Expounding the Mathematical Seed. Vol. 2: The Supplements: A by Agathe Keller

By Agathe Keller

In the 5th century, the Indian mathematician Aryabhata wrote a small yet well-known paintings on astronomy in 118 verses referred to as the Aryabhatiya. Its moment bankruptcy supplies a precis of Hindu arithmetic as much as that time, and two hundred years later, the Indian astronomer Bhaskara glossed that bankruptcy. quantity 1 of this paintings used to be an English translation of Bhaskara’s remark, and this quantity comprises causes for every verse remark translated in quantity 1.

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Extra resources for Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya

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100 , 102 , 104 ,. . ). g. 101 , 103 , 105 ,. . ). Bh¯ askara substitutes for it his own categorization. He considers the places where the digits forming the number whose root is to be extracted are to be noted. He counts them from right to left, distinguishing between places associated to an even number and places associated to an odd number. The place for the digit whose power of ten is 100 is the first to be counted, therefore the so-called “square” places are found for all odd numbers of places, and the so-called “non-square” places for all even numbers of places.

Bh¯ askara substitutes for it his own categorization. He considers the places where the digits forming the number whose root is to be extracted are to be noted. He counts them from right to left, distinguishing between places associated to an even number and places associated to an odd number. The place for the digit whose power of ten is 100 is the first to be counted, therefore the so-called “square” places are found for all odd numbers of places, and the so-called “non-square” places for all even numbers of places.

Ttaphalam| . ab. Half of the even circumference multiplied by the semi-diameter, only, is the area of the circle| In other words, for a circle of circumference C and diameter D, the area A is according to this definition: C D A= × . 2 Procedure used in examples Problem Knowing the diameter D of a circle, find its area A. 10, and a Rule of Three, find the (approximate) circumference C of the circle. 10 states that a circle of diameter 20 000 has a circumference of 62832. aphal¯ abhy¯ am . 10]...

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