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The spiral is started with an isosceles right triangle, with each leg having unit length.Another right triangle (which is the only automedian right triangle) is formed, with one leg being the hypotenuse of the prior right triangle (with length the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second right triangle is the square root of 3.
Part I mainly dealt with decimal algorithm of subtraction, multiplication, division, extraction of square root and cubic root in place value Hindu-numeral system. However, a section on "halving", was treated differently, i.e., with a hybrid of decimal and sexagesimal numeral.
Inverting this process allows square roots to be found, and similarly for the powers 3, 1/3, 2/3, and 3/2. Care must be taken when the base, x, is found in more than one place on its scale. For instance, there are two nines on the A scale; to find the square root of nine, use the first one; the second one gives the square root of 90.
The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.
For number 0, Modern Standard Hindi is more inclined towards śūnya (a Sanskrit tatsama) and Standard Urdu is more inclined towards sifr (borrowed from Arabic), while the native tadbhava-form is sunnā in Hindustani.
1.9. The diagonal of a square produces double the area [of the square]. [...] 1.12. The areas [of the squares] produced separately by the lengths of the breadth of a rectangle together equal the area [of the square] produced by the diagonal. 1.13. This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 ...
Draw half its diagonal about the centre towards the East–West line; then describe a circle together with a third part of that which lies outside the square. Explanation: [ 9 ] Draw the half-diagonal of the square, which is larger than the half-side by x = a 2 2 − a 2 {\displaystyle x={a \over 2}{\sqrt {2}}-{a \over 2}} .
Indian mathematics emerged and developed in the Indian subcontinent [1] from about 1200 BCE [2] until roughly the end of the 18th century CE (approximately 1800 CE). In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava.