Algebra of Bhaskara II

(3) Tell the sum of 3y³·k³, p, l, 3n², and ( p + n ),
given that y = 15, k = 3, p = 2, l = 11.
(4) Tell the sum of 3y, —5k·y, n, p, and 20p,
given that y = 15, k = 16, n = 120, p = 25.
(5) Find the value of 6y + 7k + 8n + 6p + 6l,
given that y = 1, k = 2, n = 3, p = 4, l = 6.
(6) Find the value of 6y²·k + 2k²·n — 11p²·n — y²·k² + p²·n²,
given that y = 3, k = 2, n = 10, p = 8.
(7) Tell the value of 9y³·k³ + 12p²·n² — 10k³·n³ + 11l²·k³ — k³·n³·p³,
given that y = 12, k = 5, n = 15, p = 18, l = 8.
(8) Tell the value of 16 p³ n⁴ + 20 y³n² + 10k⁴·l² — 22p⁴·n² — y⁴·k⁴,
given that y = 2, k = 4, n = 6, p = 8, l = 10.

The Rule for Subtraction of Positive and Negative Numbers:

A positive quantity to be subtracted becomes negative; a negative quantity becomes positive; then perform the union as described before. (1)

"To be subtracted" refers to the number, unknown, or surd that is being taken away. If it is positive, it becomes negative; if it is negative, it becomes positive; then, as mentioned before, perform the addition. This means that when one must find the difference between two numbers, one should swap the positive/negative sign of the number being subtracted, and then perform the addition as per the "union" rule mentioned earlier. The result of this is the subtraction. Sankalana addition is summing, while vyavakalana subtraction is taking away.

Negativity is defined here in three ways: by place, by time, and by nature. It is simply the opposite; for example, the western direction is the opposite of the previous eastern direction, and the southern direction is the opposite of the northern direction. Thus, if one of two places (east and west) is considered positive, the other relative to it is considered negative. For example, if eastward motion is considered positive, when a planet moves westward, its motion is counted as negative. Similarly, it should be understood for northern and southern directions. Likewise, the future and past times are considered mutually negative in cycles.

Now, let us consider the present case: assigning positive to the east and negative to the west. For example, there is a city 15 krośa unit of distance to the east of Varanasi, and a second city 7 krośa to the west of Varanasi. The distance between them is 22 krośa, which cannot be explained without addition. Therefore, the difference between a positive and negative is the sum.