The Universal System of Astronomy

Combined with 3, and divided, the result stated by the Sun and the Moon original: "Puṣpavanta," a poetic term for the two luminaries is added to the total day-count. 18. Here is the logic: a wise person should contemplate the application of the Rule of Three trairāśika: a mathematical proportion used to find an unknown fourth value from three knowns using the Constant Pulverizer sthira-kuttaka: a fixed algorithm used to solve linear indeterminate equations of the form ax + c = by. The intercalary months adhimāsa: extra lunar months added to align with the solar year of a world-age are multiplied by the elapsed time and decreased by the intercalary residue. 19. The solar months of the world-age are the divisors. From there, the multiplier and the quotient are found through the Pulverizer. The elapsed intercalary months are the result of the subtraction, while the lunar days are the measure for the additional months. 20. The dividend bhājya: the number to be multiplied (a), the divisor hāra: the dividing number (b), and the additive kṣepaka: the constant added or subtracted (c) should first be reduced by a common factor if possible, to simplify the Pulverizer process. Both the dividend and divisor must be divided by the same number. 21. When two numbers are mutually divided, the last non-zero remainder is their common factor this describes the Euclidean algorithm for finding the Greatest Common Divisor. The dividend and divisor, once divided by this factor, are called "firm" or "reduced" dṛḍha: coprime numbers. 22. Mutually divide these two reduced numbers (the dividend and divisor) until the remainder in the dividend becomes one. Place the resulting quotients one below the other in a column, and place the additive below them. 23. Multiply the second-to-last number by the one above it and add the number below it. Repeat this "churning" process from bottom to top until only two quantities remain. The top value, when divided by the dividend and reduced, gives the quotient; the other, divided by the divisor, gives the multiplier. 24. Thus, the process is completed. If the number of quotients in the chain is odd, the resulting multiplier and quotient must be subtracted from their respective reduced divisors and dividends to find the true values for the Pulverizer multiplier. 25. For a wise person, the multiplier and quotient are thus fully determined. In a "summation" type equation original: "yogaje," where the additive is positive, these are the results; in a "subtraction" type original: "viyogaje," where the additive is negative, they are applied accordingly. 26. Calculating each remainder individually would be tedious. Therefore, one should assume "one" (unity) as the residue to determine the base multiplier and quotient, which are then multiplied by the actual reduced additive. 27. Through these various methods, the multiplier is found. When the residues are multiplied by three and divided, the results represent the elapsed intercalary months from the beginning of the Great Age, which are then added to the lunar count. 28. The total day-count is then derived. Following the method of the predecessors, the remaining lunar days are determined. These two values Sun and Moon should be calculated according to the methods taught by Bhāskara referring to Bhāskara II, the famous 12th-century mathematician. Thus, a wise man should understand this. 29.