Subjects	Page Numbers
6. Calculating the Mean Node original: "पातमध्यानयनम्"; refers to the calculated average position of the lunar nodes, Rahu and Ketu	106
7. Special Remarks	107
8. Determining the Duration original: "स्थिति"; often refers to the duration of an astronomical event like an eclipse	108
9. Consideration of the Corrected Portions	108
10. Determining Duration based on the Node	109
11. Equality of Declination and Characteristics of Duration	109

Section 10: Possibility of Syzygy original: "पर्वसम्भवाधिकार"; calculating when a conjunction or opposition of the Sun and Moon is likely to result in an eclipse


1. Calculating Celestial Latitude original: "शरसाधनम्"; the angular distance of a planet north or south of the ecliptic	115
2. Calculating Zenith Distance	116
3. Possibility and Impossibility of Eclipses	117
4. Description of the Author's Lineage	119

Section 11: The Nirada Chapter original: "नीरवाध्याय"; likely a specific set of corrections or a refined method unique to this tradition


1. Clarification of the Sun's Position according to the Nirada method	120
2. The Purpose of this Method	120

Vernacular Translation Index:


1. Section on Mean Motions	122
2. Section on True Motions	125
3. Section on the Three Problems Time, Direction, and Place	130
4. Section on Lunar Eclipses	132
5. Section on Solar Eclipses	136
6. Section on Heliacal Risings and Settings	138
7. Section on the Elevation of the Moon’s Horns The phase and orientation of the crescent moon	141
8. Section on Planetary Conjunctions	142
9. Section on the Nodes	143
10. Section on the Possibility of Syzygy	145
11. The Nirada Chapter	147
12. Index of Verses	148

॥ Salutations to the Illustrious Ganesha ॥

Composed by the Great Bhaskaracharya

The Joy of Calculation (Karanakutuhala)

Accompanied by the two commentaries of

the Great Scholar Sudhakara Dvivedi and Sumatiharsha

The Invocation (Mangalacharana)—
Having bowed to Ganesha, to the Goddess of Speech (Saraswati), to the Creator (Brahma), to the Unchanging (Vishnu), to the Lord (Shiva), and to the Planets beginning with the Sun, I shall describe the concise process of planetary calculation, which is in perfect agreement with the Brahma Siddhanta. ॥ 1 ॥

Sumatiharsha's Introductory Verse:

He who, like a lotus, shines with the beauty of a pond, though immersed in the ocean of the five arrows of love by the splashing water droplets of the mountain rocks; He who is praised by millions of gods possessed of wonderful fortitude; He whose nature and majesty remain the same toward friend and foe—may the glorious Lord Parshva and his beloved protect us. This is a devotional verse to Parshvanatha, the 23rd Tirthankara of Jainism, indicating the commentator Sumatiharsha's religious background.

I, the author named Bhaskara, having bowed to Ganapati, Saraswati, Brahma, Vishnu, Shiva, and the planets starting with the Sun, shall explain the "planetary work"—that is, the method for determining the mean and true positions of the heavenly bodies. To remove any doubt regarding the authority of this work, it is described as being "in agreement with the Brahma Siddhanta." The Brahma Siddhanta is a foundational astronomical text; by claiming alignment with it, Bhaskara assures readers his shortcuts are scientifically valid.

If one wonders why this work is necessary if the meaning is already known from the Brahma Siddhanta, the answer is: this is a "concise process" (laghu-prakriya). By making the process concise, it becomes "perfectly clear," meaning easy to understand. This is the reason for the undertaking.

Now, one might ask, since the primary goal of the Siddhantas is the calculation of planets, what is the specific name and category of this science? In the science of mathematics/astronomy, there are three types: Siddhanta, Tantra, and Karana.

A Siddhanta is defined as a work that begins its calculations from the start of a Kalpa original: "कल्पादेरारभ्य"; a vast cosmic cycle of 4.32 billion years, determining the elapsed years, months, and days to find the mean positions.
A Tantra is a work that begins its calculations from the start of the current Yuga (Age).
A Karana the category of this book is a work that begins its calculations from a specific preferred day within the current Shaka era.

Furthermore, if one asks how a simple bow (invocation) has the power to destroy obstacles, the answer is: through the merit of the bow, obstacles are struck down. Even where a work is seen to be completed without an explicit invocation, it is understood that a mental salutation...