![]() ![]() We begin by setting out the sum as follows:Īnother arithmetical result presented by Brahmagupta is his algorithm for computing square roots. Consider the product of 235 multiplied by 264. ![]() Ifrah translates "gomutrika" to "like the trajectory of a cow's urine". The first method we describe is called "gomutrika" by Brahmagupta. ![]() We give three examples of the methods he presents in the Brahmasphutasiddhanta Ⓣ ( Correctly Established Doctrine of Brahma ) and in doing so we follow Ifrah in. We can also describe his methods of multiplication which use the place-value system to its full advantage in almost the same way as it is used today. However it is a brilliant attempt to extend arithmetic to negative numbers and zero. He is certainly wrong when he then claims that zero divided by zero is zero. Really Brahmagupta is saying very little when he suggests that n n n divided by zero is n / 0 n/0 n / 0. Zero divided by negative or positive numbers is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Positive or negative numbers when divided by zero is a fraction the zero as denominator. The product or quotient of a fortune and a debt is a debt.īrahmagupta then tried to extend arithmetic to include division by zero:. The product or quotient of a debt and a fortune is a debt. The product or quotient of two debts is one fortune. The product or quotient of two fortunes is one fortune. The product of zero multipliedby zero is zero. The product of zero multiplied by a debt or fortune is zero. He also gives arithmetical rules in terms of fortunes (positive numbers ) and debts (negative numbers ):-Ī debt subtracted from zero is a fortune.Ī fortune subtracted from zero is a debt. When zero is added to a number or subtracted from a number, the number remains unchanged and a number multiplied by zero becomes zero. In the Brahmasphutasiddhanta Ⓣ ( Correctly Established Doctrine of Brahma ) he defined zero as the result of subtracting a number from itself. The chapters are: examination of previous treatises on astronomy on mathematics additions to chapter 1 additions to chapter 2 additions to chapter 3 additions to chapter 4 and 5 additions to chapter 7 on algebra on the gnomon on meters on the sphere on instruments summary of contents versified tables.īrahmagupta's understanding of the number systems went far beyond that of others of the period. The remaining fifteen chapters seem to form a second work which is major addendum to the original treatise. The topics covered are: mean longitudes of the planets true longitudes of the planets the three problems of diurnal rotation lunar eclipses solar eclipses risings and settings the moon's crescent the moon's shadow conjunctions of the planets with each other and conjunctions of the planets with the fixed stars. These ten chapters are arranged in topics which are typical of Indian mathematical astronomy texts of the period. The Brahmasphutasiddhanta Ⓣ ( Correctly Established Doctrine of Brahma ) contains twenty-five chapters but the first ten of these chapters seem to form what many historians believe was a first version of Brahmagupta's work and some manuscripts exist which contain only these chapters. First let us give an overview of their contents. We look below at some of the remarkable ideas which Brahmagupta's two treatises contain. In addition to the Brahmasphutasiddhanta Ⓣ ( Correctly Established Doctrine of Brahma ) Brahmagupta wrote a second work on mathematics and astronomy which is the Khandakhadyaka Ⓣ ( 'edible bite' or 'morsel of food' ) written in 665 when he was 67 years old. Outstanding mathematicians such as Varahamihira had worked there and built up a strong school of mathematical astronomy. ![]() This was the capital of the lands ruled by the Gurjara dynasty.īrahmagupta became the head of the astronomical observatory at Ujjain which was the foremost mathematical centre of ancient India at this time. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. In particular he wrote Brahmasphutasiddhanta Ⓣ ( Correctly Established Doctrine of Brahma ), in 628. Biography Brahmagupta, whose father was Jisnugupta, wrote important works on mathematics and astronomy. ![]()
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