The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t18.34

c8.t18.34

**3.4-3.10.** *Squares of different measures and enlargement of areas.* One unit in length produces one square unit area; two units produce four square areas, and three units nine square areas, and so on. *Pramāṇamātreṇa daṇḍena pramāṇamātraṃ kṣetraṃ vidhīyate | dvipramāṇena daṇḍena catvāri pramāṇakṣetrāṇi bhavanti* (Sundararāja)a. The *sūtra Āśl.* 3.7 explains that if *ABCD* be a square of p units, it produces p² unit squares. If *ABCD* be a rectangle whose length *AB* has p units and breadth *BC* q units, then *ABCD* contains pq unit square areas (Fig. 3). According to Kapardib : *yāvatpramāṇa yāvadāyāmā rajjuḥ tāvato vargānkaroti paṅkti karoti | yāvat saṃkhyā yuktam pramāṇaṃ tāvat saṃkhyāyuktaḥ paṅktīḥ karoti | pañcamānaṃ pañcasaṃkhyā yuktānvargān karoti |* This has been beautifully explained by Karavinda as followsc : *dvipramāṇapārśvamānikam-ekapramāṇatiryaṅmāniyakam dvidhā' pacchidya dve upalabhyete | dvipramāṇa pārśvamānikaṃ tripramāṇa tiryaṅmānikaṃ prāk dvidhodak tridhā' pacchidya ṣaḍupalabhyante |* This result