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# An Introduction to the Life of Brahmagupta

Brahmagupta was born c 598 in Bhillamala which was located in Northwestern India The suffix -gupta probably indicated that the family belonged to the Vaisya caste made up of mostly farmers and merchants He likely lived the majority of his life in Ujjain India which at the time was the center of Hindu astronomy and mathematics There he had access to the best observatory in India as well as the writings of many great scientists and mathematicians who came before him such as Hero of Alexandria Ptomely Diophantus and Aryabhata In his own work he drew heavily from these sources and often corrected their mistakes At the age of 30 Brahmagupta wrote his first book Brahma Sphuta Siddhanta In 25 chapters this work explains much of his work in astronomy and mathematics One of his greatest contributions that was revealed with the Brahma Sphuta Siddhanta was the defining of zero He defined it as the result of subtracting a number from itself Some of the properties he listed follow When zero is added to a number or subtracted from a number the number remains unchanged and a number multiplied by zero becomes zero He also gave rules for zero in terms of fortunes which represent positive numbers and debts the negative numbers as well as fortunes related to debts A debt minus zero is a debt A fortune minus zero is a fortune Zero minus zero is a zero A debt subtracted from zero is a fortune A fortune subtracted from zero is a debt The product of zero multiplied by a debt of fortune is zero The product of zero multiplied zero is zero The product or quotient of two fortunes is one fortune The product or quotient of two debts is one debt The product or quotient of a debt and a fortune is a debt The product or quotient of a fortune and a debt is a debt

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