However, there were references to negative numbers far earlier...

In 200 BCE the Chinese number rod system represented positive numbers in Red and Negative numbers in black. These were used for commercial and tax calculations where the black cancelled out the red. The amount sold was positive (because of receiving money) and the amount spent in purchasing something was negative (because of paying out); so a money balance was positive, and a deficit negative.

The concept also appeared in Astronomy where the ideas of ²strong² and ²weak² were used for approximating a number from above or below. For example approaching 5 from above means for example, starting with 5.2 you can find better approximations 5.1, 5.05, 5.025. Thus 5.025 was called a ²strong² approximation and a number like 4.9 ²weak². So ²strong² numbers were called positive and ²weak² numbers negative. In India , negative numbers did not appear until about 620 CE in the work of Brahmagupta (598-670) who used the ideas of ²fortunes² and ²debts² for positive and negative. By this time a system based on place-value was established in India, with zero being used in the Indian number system. Brahmagupta used a special sign for

negatives and stated the rules for dealing with positive and negative quantities as follows. 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 or fortune is zero. The product of zero multiplied by zero is zero. The product or quotient of two fortunes is one fortune. The product or quotient of two debts is one fortune. 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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