Algebra of Bhaskara II

Example:

Tell me quickly the result of adding 3 and 4, either negative or positive.
State separately the positive and negative results, so that you understand the addition of positive and negative. (1)

Here, for the purpose of indicating the initial letters of knowns and unknowns, they should be written down, and those that are negative should be marked with a dot above.

Commentary: Here, the author presents four examples using the Upajātikā meter.
"Three and four" implies: first, both are negative; second, both are positive; third, the first is positive and the second is negative; fourth, the first is negative and the second is positive. These are the four examples regarding positive and negative. In terms of positive and negative, it means positive with positive, negative with negative, and positive with negative. Since the fourth question is included in the third, only three types of questions were specified. One might ask, how is it to be determined whether this is positive or negative, or this is a known or unknown? Therefore, the text says: "For the purpose of indicating the initial letters of knowns and unknowns, they should be written down, and those that are negative should be marked with a dot above."

Although the negative nature can be understood just as in speech, in cases with many terms, confusion regarding the negative sign might occur, or it might be simpler to indicate it; therefore, writing a dot above is more appropriate.

Now, the presentation of the first example: 3 + 4, the result is 7.
Second: 3̇ + 4̇, the result is 7̇.
Third: 3̇ + 4, since the difference of positive and negative is the sum, the result is 1.
Fourth: 3 + 4̇, the difference is the sum, the result is 1̇.

Thus, for different fractions like "three and five-sevenths" or "one-third," one should make the denominators equal using the rule of cross-multiplication, and then perform addition or subtraction as described in the text.

Vimalā (Commentary): What will be the result of adding 3 negative units to 4 negative units, 3 positive to 4 positive, 3 negative to 4 positive, or 4 positive to 3 negative? Tell me quickly, if you know how to add positive and negative.

Example —

$-3 - 4 = -7$,