By Agathe Keller

In the 5^{th} 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 2 hundred years later, the Indian astronomer Bhaskara glossed that bankruptcy. quantity 1 of this paintings was once an English translation of Bhaskara’s observation, and this quantity comprises motives for every verse statement translated in quantity 1.

**Read Online or Download Expounding the Mathematical Seed: Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya PDF**

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**Additional resources for Expounding the Mathematical Seed: Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya **

**Example text**

Or “halving upright”, probably this rule was intended originally only for equilaterals and isosceles. 23 C. 6 Figure 7: Equilateral and isoceles triangles E F K E F G K G As illustrated in Figure 8, let M N O be a triangle. If M D is the height issued from M and falling on the base N O, then the area A of M N O will be A= NO × M D. etre samaiv¯ avalambakasthitih. ’ In other words, in an equilateral triangle any height sections the corresponding base into two equal segments. 17 which states the so-called ‘Pythagoras Theorem’ to justify the following procedure: Problem Knowing the length of the sides of an equilateral or isosceles triangle, find its area.

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.

In other words, in an equilateral triangle any height sections the corresponding base into two equal segments. 17 which states the so-called ‘Pythagoras Theorem’ to justify the following procedure: Problem Knowing the length of the sides of an equilateral or isosceles triangle, find its area. Let EF G be such an equilateral triangle illustrated in Figure 7, which also shows an isoceles triangle. 24 Supplements Step 1 Compute the length of any height in the case of an equilateral, issued from the vertex in the case of an isosceles triangle.