We cannot verify your location
Browse Book and Journal Content on Project MUSE

The Siddhāntasundara of Jñānarāja

An English Translation with Commentary

Toke Lindegaard Knudsen

Publication Year: 2014

A treasure for anyone interested in early modern India and the history of mathematics, this first English translation of the Siddhāntasundara reveals the fascinating work of the scholar-astronomer Jñānarāja (circa 1500 C.E.). Toke Lindegaard Knudsen begins with an introduction to the traditions of ancient Hindu astronomy and describes what is known of Jñānarāja’s life and family. He translates the Sanskrit verses into English and offers expert commentary on the style and substance of Jñānarāja's treatise. The Siddhāntasundara contains a comprehensive exposition of the system of Indian astronomy, including how to compute planetary positions and eclipses. It also explores deep, probing questions about the workings of the universe and sacred Hindu traditions. In a philosophical discussion, the treatise seeks a synthesis between the cosmological model used by the Indian astronomical tradition and the cosmology of a class of texts sacred in Hinduism. In his discourse, which includes a discussion of the direction of down and adhesive antipodeans, Jñānarāja rejects certain principles from the astronomical tradition and reinterprets principles from the sacred texts. He also constructs a complex poem on the seasons, many verses of which have two layers of meaning, one describing a season, the other a god's activities in that season. The Siddhāntasundara is the last major treatise of Indian astronomy and cosmology to receive serious scholarly attention, Knudsen’s careful effort unveils the 500-year-old Sanskrit verses and shows the clever quirkiness of Jñānarāja's writing style, his keen use of mathematics, and his subtle philosophical arguments.

Published by: The Johns Hopkins University Press

Title page, Copyright, Dedication

pdf iconDownload PDF (69.5 KB)
pp. i-vi


pdf iconDownload PDF (90.4 KB)
pp. vii-x

List of Figures

pdf iconDownload PDF (53.6 KB)
pp. xi-xii

List of Tables

pdf iconDownload PDF (54.5 KB)
pp. xiii-xiv

read more


pdf iconDownload PDF (73.2 KB)
pp. xv-xx

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,...

read more


pdf iconDownload PDF (299.2 KB)
pp. 1-42

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...

read more

1 Chapter on Cosmology: Section 1: Lexicon of the Worlds

pdf iconDownload PDF (210.8 KB)
pp. 43-70

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....

read more

2 Chapter on Cosmology: Section 2 Rationale of Planetary Motion

pdf iconDownload PDF (130.2 KB)
pp. 71-81

This section of the Siddhāntasundara gives the theory behind planetary motion, including cosmic winds moving heavenly bodies.

(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...

read more

3 Chapter on Cosmology: Section 3 Method of Projections

pdf iconDownload PDF (132.7 KB)
pp. 82-91

This section covers the theoretical framework of the Indian planetary model.

(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...

read more

4 Chapter on Cosmology: Section 4 Description of the Great Circles

pdf iconDownload PDF (98.5 KB)
pp. 92-97

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...

read more

5 Chapter on Cosmology: Section 5 Astronomical Instruments

pdf iconDownload PDF (148.6 KB)
pp. 98-103

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,...

read more

6 Chapter on Cosmology: Section 6 Description of the Seasons

pdf iconDownload PDF (137.4 KB)
pp. 104-120

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...

read more

7 Chapter on Mathematical Astronomy: Section 1 Mean Motion

pdf iconDownload PDF (312.3 KB)
pp. 121-171

The first section of the grahagaṇitādhyāya lays the scene for the mathematical astronomy of the Siddhāntasundara by discussing mean motion.
(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...

read more

8 Chapter on Mathematical Astronomy: Section 2 True Motion

pdf iconDownload PDF (290.7 KB)
pp. 172-215

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....

read more

9 Chapter on Mathematical Astronomy: Section 3 Three Questions (on Diurnal Motion)

pdf iconDownload PDF (188.4 KB)
pp. 216-239

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...

read more

10 Chapter on Mathematical Astronomy: Section 4 Occurrence of Eclipses

pdf iconDownload PDF (130.5 KB)
pp. 240-245

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...

read more

11 Chapter on Mathematical Astronomy: Section 5 Lunar Eclipses

pdf iconDownload PDF (198.0 KB)
pp. 246-266

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....

read more

12 Chapter on Mathematical Astronomy: Section 6 Solar Eclipses

pdf iconDownload PDF (226.2 KB)
pp. 267-292

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....

read more

13 Chapter on Mathematical Astronomy: Section 7 Rising and Setting of Planets

pdf iconDownload PDF (132.9 KB)
pp. 293-301

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...

read more

14 Chapter on Mathematical Astronomy: Section 8 Shadows of Stars, Constellations, Polestars, and So On

pdf iconDownload PDF (119.8 KB)
pp. 302-309

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....

read more

15 Chapter on Mathematical: Astronomy Section 9 Elevation of the Moon’s Horns

pdf iconDownload PDF (103.2 KB)
pp. 310-316

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...

read more

16 Chapter on Mathematical: Astronomy Section 10 Conjunctions of Planets

pdf iconDownload PDF (89.1 KB)
pp. 317-320

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...

read more

17 Chapter on Mathematical: Astronomy Section 11 Occurrence of Pātas

pdf iconDownload PDF (127.7 KB)
pp. 321-328

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]...


pdf iconDownload PDF (91.8 KB)
pp. 329-338


pdf iconDownload PDF (418.5 KB)
pp. 339-351

E-ISBN-13: 9781421414430
E-ISBN-10: 1421414430
Print-ISBN-13: 9781421414423
Print-ISBN-10: 1421414422

Page Count: 336
Illustrations: 31 line drawings
Publication Year: 2014