''Laghu-mānasa'' (c. 932 CE) is a
Sanskrit
Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...
-language text on astronomy by the Indian astronomer
Mañjula. It is a ''
karana'' text containing simple rules for astronomical calculations, aimed at
panchanga
A panchāngam ( sa, पञ्चाङ्गम्; ) is a Hindu calendar and almanac, which follows traditional units of Hindu timekeeping, and presents important dates and their calculations in a tabulated form. It is sometimes spelled ''Pa ...
-makers. It remained highly popular across a vast region of present-day India for several years: the first pre-modern commentary on it was written in
Kashmir
Kashmir () is the northernmost geographical region of the Indian subcontinent. Until the mid-19th century, the term "Kashmir" denoted only the Kashmir Valley between the Great Himalayas and the Pir Panjal Range. Today, the term encompas ...
in 958, and the last one was written in 1732 in
Kerala
Kerala ( ; ) is a state on the Malabar Coast of India. It was formed on 1 November 1956, following the passage of the States Reorganisation Act, by combining Malayalam-speaking regions of the erstwhile regions of Cochin, Malabar, South ...
.
Date and authorship
''Laghu-mānasa'' is the only surviving work of Mañjula, whose geographic location is not known. Mañjula adopted 10 March 932 CE (Saturday noon of
Chaitra
Chaitra (Hindi: चैत्र) is a month of the Hindu calendar.
In the standard Hindu calendar and India's national civil calendar, Chaitra is the first month of the year. It is the last month in the Bengali calendar, where it is called Cho ...
1,
Shaka
Shaka kaSenzangakhona ( – 22 September 1828), also known as Shaka Zulu () and Sigidi kaSenzangakhona, was the king of the Zulu Kingdom from 1816 to 1828. One of the most influential monarchs of the Zulu, he ordered wide-reaching reforms that ...
854) as the
epoch
In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured.
The moment of epoch is usually decided by ...
of calculation in text, which suggests that he started composing the text sometime in 932 CE.
According to Surya-deva Yajva's commentary on the text, Mañjula studied several works on astronomy, and summarized them in an earlier work called ''Laghu-mānasa''. He asked one of his pupils to take a copy of the work to the local king. The pupil did so, but took credit for writing the work. When Mañjula later visited the king, he asked the king to test him and the pupil by making them write another text on the same day, in the king's custody. Mañjula then wrote the present-day ''Laghu-mānasa'', while the pupil was unable to write anything. The king banished the pupil, rewarded Mañjula, and popularized the latest ''Laghu-mānasa''.
Content
''Laghu-mānasa'', also called ''Laghumanāsam'', is a ''
karana'' text, that is, a work containing short and simple rules for astronomical calculations aimed to help the
panchanga
A panchāngam ( sa, पञ्चाङ्गम्; ) is a Hindu calendar and almanac, which follows traditional units of Hindu timekeeping, and presents important dates and their calculations in a tabulated form. It is sometimes spelled ''Pa ...
-makers. It is the smallest ''karana'' text of classical Indian astronomy: the main text contains 60 ''
anushtubh''-metre verses that provide the rules, plus an additional 5 ''
arya
Aryan or Arya (, Indo-Iranian *''arya'') is a term originally used as an ethnocultural self-designation by Indo-Iranians in ancient times, in contrast to the nearby outsiders known as 'non-Aryan' (*''an-arya''). In Ancient India, the term ' ...
''-metre verses that provide the
epochal constants required for the calculations. According to commentator Surya-deva Yajva, Mañjula wrote the additional verses in the ''arya'' metre so as not to mix up the constants with the main text, and to remind the reader to revise the consonants every 100 years.
The text provides much of the planetary model information known to the contemporary Indian astronomers, and appears to derive information from earlier sources including
Aryabhata
Aryabhata (ISO: ) or Aryabhata I (476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the ''Aryabhatiya'' (which ...
's various works (c. 500),
Brahmagupta
Brahmagupta ( – ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical trea ...
's ''
Brahma-sphuta-siddhanta'' (c. 628 CE), and Lata-deva's ''
Surya-siddhanta'' (6th century).
Chapters
Different commentators divide the text into chapters in different ways. The critical edition by K.S. Shukla divides the text into 9 chapters (Sanskrit names in
IAST
The International Alphabet of Sanskrit Transliteration (IAST) is a transliteration scheme that allows the lossless romanisation of Indic scripts as employed by Sanskrit and related Indic languages. It is based on a scheme that emerged during ...
):
# ''Dhruvaka-nirūpaṇādhikāraḥ'' (Dhruvakas or constant parameters): Verses 1–2, 1'-5'
# ''Madhyagatyadhikāraḥ'' (Mean motion): Verses 3-10
# ''Sphuṭa-gatyadhikāraḥ'' (True motion): Verses 11-17
# ''Prakirṇakādhikāraḥ'' (Miscellaneous topics): Verses 18-21
# ''Tripraśnādhikāraḥ'' (The three problems): Verses 22-30
# ''Graha-yuti-grahaṇadvaya-parilekhanādhikāraḥ'' (Conjunction of two planets, eclipses, and their graphical representation): Verses 31-50
# ''Grahodayādhikāraḥ'' (Rising and setting of heavenly bodies): Verses 51-55
# ''Mahāpātādhikāraḥ'' (''Vyatīpāta'' and ''Vaidhṛta''): Verse 56
# ''Candraśṛṅgonnatyadhikāraḥ'' (Elevation of moon's horns): Verses 57-77
Pratashti-dhara divides the text into 8 chapters:
# ''Dhruvaka-nirūpaṇādhikāra'': Verses 1–2, 1'-5'
# ''Madhyagatyadhikāra'': Verses 3-10
# ''Sphuṭa-gatyadhikāra'': Verses 11-17
# ''Prakirṇakādhikāra'': Verses 18-21
# ''Tripraśnādhikāra'': Verses 22-30
# ''Graha-yuti-grahaṇadvaya-parilekhanādhikāra'': Verses 31-50
# ''Grahodayāstadhikāraḥ'': Verses 51-55
# ''Mahāpātendu-śṛṅgonnatyadhikāra'': Verses 56-60
Surya-deva Yajva divides the text into 4 chapters, sub-dividing the first chapter into 3 sections:
# Chapter 1
## ''Madhyamādhikāra'': Verses 1–10, 1'-5'
## ''Sphuṭa-gatyadhikāra'': Verses 11-17
## ''Prakirṇakādhikāra'': Verses 18-21
# ''Tripraśnādhyāya'': Verses 22-30
# ''Grahaṇādhyāya'': Verses 31-50
# ''Grahodayāstamayādhikāra'': Verses 51-60
Parameshvara
Vatasseri Parameshvara Nambudiri ( 1380–1460) was a major Indian mathematician and astronomer of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama. He was also an astrologer. Parameshvara was a proponent of ob ...
's classification is almost same as that of Surya-deva Yajva, but he titles the fourth chapter ''Saṃkīrṇādhikāra''. He includes an additional verse (53' in Shukla's critical edition), but states that some people omit it.
Yallaya and Bhūdhara divide the text into 8 chapters:
# ''Madhya-grahādhikāra'': Verses 1–10, 20
# ''Graha-sphuṭādhikāra'': Verses 11–19, 21
# ''Tripraśnādhikāraḥ'': Verses 22-30
# ''Grahaṇa-graha-yuti-parilekhanādhyāya'': Verses 31-50
# ''Grahodayāstādhikāra'': Verses 53' and 53-55
# ''Mahāpātādhikāra'': Verse 56
# ''Candracchāyādhikāra'': Verse 57
# ''Candraśṛṅgonnatyadhikāra'': Verses 58', 58-60
Legacy
''Laghu-mānasa'' provides short and simple calendaric methods, generally not known to the earlier Indian astronomers, and thus, became an important work in the Indian astronomy. It is the earliest known text to use the process of differentiation in finding the velocity of a planet. It also the earliest known Indian text to outline the lunar correction comprising
evection
In astronomy, evection (Latin for "carrying away") is the largest Lunar theory#Largest or named lunar inequalities, inequality produced by the action of the Sun in the monthly revolution of the Moon around the Earth. The evection, formerly called ...
(commentator Yallaya attributes this correction to the ''Vateshvara-siddhanta'', but the surviving manuscripts of that work do not mention it). Unlike earlier astronomers, Mañjula rejects the theory of oscillatory motion of the equinoxes, and recommends a progressive precessional motion.
''Laghu-mānasa'' was popular across a vast area of present-day India, as evident from the commentaries written on it. Commentators on the work include Prashastidhara of
Kashmir
Kashmir () is the northernmost geographical region of the Indian subcontinent. Until the mid-19th century, the term "Kashmir" denoted only the Kashmir Valley between the Great Himalayas and the Pir Panjal Range. Today, the term encompas ...
, Surya-deva Yajva of Gangai-konda-Cholapuram (Tamil Nadu); Yallaya of Skanda-someshvara (Andhra Pradesh);
Parameshvara
Vatasseri Parameshvara Nambudiri ( 1380–1460) was a major Indian mathematician and astronomer of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama. He was also an astrologer. Parameshvara was a proponent of ob ...
of Alattur (Kerala), Bhudhara of
Kampilya
Kampilya was the capital of the Panchala Kingdom, which was a mahajanapada mentioned in the Mahabharata. Kampilya was the capital of southern Panchala and Ahichchhatra was the capital of northern Panchala.
Kampilya was ruled by Drupada during ...
(Uttar Pradesh), and an anonymous commentator of Karnata-desha (Karnataka). Writers from several other places adopted or referred to Mañjula's work; for example,
Bhoja
Bhoja (reigned c. 1010–1055 CE) was an Indian king from the Paramara dynasty. His kingdom was centered around the Malwa region in central India, where his capital Dhara-nagara (modern Dhar) was located. Bhoja fought wars with nearly all h ...
of Malwa (Madhya Pradesh), Dashabala of Gujarat,
Bhaskara II of Bida (Maharashtra), and Shri-datta of
Nepal
Nepal (; ne, नेपाल ), formerly the Federal Democratic Republic of Nepal ( ne,
सङ्घीय लोकतान्त्रिक गणतन्त्र नेपाल ), is a landlocked country in South Asia. It is mai ...
a.
The work was especially popular in present-day Andhra Pradesh and Kerala, as late as until the 17th-18th centuries, as attested by the composition of Telugu (1695 CE) and Malayalam (1732 CE) commentaries there.
Commentaries and derivative texts
Historical commentaries on the text include:
* Sanskrit commentary (958 CE) by Prashasti-dhara of Kashmir
* Sanskrit commentary (1248 CE) by Surya-deva Yajva of Andhra
* Sanskrit commentary (1409 CE) by
Parameshvara
Vatasseri Parameshvara Nambudiri ( 1380–1460) was a major Indian mathematician and astronomer of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama. He was also an astrologer. Parameshvara was a proponent of ob ...
of Kerala
* Sanskrit commentary (1486 CE) by Yallaya of Andhra
* Sanskrit commentary (1572 CE) by Bhudhara of Kampilya
* Sanskrit commentary by an unknown author from Karnata-desha (present-day Karnataka)
* ''Daivajñamanollāsa'' (1695 CE),
Telugu commentary by Ayyalu Somayaji Balaya
* Malayalam commentary (1732 CE), attributed to Puthumana Soamayaji
The following historical works are derived from the ''Laghu-mānasa'':
* A text (1178 CE), possibly a commentary, by Mallikarjuna Suri; quoted in Yallaya's commentary
** A commentator on Mallikarjuna's work may have been responsible for introducing two corrections in Mañjula's work.
* ''Makaranda-mānasa'' (1478 CE), a now-lost work by Makaranda; mentioned in Bhudhara's commentary; possibly a revised edition of Laghu-mānasa with new initial constants (epoch)
''Laghu-mānasaritya Surya-chandra-grahananayanam'' is a 16th-century text based on ''Laghu-mānasa''
The following texts adopt Mañjula's rules:
* ''Rajamrganka'' (11th century), attributed to
Bhoja
Bhoja (reigned c. 1010–1055 CE) was an Indian king from the Paramara dynasty. His kingdom was centered around the Malwa region in central India, where his capital Dhara-nagara (modern Dhar) was located. Bhoja fought wars with nearly all h ...
of Malwa; adopts several of Mañjula's verses with or without alteration
* ''Ganakananda'' (1460 CE) of Surya Suri alias Suryacharya of Andhra, the teacher of Yallaya
* ''Siddhanta-sara'' (1596 CE) of Mallaya Yajva of Andhra
* ''Karanamrta''(1530 CE) by Chitrabhanu of Shivapura (Covvuram) in present-day Kerala; adopts several verses
* ''Siddhanta-sangraha'' (1606 CE) of Vira Suri, son of Kottachenna of Andhra
* ''Graha-ganita-bhaskara''(1613 CE) by Tamma Yajva of Andhra
* ''Karana-kamala-martanda'' of Dashabala; adopts Mañjula's formula for evection, and improves his formula for calculating the hour-angle from the day-length
* Karanottama'' of Achyuta (died 1621) of Kerala; adopts several verses with or without alteration
Critical editions
A printed edition with commentary of Parameshvara was published as part of the Ānandāśrama Sanskrit Series from Pune in 1944. An English translation by N.K. Majumdar was published from Calcutta in 1951.
Kripa Shankar Shukla's critical edition of the text with an English translation and notes was published as a supplement to the Volume 25 of the ''Indian Journal of History of Science'' (1990) by the Indian National Science Academy, New Delhi. It was based on 11 manuscripts, available at
Government Oriental Library (Mysore; now Oriental Research Institute), Government Oriental Manuscripts Library (Madras), and
Sampurnananda Sanskrit University Library (Varanasi).
References
Bibliography
*
*
{{refend
External links
Laghu mānasa with commentary by Paramesvaraedited by Balvant Dattatreya Apte
10th-century books
10th-century Sanskrit literature