Rules · Geometry · Site · Modules
The cord stretched along the diagonal of a rectangle produces as much area as the cords along its two sides together; use this to set out right angles and to make squares of any required area.
d² = a² + b²; e.g. cords of 3, 4, 5 or 5, 12, 13 units
The Vedic altar-builders stated in words the theorem later credited to Pythagoras, and used it constantly: to make a right angle, stretch a cord with knots dividing it in the proportion of the sides of a right triangle; to make a square twice the size of a given one, build it on the diagonal; to add two squares, build a square on the diagonal of the rectangle they define. Baudhāyana also gives a rational value for the diagonal of the unit square that is correct to five decimal places.
These are surveyor’s rules. They let a building be set out full size on the ground with cords and pegs, which is how the squares of the vāstu diagram, the rathas of a temple plan and the concentric enclosures of a temple town were fixed.
Set a vertical rod at the centre of the levelled site, draw a circle round it, mark where the tip of its shadow crosses the circle before and after noon, and join the two marks: that line runs east–west.
E–W = chord through the morning and afternoon shadow points; N–S ⟂ through its midpoint
Divide the square site into a grid of equal squares (padas), most often 8 × 8 = 64 or 9 × 9 = 81, and place every part of the building according to the grid.
64 padas (maṇḍūka) or 81 padas (paramaśāyika)
Imagine the vāstupuruṣa lying face down on the diagram with his head in the north-east and his feet in the south-west, held down by the gods who occupy the padas; do not place walls, pillars or doors on his vital points.
Open the railing at the four cardinal points and mark each opening with a torana: two posts carrying three curved architraves with scrolled ends, crowned with Buddhist emblems.
Break each face of the square sanctum into projections (rathas), three, five, seven or more, that step forward towards the central one, and carry them up unbroken through the wall and the tower.
tri-ratha 3 · pancha-ratha 5 · sapta-ratha 7 projections per face
Classify the temple by the shape of its crown: square is nāgara, octagonal drāviḍa, round (or apsidal) vesara.
Cite this page Chris Paton, “The rule of the diagonal”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/sulba-diagonal. Text, drawings and models licensed under CC BY-NC 4.0.