Concise Manual on Planetary Motion with Commentary

The bow of the Lord (Ishachapam) = broken and cast aside by the bowstring (maurvika). With the sine (jiva) The Sanskrit word 'jiva' means both 'life/soul' and the geometric 'sine', he broke the mighty bow. As the lexicon Amarakosha states: "Maurvi, Jya, and Shinjini are synonyms for bowstring." This implies a method distinct from the usual operations of sines and arcs. Shining with firm multipliers and divisors (dridha-guna-hara-lasat) = beautified by stable, simplified constants used for multiplication and division. Having round arms (suvritta-bahu) = 'Vritta' means a circle; one whose arms are well-rounded. In this context, the 'arm' (sine) operation is taught within the circle (arc) itself, not merely as a straight line. The idea is that the 'arm' (sine) and 'co-arm' (cosine) are accepted here in the form of arcs. Granting good results (suphala-pradam) = it provides 'good fruits,' namely the 'slow correction' (mandaphala) and 'fast correction' (shighraphala) technical terms for planetary anomalies. Possessing the light of the gnomon (attatattra-prabham) = it incorporates the shadow of the gnomon a vertical pillar used to measure time and latitude. Rama = beautiful, in the form of Vishnu = perfectly pure. || 2 ||

1st Interpretation (Devotional): O Man! Remember the form of Vishnu, who broke Shiva's bow into three pieces upon the earth. He is adorned with the garland of the quality of goodness (Sattva-guna), the provider of livelihood to every living being, the giver of desired fruits, the one who took human form, the mover of the universe, and as beautiful as the god of love.

2nd Interpretation (Astronomical): O Calculator! Study this Karana text A 'Karana' is a concise astronomical manual for practical calculations. It is free from the complexities of sines (jiva) and arcs (chapa), adorned with stable dividends and divisors, contains the 'arm' (sine) calculations within beautiful verses, provides perfect knowledge of the planetary corrections, utilizes the shadow of the gnomon, and is delightful and pure. || 2 ||

Now, the reason for beginning the book is stated:

Now, since manuals by previous teachers already exist, why compose another? He explains the reason in the Vasantatilaka meter: "Though wise men..." etc. I, Ganesha, have set out to create a planetary manual that is 'clear'—meaning it brings the calculated positions into harmony with observation. Why? He says: although wise and great calculators have made manuals, in those manuals, if one discards the sine and arc, the 'success' (the completion of the mathematical goal) is not achieved. But this work is free from the operations of sines and arcs and is 'of great simplicity,' meaning it involves very few steps. Where planetary calculation starts from the beginning of the Kalpa an immense cosmic cycle, it is a Siddhanta; where it starts from the beginning of a Yuga an age, it is a Tantra; where it starts from a specific Saka date an era, usually 78 CE, it is a Karana. Thus, it is indicated: "I am performing the planetary calculation from the Saka era." || 3 ||

The Madhuri Commentary

Great (uravah) = principal; Wise (dhirah) = learned men; Manuals (karanani) = the work of composing astronomical texts; Although (yadyapi); They made (akarshuh) = even if they did; But because (yasmāt); In those (teshu) = in those composed books; Sine and Arc (jyaka-dhanuh); Discarding (apasya) = leaving aside; Success (siddhih) = the mathematical result; Not (na) = would not occur. For that reason, "I, Ganesha," am eager (udyatah) to compose (kartum) a planetary manual (graha-prakaranam) that is clear (sphutam), free from sine and arc operations (jya-chapa-karma-rahitam), and of great simplicity (sulaghupakaram)—meaning it has beautiful and easy operations.

In this book, Ganesha fulfills his promise by giving different names to the sines and arcs. Great scholars should consider that, in reality, he has performed all the functions of sines and arcs throughout. || 3 ||

Although great teachers created astronomical manuals, their mathematical systems do not function correctly if sines and arcs are removed. Therefore, I (Ganesha the Astrologer) am ready to create the Grahalaghava (Simplified Astronomy) with extremely simple operations, leaving aside the traditional sine and arc methods. || 3 ||