Concise Manual on Planetary Motion with Commentary

--- | By dividing the palaA traditional unit of time or measurement; here used in a sexagesimal (base-60) context etc. by 60:

The square of 2 | 5 | 35 is 4 | 22 | 51 | 10 | 25.

Now, the procedure for extracting the square root—

When the square root of a quantity with fractional parts is sought, there is a specific method described.
First, multiply the first part by three thousand six hundred original: "khashunya-ripu-tribhih" (zero-zero-six-three in reverse notation) and find its root.
Add one to the remainder of that root, multiply by sixty, and add the subsequent fractional part.
Divide this by twice the root plus two; the result is the accurate root of the fractional quantity.

There is a great distinction—that is to say, a significant difficulty—in calculating the square root of numbers with fractional parts savayava-ankaNumbers consisting of whole units and their sexagesimal fractions. This is because Kamalakara, in the Tattvaviveka, stated that for non-square numbers (those with fractions), the root is geometric/linear; otherwise, a "true" root of a non-square number cannot exist. Now, multiply the first part of the fractional number by 3600 and find the root using the method of Bhaskara Referring to Bhaskaracharya, the famous 12th-century mathematician starting with "having discarded the last odd digit's square..." and so on. Add 1 to the remainder, multiply by 60, add the next fractional part, and divide the sum by twice the root plus 2. This yields the approximate root of the fractional number.

For example, to find the square root of 63 | 50: Following the rule "multiply the first part," 63 x 3600 = 226,800. Using Bhaskara's method, the root is 476 and the remainder is 224. Adding 1 to the remainder 224 gives 225. Multiplying 225 by 60 gives 13,500; adding the 50 vikalaSeconds of arc or a third-order sexagesimal fraction gives 13,550. Now, twice the root 476 is 952; adding 2 gives 954. Dividing 13,550 by 954 gives a quotient of 14, which is the second part of the root. Dividing the first part of the root (476) by 60, the approximate root is 7 | 56 | 14.

Now, the description of Addition and Subtraction—

Addition should be performed within like categories, and subtraction likewise among like categories.
In the addition or subtraction of unlike categories, the relationship is shown by a line/sign.

Addition and subtraction occur with their own similar categories. The addition and subtraction of different categories (units) are expressed through signs/lines.

For example: In the signs etc. Astronomical notation: Signs, Degrees, Minutes, Seconds 3 | 11° | 21' | 35", adding the signs etc. 1 | 15° | 31' | 7" results in the sum 4 | 26° | 52' | 42". Similarly, subtracting 1 | 15° | 31' | 7" from 3 | 11° | 21' | 35" leaves a remainder of 1 | 25° | 50' | 28". Furthermore, adding the days etc. 11 | 6 | 4 | 32 to the signs etc. 1 | 27° | 35' | 6" is expressed as {( 1 | 27° | 35' | 6" ) + ( 11 | 6 | 4 | 32 )}. Likewise, subtracting the days etc. 11 | 6 | 4 | 35 from the signs etc. ( 1 | 17° | 7' | 27" ) is expressed as ( 1 | 17° | 7' | 27" ) — ( 11 | 6 | 4 | 35 ).