the role of the king, marriage, and suspension of Vedic recitation. Book two refers to penances, inheritance, women, householder, orders of life, ancestral offerings. Book three refers to holy householders, forest hermit and penances. Book four primarily refers to the yogic practices and penances along with offenses regarding marriage. Baudhāyana Sulbasūtra Pythagorean theorem The Baudhāyana Sulba Sūtra states the rule referred to today in most of the world as the Pythagorean Theorem. The rule was known to a number of ancient civilizations, including also the Greek and the Chinese, and was recorded in Mesopotamia as far back as 1800 BCE. For the most part, the Sulbasūtra-s do not contain proofs of the rules which they describe. The rule stated in the Baudhāyana Sulba Sūtra is: दीर्घचतुरस्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥ dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī, cha yatpṛthagbhūte kurutastadubhayāṅ karoti. The diagonal of an oblong produces by itself both the areas which the two sides of the oblong produce separately. The diagonal and sides referred to are those of a rectangle (oblong), and the areas are those of the squares having these line segments as their sides. Since the diagonal of a rectangle is the hypotenuse of the right triangle formed by two adjacent sides, the statement is seen to be equivalent to the Pythagorean theorem. Baudhāyana also provides a statement using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle: The cord which is stretched across a square produces an area double the size of the original square. Circling the square Another problem tackled by Baudhāyana is that of finding a circle whose area is the same as that of a square (the reverse of squaring the circle). His sūtra i.58 gives this construction: Draw half its diagonal about the centre towards the East–West line; then describe a circle together with a third part of that which lies outside the square. Explanation: Draw the half-diagonal of the square, which is larger than the half-side by . Then draw a circle with radius , or , which equals . Now , so the area . Square root of 2 Baudhāyana i.61-2 (elaborated in Āpastamba Sulbasūtra i.6) gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2: samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayet tac