The Sulbasutras‑1

Overview of Śul­basū­tras

The class of texts called Śul­basū­tras form a part of Kalpa, which is one of the Vedāṅ­gas. The term Vedāṅ­ga is used to refer to six branch­es of knowl­edge name­ly śikṣā, vyākaraṇaṃ, kalpaḥ, niruk­taṃ, jyotiṣaṃ and chan­daḥ. In ancient times, all these branch­es used to be stud­ied by every Vedic priest either after com­plet­ing stud­ies of the Veda, or simul­ta­ne­ous­ly along with it.

The Vedic priests had devel­oped a class of man­u­als that would assist them in the con­struc­tion of altars (called Vedis) used for per­form­ing sac­ri­fices. The word śul­ba stems from the root śulb which means ‘to mea­sure’. Since all the mea­sure­ments were done using ropes or chords in the very ear­ly times — traces of which can be found in prac­tice even today — it seems the word in due course was syn­ony­mous­ly employed to refer to the chords them­selves.

Some of the geo­met­ri­cal con­struc­tions such as the śye­nac­i­ti pre­scribed by the Śul­bakāras (the authors of the Śul­basū­tras) are quite com­plex. In fact, there are a num­ber of con­straints that need to be ful­filled in the con­struc­tion of śye­nac­i­ti such as, the num­ber of bricks in each lay­er should be con­stant (200), the area of all the bricks put togeth­er must be equal to a spec­i­fied num­ber, and so on.

The citīs or vedis can­not be sim­ply con­struct­ed with­out hav­ing a mas­tery over cer­tain tech­niques that include the pro­ce­dures for deter­min­ing the east-west direc­tion at a giv­en loca­tion, for draw­ing straight lines that are at right angles to each oth­er, for con­struct­ing a square whose side is surd times an inte­ger, for find­ing the area of cer­tain geo­met­ri­cal objects, and more such math­e­mat­i­cal prin­ci­ples. We shall see some of these impres­sive prin­ci­ples and meth­ods.

Find­ing the car­di­nal direc­tions

Hav­ing cho­sen the loca­tion at which the sac­ri­fi­cial altar is to be con­struct­ed, the first thing that needs to be done is the deter­mi­na­tion of the east-west direc­tion at that loca­tion. In fact, deter­min­ing the exact east-west line at a giv­en loca­tion, is a pre­req­ui­site for all con­struc­tions, be it a res­i­dence, a tem­ple, a sac­ri­fi­cial altar or a fire-place. The pro­ce­dure for deter­min­ing it is described by an inge­nious way in the Śul­basū­tras:समे शङ्कुं निखाय शङ्कुसम्मितया रज्ज्वा मण्डलं परिलिख्य यत्र लेखयोः शङ्क्वग्रच्छाया निपपति तत्र शङ्कू निहन्ति, सा प्राची।

(Kt. Su. I 2)Fix­ing the gno­mon (śaṅku) on lev­el ground and draw­ing a cir­cle with a cord mea­sured by the gno­mon, he fix­es pins at points on the line (of the cir­cum­fer­ence) where the shad­ow of the tip of the gno­mon falls. That is the east direc­tion (prācı̄).

Ask­ing the ques­tion as to why per­form this exper­i­ment with śaṅku 5 in order to deter­mine the direc­tion, and not sim­ply look at the sun­rise and sun­set and be with it, the com­men­ta­tor Mahı̄dhara observes that “Since the ris­ing points are many, vary­ing from day to day, the [car­di­nal] east point can­not be known [from the sun­rise point]. There­fore it has been pre­scribed that the east be deter­mined by fix­ing a śaṅku.”

Fun­da­men­tal­ly, owing to the tilt of the earth and the lat­i­tu­di­nal posi­tion, one may observe that the ris­ing point of the Sun has a north­ward and a south­ward move­ment across a year, with the days of equinox as the inflec­tion points. This makes the deter­mi­na­tion of the car­di­nal direc­tions very dif­fi­cult. This is a con­cept we shall delve fur­ther into while look­ing at ayanāmśa in Jyotiṣa.

We shall learn in detail about the break­throughs achieved in geo­met­ri­cal the­o­rems in Śul­ba-sūtras in our next arti­cle.