1. Apastamba apastamba. Born It would also be fair to say that apastamba s Sulbasutrais the most interesting from a mathematical point of view. We http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Apastamba.html

Apastamba Born: about 600 BC in India Died: about 600 BC in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index To write a biography of Apastamba is essentially impossible since nothing is known of him except that he was the author of a Sulbasutra which is certainly later than the Sulbasutra of Baudhayana . It would also be fair to say that Apastamba's Sulbasutra is the most interesting from a mathematical point of view. We do not know Apastamba's dates accurately enough to even guess at a life span for him, which is why we have given the same approximate birth year as death year. Apastamba was neither a mathematician in the sense that we would understand it today, nor a scribe who simply copied manuscripts like Ahmes . He would certainly have been a man of very considerable learning but probably not interested in mathematics for its own sake, merely interested in using it for religious purposes. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites and to improve and expand on the rules which had been given by his predecessors. Apastamba would have been a Vedic priest instructing the people in the ways of conducting the religious rites he describes. The mathematics given in the Sulbasutras is there to enable the accurate construction of altars needed for sacrifices. It is clear from the writing that Apastamba, as well as being a priest and a teacher of religious practices, would have been a skilled craftsman. He must have been himself skilled in the practical use of the mathematics he described as a craftsman who himself constructed sacrificial altars of the highest quality.

2. Apastamba Biography of apastamba (600BC540BC) To write a biography of apastamba is essentially impossible since nothing is known of him except that he be fair to say that apastamba's Sulbasutra is the http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Apastamba.html

Apastamba Born: about 600 BC in India Died: about 600 BC in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index To write a biography of Apastamba is essentially impossible since nothing is known of him except that he was the author of a Sulbasutra which is certainly later than the Sulbasutra of Baudhayana . It would also be fair to say that Apastamba's Sulbasutra is the most interesting from a mathematical point of view. We do not know Apastamba's dates accurately enough to even guess at a life span for him, which is why we have given the same approximate birth year as death year. Apastamba was neither a mathematician in the sense that we would understand it today, nor a scribe who simply copied manuscripts like Ahmes . He would certainly have been a man of very considerable learning but probably not interested in mathematics for its own sake, merely interested in using it for religious purposes. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites and to improve and expand on the rules which had been given by his predecessors. Apastamba would have been a Vedic priest instructing the people in the ways of conducting the religious rites he describes. The mathematics given in the Sulbasutras is there to enable the accurate construction of altars needed for sacrifices. It is clear from the writing that Apastamba, as well as being a priest and a teacher of religious practices, would have been a skilled craftsman. He must have been himself skilled in the practical use of the mathematics he described as a craftsman who himself constructed sacrificial altars of the highest quality.

3. References For Apastamba References for apastamba. Books GG Joseph The URL of this page ishttp//wwwhistory.mcs.st-andrews.ac.uk/References/apastamba.html. http://www-gap.dcs.st-and.ac.uk/~history/References/Apastamba.html

References for Apastamba Books: G G Joseph, The crest of the peacock (London, 1991). Articles: R P Kulkarni, The value of known to Sulbasutrakaras, Indian J. Hist. Sci. G Kumari, Some significant results of algebra of pre-Aryabhata era, Math. Ed. (Siwan) A E Raik and V N Ilin, A reconstruction of the solution of certain problems from the Apastamba Sulba Sutra Apastamba (Russian), in A P Juskevic, S S Demidov, F A Medvedev and E I Slavutin, Studies in the history of mathematics "Nauka" (Moscow, 1974), 220-222; 302. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR November 2000 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Apastamba.html

4. Apastamba Sutras Translated By George Buhler This section presents the translation of the apastamba Sutras, the Sacred lawsof the Aryans as taught in the schools of apastamba, Guatama, Vasishtha, and http://hinduwebsite.com/sacredscripts/dharma/apaindex.htm

Home Hinduism Buddhism Jainism ... Âpastamba Prasna Ii, Patala 11, Khanda 29. The material presented in this page is in the public domain and reproduced according to the Berne Convention for the benefit of our readers. Hinduwebsite.com About Us Privacy Policy Contact Us Terms of use ... Add your link

5. Apastamba Sutras This section presents the translation of the apastamba Sutras, the Sacred laws of the Aryans as taught in the schools of apastamba, Guatama, Vasishtha, and Baudhayana, translated by Georg Büler http://www.hinduwebsite.com/sacredscripts/dharma/apacontents.htm

Home Hinduism Buddhism Jainism ... Gautama Sutras THE SACRED LAWS OF THE ARYAS AS TAUGHT IN THE SCHOOLS OF APASTAMBA, GUATAMA, VASISHTHA, AND BAUDHAYANA TRANSLATED BY GEORG BÜLER. PART I APASTAMBA AND GAUTAMA Sacred Books of the East, Volume II F. Max Müller, editor (The Dharma Sutras) CONTENTS INTRODUCTION TO ÂPASTAMBA INTRODUCTION TO GAUTAMA ÂPASTAMBA'S APHORISMS ON THE SACRED LAW. General Rules Initiation Studentship A Student who has returned Home The Study of the Veda A Student who has returned Home Saluting Purification Eating, and Forbidden Food Lawful Livelihood Penance Rules for a Snâtaka The Duties of a Householder Inheritance Funeral Mations The Four Orders The King GAUTAMA'S INSTITUTES OF THE SACRED LAW. Initiation Purification Studentship The Ascetic The Hermit The Householder Saluting Times of Distress A King and Brâhmana versed in the Vedas The Duties of a Snâtka Lawful Occupations and Livelihood The Duties of a King Civil and Criminal Law Witnesses Impurity Funeral Oblations The Study of the Veda Eating, and Forbidden Food

6. ABBREVIATIONS Note For Ready Reference, The Five Historical AA AustroAsiatic AB aitareya brAhmaNa (4, W E) Akkad. Akkadian ApDhS apastambadharmasUtra (5 C) ApZS apastamba zrautasUtra (5 C) Armen. Armenian Austro-As. http://users.primushost.com/~india/ejvs/ejvs0501/ejvs0501d.txt

< *mEcca 'defective' (Turner, CDIAL 10389. Parpola 1994: 174 has attempted a Dravidian explanation. He understands meluHHa (var. melaHHa) as Drav. *mElakam [mElaxam] 'high country' (= Baluchistan) (=ta-milakam) and points to Neo-Assyr. baluHHu 'galbanum', sinda 'wood from Sindh'. He traces mlech, milakkha back to *mlekS, which is seen as agreeing, with central Drav. metathesis with *mlExa = mElaxa-m. Kuiper 1991:24 indicates not infrequent elision of (Dravid.) -a- when taken over into Skt. Shafer 1954 has a Tib-Burm. etymology *mltSe; Southworth 1990: 223 reconstructs PDrav. 2 *mu.z.i/mi.z.i 'say, speak, utter', DEDR 4989, tami.l. 'Tamil' < 'own speech'. (6) The earliest archaeologically found rice is said to come from Koldihwa near Allahabad (c. 5440/5430 BCE or even earlier); this has been doubted. A more probable date is c. 4000 BCE, at Chirand in Bihar. (7) Southworth 1990: 229, n.10: PIA *camala/cAvala < TB ca-? (dza); cf. Southworth 1974, with an early Drav. substrate in the northwest and in the Gangetic plains: < Tib.-Burm. *cA + vAl/vAr

7. Buy The Dharmasutras The Law Codes Of Apastamba, Gautama The Dharmasutras The Law Codes of apastamba, Gautama, Baudhayana, and Vasistha by Patrick Olivelle in Paperback. ISBN 0192838822. The Dharmasutras are the four surviving written works of the http://rdre1.inktomi.com/click?u=http://na.link.decdna.net/n/3532/4200/www.walma

8. The Kaushikas GOTRA. PRAVARA RSHIs. SUTRA. vishvAmitra. vaishvAmitra, daivarAta,audala. Baudhayana, apastamba, Katyayana, Asvalayana, Manava. shraumata http://www.bharatavarsha.com/iyer/gotra/kaushika.html

THE KAUSHIKAs The kaushika (descendents of the influential kushika) include such intellectual giants as vishvAmitra and madhucchandasa. What is arguably the single most important verse in all the vedas - the gAyatri mantra- was composed by vishvAmitra. This set of lineages has kshatriya origins. vishvAmitra himself was a king of some importance during the vedic age. The accounts of his rivalry with vasishTha make up one of the great dramas in the vedas and the post-vedic literature. All the kaushika lineages have come down through vishvAmitra. The vaishvAmitras may be divided into 20 gotra-gaNas as shown below: NOTE: In the table below, the subdivisions of the kaushikas are listed. The name of the gotra is listed in the first column, and the corresponding pravara rshi set is in the second column. Since some of the pravara lineages are specific to the followers of certain sutras, the appropriate sutra is given in the third column. Wherever there are two or more sets of pravara rshis, it should be taken to mean that there are different lineages that correspond to a certain gotra. In general, the set of pravara rshis is a more accurate indicator of a person's descent, than simply the gotra itself. GOTRA PRAVARA RSHIs SUTRA vishvAmitra vaishvAmitra, daivarAta, audala

9. Apastamba Sutras, Prasna1, Patala1, Khanda 2 This section presents the translation of the apastamba Sutras, the Sacred laws of the Aryans as taught in the schools of apastamba, Guatama, Vasishtha, and Baudhayana, translated by Georg Büler http://www.hinduwebsite.com/sacredscripts/dharma/apa00.htm

Home Hinduism Buddhism Jainism ... Gautama Sutras INTRODUCTION TO ÂPASTAMBA. The Apastamblya Dharma-sûtra forms part of an enormous Kalpa-sûtra or body of aphorisms, which digests the teaching of the Veda and of the ancient Rishis regarding the performance of sacrifices and the duties of twice-born men, Brâhmanas, Kshatriyas, and Vaisyas. and which, being chiefly based on the second of the four Vedas, the Yagur-veda in the Taittirîya recension, is primarily intended for the benefit of the Adhvaryu priests in whose families the study of the Yagur-veda is hereditary. The position of the Dharma-sûtra in the middle of the collection at once raises the presumption that it originally formed an integral portion of the body of Sûtras and that it is not a later addition. Had it been added later, it wouid either stand at the end of the thirty Prasnas or altogether outside the collection, as is the case with some other treatises attributed to Âpastamba [7]. The Hindus are, no doubt, unscrupulous in adding to the works of famous teachers. But such additions, if of considerable extent, are usually not embodied in the works themselves which they are intended to supplement. They are mostly given as seshas or parisishtas, tacked on at the end, and generally marked as such in the MSS. Who this author really was, is a problem which cannot be solved for the present, and which probably will. always remain unsolved, because we know his family name only. For the form of the word itself shows that the name Âpastamba, just like those of most founders of Vedic schools, e. g. Bhâradvâga, Âsvalâyana, Gautama, is a patronymic. This circumstance is, of course, fatal to all attempts at an identification of the individual who holds so prominent a place among the teachers of the Black Yagur-veda.

10. The Bhargavas Baudhayana, apastamba, Asvalayana, Katyayana, Manava. bhArgava, aurva,jAmadagnya. apastamba. bhArgava, ArshtisheNa, AnUpa. apastamba. http://www.bharatavarsha.com/iyer/gotra/bhargava.html

THE BHARGAVAs The Bhargavas (descendents of Bhrgu) include such illustrious names like Chyavana, Jamadagni and Parasu-rama (usually referred to as ramo bhargava, or simply as bhargava). The Bhargavas may be divided into the 5 subsets. The first subset may be called simply Bhargava, constituted by 11 gotras. The remaining 4 subsets of the Bhargavas are individual gotras by themselves. Collectively these 4 subsets are called the Kevala Bhargavas. NOTE: In the table below, the subdivisions of the Bhargavas are listed. The name of the gotra is listed in the first column, and the corresponding pravara rshi set is in the second column. Since some of the pravara lineages are specific to the followers of certain sutras, the appropriate sutra is given in the third column. Wherever there are two or more sets of pravara rshis, it should be taken to mean that there are different lineages that correspond to a certain gotra. In general, the set of pravara rshis is a more accurate indicator of a person's descent, than simply the gotra itself. GOTRA PRAVARA RSHIs SUTRA I. Bhargava

11. TITUS Texts: Black Yajurveda: Apastamba-Dharmasutra: Index TITUS Black Yajurveda apastambaDharmasutra Index First select here Text levelno. 1 Text collection YVS Text level no. 2 Text ApDhS Text level no. http://titus.uni-frankfurt.de/texte/etcs/ind/aind/ved/yvs/dhs/apdhs/apdhsx.htm

TITUS Black Yajurveda: Apastamba-Dharmasutra Index First select here: Text level no. 1: Text collection: YVS Text level no. 2: Text: ApDhS Text level no. 3: Part: Then select next level from list below and press "lookup"

12. History Of Mathematics: Chronology Of Mathematicians 630c 550) *MT. apastamba (c. 600) Anaximander of Miletus (c http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan Table of Contents 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below List of Mathematicians 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *MT 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB

13. TITUS Texts: Yajur-Veda: Apastamba-Srautasutra: Index TITUS YajurVeda apastamba-Srautasutra Index First select here Text levelno. 1 Text collection YVB Text level no. 2 Text ApSS Text level no. http://titus.uni-frankfurt.de/texte/etcs/ind/aind/ved/yvs/apss/apssx.htm

TITUS Yajur-Veda: Apastamba-Srautasutra Index First select here: Text level no. 1: Text collection: YVB Text level no. 2: Text: ApSS Text level no. 3: Chapter: Then select next level from list below and press "lookup"

14. INDIA'S CONTRIBUTION TO MATHEMATICS (ALGEBRA, ALGORITHM, GEOMETRY, TRIGNOMETRY & Some of important works in this field are by apastamba, Baudhayana, Hiranyakesin, Manava, Varaha and Vadhula http://india.coolatlanta.com/GreatPages/sudheer/maths.html

You are watching India.CoolAtlanta.com -> Culture -> Sudheer Ancient India's Contribution to Mathematics "India was the motherland of our race and Sanskrit the mother of Europe's languages. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity... of self-government and democracy. In many ways, Mother India is the mother of us all." - Will Durant - American Historian 1885-1981 Mathematics represents a high level of abstraction attained by the human mind. In India, mathematics has its roots in Vedic literature which is nearly 4000 years old. Between 1000 B.C. and 1000 A.D. various treatises on mathematics were authored by Indian mathematicians in which were set forth for the first time, the concept of zero, the techniques of algebra and algorithm, square root and cube root. This method of graduated calculation was documented in the Pancha-Siddhantika (Five Principles) in the 5th Century But the technique is said to be dating from Vedic times circa 2000 B.C. Table of Contents Home Introduction Chapter 1: Production Technology and Mechanical Engineering Chapter 2 Shipbuilding and Navigation Chapter 3 Architecture and Civil Engineering You are currently viewing Chapter 4 on Mathematics Chapter 5 Astronomy Chapter 6 Physics and Chemistry Chapter 7 Medical Science Chapter 8 Fine Arts Chapter 9 Sports and Games Chapter 10 Philosophy Chapter 11 Summing Up Glossary Sanskrit-English Glossary Next Book A Search for Our Present in History As in the applied sciences like production technology, architecture and shipbilding, Indians in ancient times also made advances in abstract sciences like Mathematics and Astronomy. It has now been generally accepted that the technique of algebra and the concept of zero originated in India.

15. Apastamba-Dharmasutra = Aapastamba DHARMASUUTRA = The coding of the following text was a part of http://www.sub.uni-goettingen.de/ebene_1/fiindolo/gretil/1_sanskr/6_sastra/4_dha

=== AAPASTAMBA DHARMASUUTRA === Input by Y.Ikari; Proofed and KSS variants are added by K.Kano March 1992. Sanskrit Seires Nos.LIV and L), 3rd ed. 1932. Variant reading is in the parenthesis after the end of each suutra, according to Kashi Sanskrit Seires No.93 (K) edited by A.Chinnaswami, Benares 1932. Examples : 1) aaaaa# / ( K bbbbb ) KSS reads "bbbbb" instead of "aaaaa". 2) aaaaa# bbbbb# - / ( K ccccc.ddddd ) KSS reads "ccccc.ddddd" instead of "aaaaa bbbbb". 3) - aaaaa#1 - bbbbb#2 ( K 1:ccccc, 2:ddddd ) KSS reads "ccccc" instead of "aaaaa", and "ddddd" instead of "bbbbb". 4) Ap.a.a.a.5 - / ( = K 6 ) a.a.a.5 in BSS corresponds a.a.a.6 in KSS. 5) Ap.a.a.a.5 / ( = K 5+6 ) a.a.a.5 in BSS corresponds a.a.a.5 and a.a.a.6 in KSS. 6) Ap.a.a.a.5 / Ap.a.a.a.6 / ( 5+6 = K 5 ) a.a.a.5 in KSS corresponds a.a.a.5 and a.a.a.6 in BSS. 7) /# / ( K om. / ) KSS omits / ( daNDa ). Differences of Sandhi are neglected and clear misprints are corrected. TEXT INPUT SYSTEM - Members of a compound are separated by periods.

16. Political And Social Ethics Of India By Sanderson Beck he was allowed to take his things. The apastamba Sutra concludes with the idea that duties not taught 149. 7. apastambaDharma Sutra 292110 in The http://www.san.beck.org/EC10-Social.html

BECK index Political and Social Ethics of India This chapter is part of the book ANCIENT WISDOM AND FOLLY, which has now been published. For information on ordering click here. Magadhan Ascendancy Alexander's Invasion of India Mauryan Empire, Ashoka and History ... Kama Sutra So far most of our knowledge about the ethics of ancient India has come to us from the religious writings of the Vedas Brahmanas Aranyakas Upanishads ... Jainism , and Buddhism . These are the oldest sources, as there were no significant historians of ancient India except for the Greek and Roman accounts of Alexander's conquests. Later we shall see what epic poetry revealed about Indian civilization. This chapter will review what we do know about the history of ancient India and then examine the writings about dharma (law, duty), politics, and pleasure. As we learned from the Vedas , ancient India was ruled by kings and councils of prominent men in varying degrees of monarchy and republican influence. Megasthenes, a Greek ambassador to India shortly after Alexander's death, wrote a book on India stating that monarchies were dissolved and democratic governments were set up in the cities. Jainism and Buddhism flourished particularly in the independent clans. According to Buddhist texts, in the sixth century BC there were sixteen major states in northern India of which Magadha, Kosala, and Vatsa were the most powerful. Our last chapter recounted how Kosala massacred the Shakya clan; after Buddha's death Kosala also took over Kashi.

17. Urejevanje Apastamba - Uredi - Wikipedija Re beef 1. RigVeda, X, 85, 13 2. RigVeda, X, 86, 13 3. ManuSmriti, 3, 226, 227 4. apastamba,Prasna, I, 5, 17, 31 5. apastamba, Prasna, II, 7, 16, 2628 6. apastamba http://sl.wikipedia.org/w/wiki.phtml?title=Apastamba&action=edit

18. References For Apastamba References for the biography of apastamba of the solution of certain problems from the apastamba Sulba Sutra apastamba (Russian), in A P Juskevic, S S Demidov, F http://www-groups.dcs.st-and.ac.uk/~history/References/Apastamba.html

References for Apastamba Books: G G Joseph, The crest of the peacock (London, 1991). Articles: R P Kulkarni, The value of known to Sulbasutrakaras, Indian J. Hist. Sci. G Kumari, Some significant results of algebra of pre-Aryabhata era, Math. Ed. (Siwan) A E Raik and V N Ilin, A reconstruction of the solution of certain problems from the Apastamba Sulba Sutra Apastamba (Russian), in A P Juskevic, S S Demidov, F A Medvedev and E I Slavutin, Studies in the history of mathematics "Nauka" (Moscow, 1974), 220-222; 302. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR November 2000 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Apastamba.html

19. ANCIENT HISTORY OF ANDHRAS apastamba rules (a pastamba gruhya sootra lu) have been widely in practiceamong Andhra Brahmin families today. apastamba was one such teacher. http://www.teluguworld.org/Telugu/Andhra_history.html

ANCIENT HISTORY OF ANDHRAS By Etukoori Balaraama Moorti in Andhra Samkshipta Charitra English translation : PALANA (nparinand@cas.org) It is impossible to confirm the origin of a culture and the date of its origin. Different tribes, classes, and societies gradually combined over a period of time and a transformed society had evolved. This is the evolution of a society. Andhra society is one of the ancient societies of India. One can encounter several tales about Andhras in epics like Mahabharatam and Ramayanam, in great puranas, and Budhdhist Jataka Tales. This confirms the ancient nature of Andhra society. Andhras and Kalingas (ka'Limgulu) supported the Kauravas during the battle between Kauravas and Pandavas (the Bharata yudhdham). Sahadeva defeated the kingdoms of Pandya, Dravida, Odhra, Kerala, Andhra, and Kalinga while performing the Rajasooya yajna. This is depicted in the Mahabharatam. Chanoora (ca'NooruDu) was killed by Srikrishna in Madhura. Harivamsapuranam corroborates the fact that Chanoora was the king of Karoosa Desa (karooSa dESam) (on the North side of Vindhya and on the North banks of Yamuna river) and was an Anhdra (Andhrudu) too. Ramayanam depicts an interesting tale. Viswamitra condemned the "Naramedha Yagam", freed Sunassepu (SunaSSEpu, the yajna paSuvu), and adopted him as his son. Viswamitra's children diliked this act by thier father and were cursed. Then Viswamitra's children migrated towards east and south. It is understood from this tale that these children of Viswamitra were Andhras (a'mdhrulu).

20. - Women In The Sacred Laws - The Dharma Sutras ( Page 21) This importance of initiation, which had been developed by apastamba’s time, badprobably caused the lawgiver to begin his treatise with it, as it formed http://www.hindubooks.org/women_in_the_sacredlaws/the_dharma_sutras/page21.htm

Women In The Sacred Laws Kulapati's Preface The Author Foreword Prologue ... Espirit Des Lois THE DHARMA SUTRAS This importance of initiation, which had been developed by Apastamba’s time, bad probably caused the law-giver to begin his treatise with it, as it formed the beginning of the intellectual life of a man and we find Apastamba laying down strict rules at length for such a student. It was a sin to look at a woman and sacred texts could not be uttered when a Sudra woman looked at a Brahmana. As the Dharma-Sutra of Apastamba formed a supplement to the Grhya-Sutra, we do not find the details of -marriage as they have been described in the Grhya Sastras. And, as woman’s sphere became much restricted in society, the reference to women in the general rules laid down for man is very few. Apastamba recognises six kinds of marriages as legal ; the Brahma, Arsha, Daiva, Gandharva, Asura and Rakshasa rites. Of these the first three alone the Brahma, Arsha and Daiva marriages-are praiseworthy.

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