.[]This diagram comes from an ancient proof of Plato's Theorem:
STEP 2. A circle is inscribed within the smaller square so as to be tangent to all sides.
[]This diagram is the Templar Variation of Plato's Theorem:
The TILTED TRIANGLE:
STEP 3. The all-important equilateral triangle (all sides equal, all angles equaling 60 degrees) A—V1—V2 is drawn with all sides tangent to the circle. This is the so-called “Tilted Triangle” that one searches for among the painted features in a composition. The letters J and M identify the fact that this triangle is “tilted” downwards 15 degrees from the horizontal line AB. The point A is often called “The Northwest Point” when the Grail Geometry, hidden a painting, is transferred to the landscape at the proper scale and in registration with certain predetermined permanent landmarks on the map