By S. Yamamuro
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Extra resources for A Theory of Differentiation in Locally Convex Spaces / Memoirs No. 212
Note :-This availablity of the same result in several easy ways is a very common feature of the Vedic system and is of great advantage and help to the student (as it enables him to test and verify the correctness of his answer, step by step). (vi) Now, vertically multiply the two deficit figures (1 and 3). The product is 3. And this is the righthand-side portion of the answer. (10) 9-1 (vii) Thus 9x7=63. This method holds good in all cases and is, therefore, capable of infinite application. In fact, old historical traditions describe this cross-subtraction process as having been responsible for the acceptance of the x mark as the sign of multiplication.
5) 123x112 (Nikhilawij (i) 123 (if) As all the digists (iii) 123+23 112 are within 5, the 112+12 Vinculum method -----13276 is manifestly out 135 /,76 6 of place. =I37 176 -- ---- =I3776 Both the first and the third methods seem equally good. 10947 =10947 + - (4) 652 x 4 3 (i) 652 043 04836 232 I I --- I 28036 I b - --- -- --- -- 20026 20646 62002 67373 --- (ii) The Vinculnm method is manifestly cumbrous in this case and need not be worked out. =32226 --=31746 --=a4102 --=68373 (11)889X 898 (152 X 0043) --- (iii) The Nikhilam method may be uscd and will he cluite easy; but we will have to take a multiple of 43 which will bring it very near 1000.
Iv) The right-hand-side portion (81) remains un-affected. (v) The answer therefore is 1681. OR, secondly, instead of taking 100 as our theoretical base and its half (50) 41-9 41-9 --- 2)32/81 I as our working base (and dividing 10X5=50 32 by 2), we may take 10, as our -theoretical base and its multiple 50 as 41-9 our working base and ultimately 41-9 multiply 32 by 5 and get 160 for the left-hand side. And as 10 was our 32 / theoretical base and we are therefore X 518 entitled to only one digit on the right l60/ 81-1681 hand side, we retain 1 (of the 81) on the right hand side, "carry" the 8 (of the 81) over to the left, add it to the 160 already there and thus obtain 168 as our left-hand-side portion of the answer.