Algebra of Bhaskara II

Fifth meaning in the context of the father: In the context of the father, I salute the father, the giver of knowledge, whom the astrologers who know mathematics call the algebra established by that Supreme Being (Maheśvara-kṛti/Maheśvara the creator). It is said that Maheśvara-kṛti is extremely profound in algebra. (Bhāskarācārya learned the science from his father, Maheśvara-kṛti).

Now, he shows the four subjects of inquiry—subject matter, purpose, relationship, and the qualification of the student—using the Śālinī meter:

The manifest was stated previously; the unmanifest is the seed. Questions are generally not capable of being known by the slow-witted without the algebra of the unmanifest; therefore, I speak of algebraic operations. (2)

Subodhinī: "Previously stated," etc. For that reason, I explain the operations, the modus operandi of algebra, which is performed by the assumption of variables like "so many" yāvattāvat. Since the manifest mathematics, which is independent of the assumption of unmanifest variables, was stated previously, what follows? To this, he says, "The unmanifest is the seed." Algebra is the root. Even if the manifest was stated previously, it is not fully known as long as the algebraic operations are not provided. Is the start made only for the knowledge of the manifest? No, he says that even for the wise, without the algebra of the unmanifest, questions generally cannot be known, and for the slow-witted, they are entirely impossible to know. The questions here are those mentioned in the Śiromaṇi The author's previous work, and others are to be known by the desire of the questioner. Here, by saying "I speak of algebraic operations," he has shown as the subject matter the four-fold mathematics, which is not different from the single-variable equation, the multi-variable equation, the reduction of the middle term, and the product bhāvita product of variables. As the subject, the six operations of positive/negative, the six operations of zero, the six operations of variables, the six operations of surds, the pulverizer, the square nature, and the cyclic method are also shown as subjects. The relationship of the subject and the science is also shown by the phrase "I speak of algebraic operations." The purpose is the knowledge of questions and answers and the knowledge of the sphere; and indirectly, for those who study it, the attainment of righteousness, wealth, and desire, as it is a Vedāṅga.

Vimalā: I have already stated the manifest (Arithmetic/Līlāvatī), of which the unmanifest (Algebra) is the root cause. But without the techniques of algebra, even pandits cannot know the methods of questions and answers, and the slow-witted cannot know them at all. Therefore, I speak of algebraic operations. (2)

Special Note: Contextually, I will explain the signs of positive, negative, multiplication, division, etc., in a new way.

The Positive sign (+):
This + sign is called the positive sign. When this sign is placed before a number, it means that this number should be added to the preceding number. For example, if one has to write "y" plus "k," it will be written as y+k. If y equals 12 and k equals 3, this should be written as 12+3.