The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t28.13

c8.t28.13

**19.1.** *The tail* . As per measurements given, *ABCD* is the shape of the tail, where AD = 60 *aṅg.*, BC = 240 *aṅg.*, and AE (= DF = BE = CF) = 90 *aṅg.* The measurement of each of the two sides *AB* and *DC* is given in the text as *aṣṭādaśakaraṇī*. It means a side that produces a square equal to the area of 18 squares. Obviously, these 18 squares are 18 *ṣoḍaśīs*, that is, 18/16 *sq pu.* or 900 × 18 sq. *aṅg.* The required side is therefore ¼√18 pu. or 30√18 ang. The point is explained by Karavinda as follows: *aṣṭādaśa karotītyaṣṭādaśakaraṇī | ṣoḍaśīnāṃ prākṛtatvāttāsām aṣṭādaśānāṃ karaṇī | te khalu triṣoḍaśīpramāṇanavatyangulasamacaturaśrasyākṣṇayābhūte |* Thus, Karavinda puts it as the diagonal of a square of side 90 *aṅg.* (Fig. 19(b)), which again equals 30√18 ang. That the area of the tail is equivalent to that of 15 *ṣoḍaśīs* is clear from the figure.