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The Wonder of Calculation (Karana Kutuhala) (Unknown) - Page 11 - Source Library

The Wonder of Calculation (Karana Kutuhala)

Bhaskara II · Unknown

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English

Table of Contents (Continued)

Subjects	Page Numbers
14. Calculation of the Precession of Equinoxes original: "अयनांश"; the slow shift of the orientation of Earth's axis, essential for aligning solar and sidereal calendars	28
15. Difference in Rising Times original: "उदयान्तरं"; similar to the modern 'Equation of Time,' correcting for the Sun's irregular motion	29
16. Ascensional Difference original: "चरकर्म"; a correction for the observer's latitude to determine the length of day and night	30
17. Calculation of Lunar Days, Half-Days, Asterisms, and Junctions original: "तिथि-करण-नक्षत्र-योग"; the five elements of the traditional Hindu calendar (Panchangam)	31

Section 3: The Three Problems of Time, Direction, and Place


1. Calculating Local Rising Times and the Ascendant original: "लग्न"; the point of the zodiac rising on the eastern horizon at a specific time	35
2. Finding the Elapsed Time from the Ascendant	36
3. Calculating Zenith Distance and the Hour Angle original: "नतोन्नत"; terms describing the position of a celestial body relative to its highest point (zenith)	38
4. Calculating Shadow Length from Time and Time from Shadow Length	39
5. Finding Declination using the Gnomon original: "क्रान्तिदण्ड"; a vertical rod used to measure shadows for astronomical calculations	43
6. Alternative Method for Calculating Declination	44
7. Calculating Local Latitude original: "अक्षांश"; the distance of the observer north or south of the equator	45

Section 4: Lunar Eclipses


1. Calculating the Zenith Distance	48
2. Calculating Instantaneous Planetary Positions	50
3. Calculation of Celestial Latitude original: "शर"; literally 'arrow,' referring to the angular distance of a planet north or south of the ecliptic	51
4. Knowledge of Precession and an Alternative Calculation for Latitude	51
5. Calculating the Diameters of the Moon and the Earth’s Shadow	52
6. Calculating the Magnitude of Obscuration original: "ग्रासमान"; the extent to which the celestial body is covered during an eclipse	53
7. Calculating the Duration of the Eclipse and Total Obscuration	54
8. Calculating the Five Key Times of an Eclipse beginning, start of totality, middle, end of totality, and final contact	54
9. Calculation of the Deflection original: "वलन"; the angle used to orient the eclipse diagram correctly against the horizon	56
10. Calculating Latitude at the Moments of Contact and Separation	59
11. Description of Graphical Projection original: "परिलेख"; the method of drawing a diagram to visualize the eclipse's path	60
12. Identifying the Points of Contact, Middle, and Separation	61
13. Calculating Obscuration at any Desired Time	61

Section 5: Solar Eclipses


1. The Nature of Zenith Distance and Hour Angle	64
2. Calculating Parallax in Longitude and Latitude original: "लम्बन" and "नति"; corrections needed for solar eclipses because the observer is not at the Earth's center	65
3. Alternative Method for Calculating Parallax	67

Subjects	Page Numbers
4. Calculating the Duration and Other Phases	68
5. Calculating the Moments of Contact and Separation	69
6. The Colors of the Sun and Moon during an Eclipse	73

Section 6: Rising and Setting of Planets


1. Calculating the Rising and Setting of Jupiter	75
2. Calculating the Rising and Setting of Venus	78
3. Calculating Retrograde Motion from the Anomaly	80
4. Rising and Setting Times for Mars, Jupiter, and Saturn	80
5. Knowledge of the Rising and Setting of Mercury and Venus	81
6. Calculating the Duration of Retrograde Motion and Other Phases	81
7. Time-Degrees, Nodes, and Latitudinal Deflections of Planets	82
8. Description and Calculation of Planetary Latitudes	83
9. Visibility Corrections and Rising/Setting Calculations	83
10. Special Instructions and Exceptions	85
11. The Rising and Setting of the Star Canopus original: "अगस्त्य"; an important star for navigation and calendar-keeping in India	86

Section 7: Elevation of the Moon's Horns


1. Calculation of the Deflection	90
2. Description of the Bright and Dark Portions of the Moon	91
3. Description of the Graphical Projection of the Lunar Crescent	91

Section 8: Planetary Conjunctions


1. Calculating the Angular Diameters of Mars and Other Planets	95
2. Knowledge of the Time of Conjunction	96
3. Calculation of the Conjunction original: "युति"; the moment when two celestial bodies appear close together in the sky	96

Section 9: The Special Conjunctions (Pata)


1. Possibility of a Special Conjunction and Past/Future Events original: "पात"; specifically referring to the rare and inauspicious times when the Sun and Moon have equal declinations	103
2. Knowledge of the Motion and Future Occurrence of the Conjunction	103
3. Positive and Negative Values of Declination Segments	104
4. Calculating the Elapsed Segments	105
5. Calculating Past and Future Occurrences of the Conjunction	105

This concludes the general Table of Contents for the mathematical sections of the text.

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