The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t2.99
The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t2.99
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c8.t2.99
More or less the same method is given by Cantor.e (ii) Müller's derivationa is as follows : $2a = 3/(2 + √2) d = (3 √2)/(2 √2 + 2) d = 3/2 · (√2)/(1 + √2) d$ $= ( 3/2 · (17 - 1/34)/(29 - 1/34) ) d = ( (51 - 3/34)/(58 - 2/34) ) d √2 = 17/12 - 1/12.34$ $= ( 1 - (7 + 1/34)/(58 - 2/34) ) d$ $= d - ⅛ · ( (56 + 8/34)/(58 - 2/34) ) d = d - ⅛ [ 1 - (2 - 10/34)/(58 - 2/34) ] d$ $= d - ⅛ [ 1 - 1/29 ( 1 - (10/34 - 2/34.29)/(2 - 2/34.29) ) ] d$ $= d - ⅛ d [ 1 - 1/29 1 - ⅙ ( 1 - (4 + 5/29)/(34 - 1/29) ) ]$ $= d - ⅛ d + 1/8.29 d [ 1 - ⅙ 1 - ⅛ ( 1 - (2 - 41/29)/(34 - 1/29) ) ]$