Short manuals, attached to the ritual literature of the Vedas, that explain how to lay out fire altars of exact shape and area using nothing but a cord and pegs. They are the oldest Indian texts on geometry and the ancestors of every later rule for setting out a building on the ground.
The Vedic sacrifice demanded altars (vedi) and brick fire-altars (citi) of prescribed shapes (squares, rectangles, trapezia, circles, and, for the greatest rites, the outline of a falcon with spread wings) and of exactly prescribed areas. Getting the geometry wrong was thought to spoil the sacrifice. The śulba (cord) texts are the practical appendices that told the priest-surveyor how to do it: stretch a cord between two pegs to make a line, swing it round a peg to make a circle, fold and mark it to divide a length.
Four collections survive under the names of Baudhāyana, Āpastamba, Kātyāyana and Mānava. They show how to fix the east–west line, how to construct a right angle with cords whose lengths are in the proportions of a right triangle (3, 4, 5 or 5, 12, 13, for example), how to turn a rectangle into a square of equal area and a square into a circle of nearly equal area, and how to enlarge an altar while keeping its shape. Baudhāyana states, in words, the relation between the sides and the diagonal of a rectangle that the Greeks would attribute to Pythagoras, and gives a remarkably close rational value for the diagonal of a square.
The great falcon altar was built in five layers of fired bricks, two hundred bricks to a layer, with the joints of each layer falling over the solid bricks of the one below: the first bonded masonry described in an Indian text. The altar texts matter to architecture because they establish habits that last for two thousand years: a building is set out from a ritually determined centre and orientation; its outline is generated by the cord from simple units; and its area and shape carry meaning. The squared diagrams of the later vāstu treatises are their direct descendants.
The English translation by George Thibaut (1875) is in the public domain; modern editions and commentaries are listed by historians of mathematics.
The book, part by part
I Orientation and the right angle
Fixing the east–west line; constructing squares and right angles with cords divided in the proportions of a right-angled triangle.
Rules: The rule of the diagonal · Find the cardinal points with a gnomon
II Transformations of area
Rectangle into square, square into circle and back; enlarging an altar while keeping its shape.
III The brick altars
The falcon altar (śyenaciti) of five courses of bricks with staggered joints, and other shaped altars.