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modifications
« Pancha-Siddhantika » : différence entre les versions
→Surya Siddhanta
| Ligne 31 : | Ligne 31 : | ||
The table of contents in this text are: | The table of contents in this text are: | ||
1. The Motions of the Planets | : 1. The Motions of the Planets | ||
2. The Places of the Planets | : 2. The Places of the Planets | ||
3. Direction, Place and Time | : 3. Direction, Place and Time | ||
4. The Moon and Eclipses | : 4. The Moon and Eclipses | ||
5. The Sun and Eclipses | : 5. The Sun and Eclipses | ||
6. The Projection of Eclipses | : 6. The Projection of Eclipses | ||
7. Planetary Conjunctions | : 7. Planetary Conjunctions | ||
8. Of the Stars | : 8. Of the Stars | ||
9. Risings and Settings | : 9. Risings and Settings | ||
10. The Moon's Risings and Settings | : 10. The Moon's Risings and Settings | ||
11. Certain Malignant Aspects of the Sun and Moon | : 11. Certain Malignant Aspects of the Sun and Moon | ||
12. Cosmogony, Geography, and Dimensions of the Creation | : 12. Cosmogony, Geography, and Dimensions of the Creation | ||
13. The Gnomon | : 13. The Gnomon | ||
14. The Movement of the Heavens and Human Activity | : 14. The Movement of the Heavens and Human Activity | ||
Methods for accurately calculating the shadow cast by a gnomon are discussed in both Chapters 3 and 13. | Methods for accurately calculating the shadow cast by a gnomon are discussed in both Chapters 3 and 13. | ||
The astronomical time cycles contained in the text were remarkably accurate at the time. The Hindu Time Cycles , copied from an earlier work, are described in verses 11–23 of Chapter 1: | The astronomical time cycles contained in the text were remarkably accurate at the time. The Hindu Time Cycles , copied from an earlier work, are described in verses 11–23 of Chapter 1 : | ||
11. That which begins with respirations (prana) is called real.... Six respirations make a vinadi, sixty of these a nadi; | : 11. That which begins with respirations (prana) is called real.... Six respirations make a vinadi, sixty of these a nadi; | ||
12. And sixty nadis make a sidereal day and night. Of thirty of these sidereal days is composed a month; a civil (savana) month consists of as many sunrises; | : 12. And sixty nadis make a sidereal day and night. Of thirty of these sidereal days is composed a month; a civil (savana) month consists of as many sunrises; | ||
13. A lunar month, of as many lunar days (tithi); a solar (saura) month is determined by the entrance of the sun into a sign of the zodiac; twelve months make a year. This is called a day of the gods. | : 13. A lunar month, of as many lunar days (tithi); a solar (saura) month is determined by the entrance of the sun into a sign of the zodiac; twelve months make a year. This is called a day of the gods. | ||
14. The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise of the demons. | : 14. The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise of the demons. | ||
15. Twelve thousand of these divine years are denominated a caturyuga; of ten thousand times four hundred and thirty-two solar years | : 15. Twelve thousand of these divine years are denominated a caturyuga; of ten thousand times four hundred and thirty-two solar years | ||
16. Is composed that caturyuga, with its dawn and twilight. The difference of the krtayuga and the other yugas, as measured by the difference in the number of the feet of Virtue in each, is as follows: | : 16. Is composed that caturyuga, with its dawn and twilight. The difference of the krtayuga and the other yugas, as measured by the difference in the number of the feet of Virtue in each, is as follows: | ||
17. The tenth part of a caturyuga, multiplied successively by four, three, two, and one, gives the length of the krta and the other yugas: the sixth part of each belongs to its dawn and twilight. | : 17. The tenth part of a caturyuga, multiplied successively by four, three, two, and one, gives the length of the krta and the other yugas: the sixth part of each belongs to its dawn and twilight. | ||
18. One and seventy caturyugas make a manu; at its end is a twilight which has the number of years of a krtayuga, and which is a deluge. | : 18. One and seventy caturyugas make a manu; at its end is a twilight which has the number of years of a krtayuga, and which is a deluge. | ||
19. In a kalpa are reckoned fourteen manus with their respective twilights; at the commencement of the kalpa is a fifteenth dawn, having the length of a krtayuga. | : 19. In a kalpa are reckoned fourteen manus with their respective twilights; at the commencement of the kalpa is a fifteenth dawn, having the length of a krtayuga. | ||
20. The kalpa, thus composed of a thousand caturyugas, and which brings about the destruction of all that exists, is a day of Brahma; his night is of the same length. | : 20. The kalpa, thus composed of a thousand caturyugas, and which brings about the destruction of all that exists, is a day of Brahma; his night is of the same length. | ||
21. His extreme age is a hundred, according to this valuation of a day and a night. The half of his life is past; of the remainder, this is the first kalpa. | : 21. His extreme age is a hundred, according to this valuation of a day and a night. The half of his life is past; of the remainder, this is the first kalpa. | ||
22. And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvant, twenty-seven caturyugas are past; | : 22. And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvant, twenty-seven caturyugas are past; | ||
23. Of the present, the twenty-eighth, caturyuga, this krtayuga is past.... | : 23. Of the present, the twenty-eighth, caturyuga, this krtayuga is past.... | ||
When computed, this astronomical time cycle would give the following results: | When computed, this astronomical time cycle would give the following results: | ||
* The average length of the tropical year as 365.2421756 days, which is only 1.4 seconds shorter than the modern value of 365.2421904 days (J2000). This estimate remained the most accurate approximation for the length of the tropical year anywhere in the world for at least another six centuries, until Muslim mathematician Omar Khayyam gave a better approximation, though it still remains more accurate than the value given by the modern Gregorian calendar currently in use around the world, which gives the average length of the year as 365.2425 days. | |||
* The average length of the sidereal year, the actual length of the Earth's revolution around the Sun, as 365.2563627 days, which is virtually the same as the modern value of 365.25636305 days (J2000). This remained the most accurate estimate for the length of the sidereal year anywhere in the world for over a thousand years. | |||
The actual astronomical value stated for the sidereal year however, is not as accurate. The length of the sidereal year is stated to be 365.258756 days, which is longer than the modern value by 3 minutes 27 seconds. This is due to the text using a different method for actual astronomical computation, rather than the Hindu cosmological time cycles copied from an earlier text, probably because the author didn't understand how to compute the complex time cycles. The author instead employed a mean motion for the Sun and a constant of precession inferior to that used in the Hindu cosmological time cycles. | The actual astronomical value stated for the sidereal year however, is not as accurate. The length of the sidereal year is stated to be 365.258756 days, which is longer than the modern value by 3 minutes 27 seconds. This is due to the text using a different method for actual astronomical computation, rather than the Hindu cosmological time cycles copied from an earlier text, probably because the author didn't understand how to compute the complex time cycles. The author instead employed a mean motion for the Sun and a constant of precession inferior to that used in the Hindu cosmological time cycles. | ||