The Siddhāntasundara of Jñānarāja
An English Translation with Commentary
Publication Year: 2014
Published by: The Johns Hopkins University Press
Title page, Copyright, Dedication
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List of Figures
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List of Tables
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My work with the Siddhāntasundara of Jñānarāja has been a journey of many years. Nearly a decade and a half ago, in 2000, I corresponded with David Pingree about my plans for combining my background in mathematics with my studies of the Sanskrit language to pursue a PhD degree on mathematics in India. Pingree suggested some possible topics for a dissertation,...
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Astronomy is a science that has been practiced in India since ancient times. It has served as a companion to astrology, providing the methods by which planetary configurations could be computed for a given time, or a lunar eclipse predicted. Astronomy was also practiced in the service of ritual and used to determine the cardinal directions and the correct timing for a sacrifice. Cosmology has been a close companion of astronomy in...
1 Chapter on Cosmology: Section 1: Lexicon of the Worlds
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The first section of the Siddhāntasundara, which is also the first part of the Chapter on Cosmology in the work, is entitled Lexicon of the Worlds. In many ways, this section is the most important one in the Siddhāntasundara, as it lays out many of the ideas held by its author, Jñānarāja, including virodhaparihāra....
2 Chapter on Cosmology: Section 2 Rationale of Planetary Motion
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This section of the Siddhāntasundara gives the theory behind
planetary motion, including cosmic winds moving heavenly
(1) At noon, according to the solar day at the beginning of the bright pakṣa in the month of madhu, the Creator [that is, the god Brahmā], residing in Siddhapura...
3 Chapter on Cosmology: Section 3 Method of Projections
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This section covers the theoretical framework of the Indian
(1) He who supports the earth, on the surface of which there are gods, mountains, and clouds, and who is causing the planets to move in the wind on the revolving circle of stars for the sake of the good of all people...
4 Chapter on Cosmology: Section 4 Description of the Great Circles
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This section of the Siddhāntasundara is dedicated to a description
of the great circles that play a role in Indian astronomy.
(1–2) The east-west [circle] that passes through the local zenith is called the prime vertical, and the northsouth [circle passing through the zenith] is called the meridian. The [circle] known as the horizon for those that dwell at the center of the earth is at a distance of...
5 Chapter on Cosmology: Section 5 Astronomical Instruments
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This section discusses astronomical instruments, which are
necessary for the actual practice of astronomy.
(1) Since a tantra possesses astonishment through [the use of] instruments, therefore I will here explain [some of these] instruments, [such as] the cakra-yantra,...
6 Chapter on Cosmology: Section 6 Description of the Seasons
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Being a poetic description of the seasons, this section of the
Siddhāntasundara truly stands out from the remainder of the
work. The poem has already been described in the Introduction
(see page 35).
The existence of two registers of meaning for many verses in the ṛtuvarṇana poem means that it is necessary to provide...
7 Chapter on Mathematical Astronomy: Section 1 Mean Motion
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The first section of the grahagaṇitādhyāya lays the scene for
the mathematical astronomy of the Siddhāntasundara by discussing
(1) I salute Gaṇeśa, whose five lofty faces are the elephants of the quarters, in whose belly is the whole universe, whose crest-jewel is a necklace of thousands of mountains, who has the blue sky as his garment, who takes away the inner darkness, who is bearing the crescent...
8 Chapter on Mathematical Astronomy: Section 2 True Motion
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Having covered mean motion in the previous section, Jñānarāja now turns his attention to true motion. Mean motions only give mean positions of the planets, but in practical reality, we need their true motions. To accomplish this, trigonometry is needed, which is where the section begins....
9 Chapter on Mathematical Astronomy: Section 3 Three Questions (on Diurnal Motion)
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This section deals with questions pertaining to diurnal motion.
The “three” in the title refers to direction, place, and time.
(1) For the sake of computing the results caused by direction, place, and time, I will now present the section entitled “Three Questions” in the...
10 Chapter on Mathematical Astronomy: Section 4 Occurrence of Eclipses
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This section formally deals with the occurrence of eclipses,
but its content does not appear unified, and much of it is unclear.
(1–2) The weekday, located from the star of the sun [?], is diminished by 39, 30, 24, 21, 20, 20, 20, 20, 22, 26, 33, 45, 73, 200 palas owing to the [cosmic] wind, and increased by 400, 100, 60, 49, 44, 44, 44, 52, 72, 132, 0, 114 palas [respectively]. At a syzygy, [the longitude of] the sun...
11 Chapter on Mathematical Astronomy: Section 5 Lunar Eclipses
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Eclipses have always played a major role in human imagination. Most often they are seen as inauspicious omens, and thus being able to predict when they occur is significant. The computation of an eclipse is a major part of astronomy. The present section of the Siddhāntasundara covers how to compute a lunar eclipse....
12 Chapter on Mathematical Astronomy: Section 6 Solar Eclipses
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After a careful discussion of lunar eclipses, this section turns to solar eclipses. Much of the material is the same, but solar eclipses are more complicated. During a lunar eclipse, the moon and the portion of the earth’s shadow obscuring it are at the same distance from the earth, and so it is not necessary to take parallax into account. For a solar eclipse, however, it is essential to compute parallax....
13 Chapter on Mathematical Astronomy: Section 7 Rising and Setting of Planets
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This section deals with the rising and setting of planets, including
the conditions for it to happen, computing the time until
the next rising or setting, and so on.
(1) A planet with a velocity less than [that of] the sun rises [heliacally] in the east when the sun passes in front of it, and [a planet] with a greater velocity [than that of the sun] rises [heliacally] in the west when it...
14 Chapter on Mathematical Astronomy: Section 8 Shadows of Stars, Constellations, Polestars, and So On
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This section of the Siddhāntasundara deals with a broad content.
Among other things, longitudes and latitudes of constellations
and stars are given.
As has been noted in the Introduction (see page 26), verses 14–23 of this section occur again in some manuscripts as a separate section between the present sections 10 and 11. In this translation, the verses are kept in section 8....
15 Chapter on Mathematical: Astronomy Section 9 Elevation of the Moon’s Horns
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With the exception of the four quadratures of the moon (that is, when the sun and the moon are in conjunction, and the moon is invisible; at full moon; and at the two points where precisely half of the moon’s disk is illumined by the sun), the moon displays “horns.” When the illumined portion of the disk is smaller than the dark portion, the horns are said to be “bright”; if it...
16 Chapter on Mathematical: Astronomy Section 10 Conjunctions of Planets
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This section investigates the occurrence of conjunctions of
planets, including computation of the time for a conjunction.
(1–2b) After applying the visibility correction and the ayanavalana to the corrected [longitudes of two given] planets based on the given directions, the minutes of arc in the difference [of the longitudes] divided by the...
17 Chapter on Mathematical: Astronomy Section 11 Occurrence of Pātas
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The Sanskrit term pāta, in addition to denoting the node of
a planet, also denotes peculiar configurations of the sun and the
moon, as will be described below. The interest in finding when
these configurations occur is due to their ominous nature.
(1) The ancients say: “If the sun and the moon are on the same or different [side] of the equator when the equinox is derived from the sum [of the true longitudes]...
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Page Count: 336
Illustrations: 31 line drawings
Publication Year: 2014