Laghumānasa

Laghu-mānasa is a Sanskrit-language text on astronomy by the Indian astronomer Mañjula. It is a karana text containing simple rules for astronomical calculations, aimed at panchanga-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 in 958, and the last one was written in 1732 in Kerala.

Date and authorship

Laghu-mānasa is the only surviving work of Mañjula, whose geographic location is not known. Mañjula adopted 10 March 932 CE as the epoch 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-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-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's various works, Brahmagupta's Brahma-sphuta-siddhanta, and Lata-deva's Surya-siddhanta.

Verse	Content
1	Introduction: description of the author as a Brahmana of the Bharadvaja gotra; objective of the text - to provide short and unprecedented rules for astronomical calculations
2	Conditions under which the specified rules will give accurate results
3-4	Calculation of dyugana, a variable used in other calculations
5-10	Rules for calculating mean positions
11-12	Definition of the terms kendra, bhuja, and koti used in other calculations
13-17	Computation of the equations of the centre and the true mean velocity of a planet
18-19	Lunar correction comprising the evection and the deficit of the Moon's equation of the centre
20	Correction for the local longitude
21	Calculation of the elements of the panchanga: tithi, karana, nakshatra, and yoga
22	Ascensional difference of the Sun
23	Oblique ascensions of the tropical signs
24	Longitude of the rising point of the ecliptic and the corresponding time in nadis
25	Length of the day and the Sun's hour angle
26-28	Shadow of the gnomon
29-30	The sun's hour angle
31-32	Occurrence of the conjunction of two planets, and days elapsed since the conjunction
33-35	Diameters of the sun, the moon, the earth's shadow cone at the moon's distance, and the planets
36-37	Latitudes of the moon etc.
38	Distance between the centres of two planets at the time of their conjunction
39	Parallax in longitude
40	Meridian ecliptic point
41	Parallax in latitude
42	Correction for parallax in latitude
43-52	Eclipse-related calculations
53	Position of the sun at the time of the helical rising or setting of a planet
53'	In Yallaya's commentary and a manuscript, this verse replaces verses 51–52, and provides rule for visibility corrections
54	Helical rising and setting of Canopus
55	True ascensional difference for a planet
56	Duration of the vyatīpāta and vaidhṛta phenomena
57	Shadow cast by the gnomon due to moonlight
58	Measure of bright or dark part of the moon
59	Depiction of the bright or dark part of the moon in the diagram
59'	In Yallaya's commentary and a manuscript, this verse supplements verse 59
60	Conclusion: number of verses in the book, warning to imitators
1'-5'	Arya metre verses providing the epochal constants. Mañjula has provided certain constants, and the later commentators have revised these to suit their own period. One manuscript replaces these verses with 9 verses that provide the same constants plus some additional constants.

Chapters

Different commentators divide the text into chapters in different ways. The critical edition by K.S. Shukla divides the text into 9 chapters :

Dhruvaka-nirūpaṇādhikāraḥ : Verses 1–2, 1'-5'
Madhyagatyadhikāraḥ : Verses 3-10
Sphuṭa-gatyadhikāraḥ : Verses 11-17
Prakirṇakādhikāraḥ : Verses 18-21
Tripraśnādhikāraḥ : Verses 22-30
Graha-yuti-grahaṇadvaya-parilekhanādhikāraḥ : Verses 31-50
Grahodayādhikāraḥ : Verses 51-55
Mahāpātādhikāraḥ : Verse 56
Candraśṛṅgonnatyadhikāraḥ : 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's classification is almost same as that of Surya-deva Yajva, but he titles the fourth chapter Saṃkīrṇādhikāra. He includes an additional verse, 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. 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, Surya-deva Yajva of Gangai-konda-Cholapuram ; Yallaya of Skanda-someshvara ; Parameshvara of Alattur, Bhudhara of Kampilya, and an anonymous commentator of Karnata-desha. Writers from several other places adopted or referred to Mañjula's work; for example, Bhoja of Malwa, Dashabala of Gujarat, Bhaskara II of Bida, and Shri-datta of Nepala.
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 and Malayalam commentaries there.

Commentaries and derivative texts

Historical commentaries on the text include:

Sanskrit commentary by Prashasti-dhara of Kashmir
Sanskrit commentary by Surya-deva Yajva of Andhra
Sanskrit commentary by Parameshvara of Kerala
Sanskrit commentary by Yallaya of Andhra
Sanskrit commentary by Bhudhara of Kampilya
Sanskrit commentary by an unknown author from Karnata-desha Daivajñamanollāsa, Telugu commentary by Ayyalu Somayaji Balaya
Malayalam commentary, attributed to Puthumana Soamayaji

The following historical works are derived from the Laghu-mānasa:

A text, 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, a now-lost work by Makaranda; mentioned in Bhudhara's commentary; possibly a revised edition of Laghu-mānasa with new initial constants

Laghu-mānasaritya Surya-chandra-grahananayanam is a 16th-century text based on Laghu-mānasa
The following texts adopt Mañjula's rules:Rajamrganka, attributed to Bhoja of Malwa; adopts several of Mañjula's verses with or without alterationGanakananda of Surya Suri alias Suryacharya of Andhra, the teacher of YallayaSiddhanta-sara of Mallaya Yajva of AndhraKaranamrta by Chitrabhanu of Shivapura in present-day Kerala; adopts several versesSiddhanta-sangraha of Vira Suri, son of Kottachenna of AndhraGraha-ganita-bhaskara by Tamma Yajva of AndhraKarana-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 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 by the Indian National Science Academy, New Delhi. It was based on 11 manuscripts, available at Government Oriental Library, Government Oriental Manuscripts Library, and Sampurnananda Sanskrit University Library.