The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t2.31

c8.t2.31

The sq. ABCD is broken into a rect. ABEF making its side BE (=4 units) equal to the desired shorter side of the rectangle, and rectangle OECP (where EC=2 units), together with a square FOPD. The rectangle OECP is transferred to the other side, and GAFH is its new position. Next the smaller square FOPD (2 units × 2 units) is changed into a rectangle (of 1 unit by 4 units) and IGHJ becomes its new position (Fig. 17). Hence BI (6 + 2 + 1 = 9 units) is the length of the new rectangle. Similarly, if we change a square of 7 units into a rectangle of 5 units by 49/5 (= 7 + 2 + ⅘) units, we have to construct a rectangle of ⅘ unit by 5 units from a square of 2 units by 2 units. This is actually no solution to the problem since the transformation of square FOPD to a rectangle IGHJ is again a problem of fundamental nature.