Obtaining smaller guṇas and hāras (original) (raw)
International Seminar Proceeding, 2019
Matematika Veda adalah nama yang digunakan secara khusus untuk membahas solusi/rumus lain yang lebih cepat dari solusi umum dalam menyelesaikan permasalahan matematika. Istilah matematika Veda didasarkan pada sistem matematika yang bersumber dari kitab suci Atharvaveda. Pada penelitian ini, sutra (rumus) dalam matematika Veda yang diaplikasikan adalah Nikhilam sutra bagian dari 16 sutra yang ada pada matematika Veda. Nikhilam sutra dimanfaatkan dalam menyelesaikan operasi perkalian dan pembagian. Subjek penelitian ini adalah mahasiswa pada Program Studi Pendidikan Guru Sekolah Dasar (PGSD) Sekolah Tinggi Agama Hindu Dharma Sentana (STAHDS) Sulawesi Tengah. Metode penelitian yang digunakan adalah metode penelitian Open-Ended yang dikembangkan oleh Takhasi yang bertujuan untuk mengetahui bagaimana penerapan matematika veda dan peningkatan hasil belajar serta respon mahasiswa terhadap metode tersebut. Dari penelitian diperoleh hasil bahwa terjadi peningkatan rata-rata nilai dari 68 menjadi 80 setelah diterapakan Nikhilam sutra dalam pembelajaran materi Perkalian dan Pembagian. Selain itu, dari angket yang diberikan 90% mahasiswa sangat setuju dengan penggunaan matematika Veda dalam pembelajaran.
Ahargana in Makarandasarini and Other Indian Astronomical Texts
Indian Journal of History of Science, 2018
Ahargaa is a basic parameter used for calculating mean positions of planets and other elements. The number of civil days elapsed since a chosen fixed epoch is called 'ahargaa', literally meaning 'heap of days'.The intercalary months (adhikamāsa) play an important role in calculating ahargaa. The present paper deals with different procedures for finding ahargaas according to different Indian astronomical texts in detail with concrete examples. It could be seen how easier it is to convert a given traditional lunar calendar date into Julian/Gregorian date by using the vallī components of Makarandasāriī, and also a given Julian or Gregorian date into ahargaas by using various tables.
Amrtotsavagranthamala , 2024
A question that often arises is about positive sciences of India before the Common Era and their links with the Vedas. As an answer, the present monograph brings out for the first time the Mahāsalilaṁ part of the Vṛddhagārgīya Jyotiṣa, critically edited from eleven hitherto unpublished manuscripts collected from libraries in India and abroad. Salilaṁ is the name of the primordial state of dark-matter called andhaṁ-tamaḥ out of which all creation including the celestial bodies emerged. The Mahāsalilaṁ in prose, introduces observations and quantification in terms of numbers, through a set of nearly one hundred questions and explanations, in a style that is archaic and original as emanating from the Vedic world view. Foundational concepts of astral sciences that over centuries evolved into full-fledged Indian astronomy and astrology can be traced to this source in seed form. Earliest description of the five planets in terms of their brightness, six monthly lunar eclipse period, classification of comets, a theory of rainfall, instant of full moon as pūrṇatithi, astronomical background of the Vedic sānnāyya, are here. The Prajāpati-Rohiṇī-Soma legend is explained in new light, leading to Soma as primal Time, moon being a proxy. The synchronization of the five-year solar cycle with the sixty-seven sidereal lunar cycle is given. The text belongs to the maghādi era (c 1800-1600 BCE) when the summer solstice was with the maghā nakṣatra, centuries before the śraviṣṭhādi winter solstice calendar of Lagadha.
This paper attempts to provide a clear concept about the Vedic metres, especially their etymological connotations. What is the origin of the metre? What is the parameter through which we can differentiate the metres one from another? The etymology and the evolution of the seven Vedic metres are thoroughly discussed in this paper. Present researcher tries to highlight the usefulness of chandas as an important part (aṅga) of the Vedas. Discussion over the opinions of our pūrvācāryas about chandas is a significant aspect of this paper.
--वसुदेवसुतं देवं कंस चाणूर मर्दनम् । A breath-taking moment of divine manifestation detailed in MBh with jyotiṣa pramāṇa. --rationale for the next Kali Era 3102 BCE; to underscore the importance of ethical behaviour by sovereign rulers, kings. --Why was the Saptarṣi maṇḍala, an era which started in 3176 BCE was followed by Kali Yuga Era calendar starting 3102 BCE? This date occurred in the life-time of Śrī Kr̥ṣṇa who lived through the Kali Yuga and exited in 3031 a year after the Yadava Civil War. See: Krishna avatāra occurs between 3112 and 3031 BCE --ज्योतिष view presented by Prof. Srinivasa Raghavan https://tinyurl.com/yhjdrn88 --I submit that the Kali Yuga Era calendar start year 3102 is related to the manifestation of Śrī Kr̥ṣṇa avatāra, recording the killing of Kamsa by a 11-year young Kr̥ṣṇa evidencing his Kr̥ṣṇa avatāra, divine manifestation. This event occurred to infuse an ethic in sovereigns; this is explained by Śrī Kr̥ṣṇa. -- I submit that the Kali Yuga Era start date 3102 of the Calendar is NOT related to the end of Kr̥ṣṇa avatāra with the ascent of Kr̥ṣṇa to heaven in 3031 BCE. -- The start date of 3102 is chosen by astronomers because of the unique assemblage of planets in that year, a year in which the divine manifestation event occurred -- वसुदेवसुतं देवं कंस चाणूर मर्दनम् । There is another ephocal reason which is related to the restoration of ethical behaviour by sovereign rulers, kings; Kamsa had transgressed the ethical responsibility and became an embodiment of unethical rule. Kamsa dethroned his own father Ugrasena. Kamsa became tyrant ruler of the Vrishni kingdom with its capital at Mathura. Killing of Kamsa occurred in 3102 BCE and is narrated in Udyoga Parva, by daśārha who is Kṛṣṇa https://tinyurl.com/mnf82tbe This episode explains the significance of the killing of Kamsa, an episode recollected when Bhishma expresses his anguish at Duryodhana's irresponsible behaviour.Kr̥ṣṇa responds and comments on the behaviour of Duryodhana and suggests that time has come for Kuru elders to forcibly seize and bind the wicked king Duryodhana:“…this is great transgression, of which all the elders of the Kuru race are becoming guilty, for they do not forcibly seize and bind this wicked king in the enjoyment of sovereignty. Ye chastiser of foes, I think the time hath come for doing this. Then, he goes on to explain the thrilling episode of a 11-year old son of Devaki killing Kamsa. This killing of Kamsa is clearly an epochal event which happened in 3102 BCE when Kr̥ṣṇa was 11 years’ young. This may explain why the Hindu tradition chose the date 17/18 February 3102 BCE as the date of start of Kali Yuga. Source. KD Abhyankar and GB Bhallabh --ṛtv-ij m. (k) a priest (usually four are enumerated, viz. Hotṛ, Adhvaryu, Brahman, and Udgātṛ; each of them has three companions or helpers, so that the total number is sixteen, viz. hotṛ, Maitrāvaruṇa, Acchāvāka, Grāva-stut; adhvaryu, Prati-prasthātṛ, Neṣṭṛ, Un-netṛ; brahman, Brāhmaṇācchaṉsin, Agnīdhra, Potṛ; udgātṛ, Prastotṛ, Pratihartṛ, Subrahmaṇya, ĀśvŚr. iv, 1, 4-6 ), RV. ; AV. ; TS. ; ŚBr. ; KātyŚr. सप्तर्षि पु० ब० व० । सप्त ऋषयः संज्ञात्वात् कर्म० । “मरीचि-रत्रिः पुलहः पुलस्त्यः क्रतुरङ्गिराः । वशिष्ठश्चमहाभाग! सप्तैते ब्रह्मणः सुताः” इत्युक्तेषु सप्तसु ऋषिषु ।मन्वन्तरभेदे तेषा नामभेदा ऋषिशब्दे उक्ता १४५३ पृ०दृश्या । सप्तर्षिमण्डल त्रि० ६ त० । आकाशे नित्यं ध्रुवनक्षत्रपरि-भ्र मके नक्षत्रसप्तकात्मके नक्षत्रमण्डलभेदे “सप्तर्षिमण्डलंतस्माद्दृश्यते सर्वकोपरीति” पुराणम् तच्चारादिऋषिशब्दे १४५२ पृ० दृश्यम् ।--वाचस्पत्यम् सप्तर्षयः, पुं, भूम्नि, (सप्त ऋषयः ।) सप्तसंख्यकर्षयःतेषां नामानि यथा । मरीचिः १ अत्रिः २अङ्गिराः ३ पुलस्त्यः ४ पुलहः ५ क्रतुः ६ वशिष्ठः ७ ।इत्यमरः ॥ अपि च ।“मप्तर्षिमण्डलं तस्माद्दृश्यते सर्व्वतोपरि ।तत्र सप्तर्षयः सन्ति विनियुक्ताः प्रजासृजा ॥मरीचिरत्निः पुलहः पुलस्त्यः क्रतुरङ्गिराः ।वशिष्ठश्च महाभाग ब्रह्मणो मानसाः सुताः ॥सप्तब्राह्मण इत्येते उच्यन्ते ब्रह्मवादिभिः ।संभूतिरनसूया च क्षमा प्रीतिश्च सन्नतिः ॥अरुन्धतिस्तथा लज्जा तत्पत्न्यौ लोकमातरः ।एतासां तपसा चैतद्धार्य्यते भुवनत्रयम् ॥सन्ध्यात्रयमुपासीना गायत्त्रीजपतत्पराः ।तस्मिन्लोके वसन्त्येते ब्राह्मणाः ब्रह्मवादिनः ॥”इति पाद्मे स्वर्गखण्डे ११ अध्यायः ॥(प्रतिमन्वन्तरे सप्तर्षयो भिन्ना एवासन् । तद्-वृत्तान्तस्तु ऋषिशब्दे द्रष्टव्यः ॥)--शब्दकल्पद्रुमः In traditional Hindu astronomy, seven stars of Ursa Major are identified with the names of Saptarṣi. In ancient Indian astronomy, the asterism of the Big Dipper (part of the constellation of Ursa Major) is called saptarishi, with the seven stars representing seven rishis, namely "Vashistha", "Marichi", "Pulastya", "Pulaha", "Atri", "Angiras" and "Kratu". There is another star slightly visible within it, known as "Arundhati". Arundhati and Vashishtha are married, and together form the Mizar double. Saptarishis in each manvantara of the current kalpa (Śveta-Vārāha Kalpa) Manu (manvantara) Saptarishis Svayambhuva Marichi, Atri, Angiras, Pulaha, Kratu, Pulastya, and Vasishtha Svarocisha Urja, Stambha, Prana, Nanda, Rishabha, Nischara and Arvarivat Uttama Kaukundihi, Kurundi, Dalaya, Sankha, Pravahita, Mita and Sammita (Sons of Vasistha) Tapasa/Tamasa Jyotirdhama, Prithu, Kavya, Chaitra, Agni, Vanaka and Pivara Raivata Hirannyaroma, Vedasrí, Urddhabahu, Vedabahu, Sudhaman, Parjanya and Mahamuni Chakshusha Sumedhas, Virajas, Havishmat, Uttama, Madhu, Abhinaman, and Sahishnnu Vaivasvata (current) Jamadagni, Kashyapa, Atri, Vashista, Gautama, Vishvamitra, Bharadvaja Surya-savarni Diptimat, Gslava, Parasurama, Kripa, Drauni or Ashwatthama, Vyasa and Rishyasringa Daksha-savarni Savana, Dyutimat, Bhavya, Vasu, Medhatithi, Jyotishman, and Satya Brahma-savarni Havishman, Sukriti, Satya, Apammurtti, Nabhaga, Apratimaujas and Satyaketu Dharma-savarni Nischara, Agnitejas, Vapushman, Vishnu, Aruni, Havishman and Anagha Rudra-savarni Tapaswi, Sutapas, Tapomurti, Taporati, Tapodhriti, Tapodyuti and Tapodhana Deva-savarni Nirmoha, Tatwadersin, Nishprakampa, Nirutsuka, Dhritimat, Avyaya and Sutapas Indra-savarni Agnibshu, Suchi, Aukra, Magadha, Gridhra, Yukta and Ajita Wilson, Horace Hayman; trans. (1840) "Vishńu Puráńa", Sacred-Texts.com. Contains an account of the several Manus and Manwantaras. https://en.wikipedia.org/wiki/Saptarishi Saptarṣi maṇḍala; Ursa Major Constellation As many of its common names allude, its shape is said to resemble a ladle, an agricultural plough, or wagon. In the context of Ursa Major, they are commonly drawn to represent the hindquarters and tail of the Great Bear. Starting with the "ladle" portion of the dipper and extending clockwise (eastward in the sky) through the handle, these stars are the following: • α Ursae Majoris, known by the Arabic name Dubhe ("the bear"), which at a magnitude of 1.79 is the 35th-brightest star in the sky and the second-brightest of Ursa Major. • β Ursae Majoris, called Merak ("the loins of the bear"), with a magnitude of 2.37. • γ Ursae Majoris, known as Phecda ("thigh"), with a magnitude of 2.44. • δ Ursae Majoris, or Megrez, meaning "root of the tail," referring to its location as the intersection of the body and tail of the bear (or the ladle and handle of the dipper). • ε Ursae Majoris, known as Alioth, a name which refers not to a bear but to a "black horse," the name corrupted from the original and mis-assigned to the similarly named Alcor, the naked-eye binary companion of Mizar.[8] Alioth is the brightest star of Ursa Major and the 33rd-brightest in the sky, with a magnitude of 1.76. It is also the brightest of the chemically peculiar Ap stars, magnetic stars whose chemical elements are either depleted or enhanced, and appear to change as the star rotates.[8] • ζ Ursae Majoris, Mizar, the second star in from the end of the handle of the Big Dipper, and the constellation's fourth-brightest star. Mizar, which means "girdle," forms a famous double star, with its optical companion Alcor (80 Ursae Majoris), the two of which were termed the "horse and rider" by the Arabs. The ability to resolve the two stars with the naked eye is often quoted as a test of eyesight, although even people with quite poor eyesight can see the two stars. • η Ursae Majoris, known as Alkaid, meaning the "end of the tail". With a magnitude of 1.85, Alkaid is the third-brightest star of Ursa Major. https://en.wikipedia.org/wiki/Ursa\_Major The earliest list of the Seven Rishis is given by Jaiminiya Brahmana 2.218–221: Agastya, Atri, Bhardwaja, Gautam, Jamadagni, Vashistha and Vishvamitra followed by Brihadaranyaka Upanisad 2.2.6 with a slightly different list: Atri, Bharadvaja, Gautama, Jamadagni, Kashyapa, Vashistha and Vishwamitra. The late Gopatha Brahmana 1.2.8 has Vashistha, Vishvamitra, Jamadagni, Gautama, Bharadvaja, Gungu, Agastya and Kashyapa. Story of Parīkṣit A brilliant King of Candravaṃśa. He was the grandson of Arjuna and son of Abhimanyu. (For genealogy see under Abhimanyu). Birth. Parīkṣit was the son born to Abhimanyu of Uttarā. This was a still-born child and it was Śrī Kṛṣṇa who gave it life. There is a story in Mahābhārata about this: Uttarā, wife of Abhimanyu, was pregnant when the war between the Pāṇḍavas and Kauravas started at Kurukṣetra. Aśvatthāmā, son of Droṇa, entered the camp of the Pāṇḍavas at night and slew Dhṛṣṭadyumna. He then sent the most fierce Brahmaśirāstra (missile of Brahmaśira) to exterminate the Pāṇḍavas. To face it and oppose it Arjuna also sent an equally fierce Brahmaśirāstra. The sight of two such powerful weapons opposing each other made all the sages anxious and they led by Vyāsa entered the field and requested them to withdraw their missiles. It was in vain. The missile of Aśvatthāmā went and struck the womb of Uttarā. Once when the Pāṇḍavas after their exile were staying in the village of Upaplavya a brahmin had predicted to Uttarā that at the fag end of the life of the Pāṇḍavas Uttarā would bear a son who would be tested even while in her womb and that the child should be named Parīkṣit. (Parīkṣā = test).
2021, BM 47042+47064: How To Divide a Mina (Preprint version 3)
2021
Edition and discussion of the Late Babylonian tablet BM 47042+47064 with a previously unknown type of Babylonian metrological table. Each entry of the table is concerned with dividing 1 mina of weight by a different number. Not only the final result but also the operational steps by which the division is achieved are presented in the table. They can be summarized as follows: 1) number N in absolute decimal notation, 2) conversion to floating sexagesimal n, 3) finding its reciprocal 1/n (using table of reciprocals), 4) conversion to absolute weight 1/N mina (using metrological conversion table). To be published in an upcoming edition of Late Babylonian mathematical texts from the British Museum (DFG project "Late Babylonian Mathematical Practices")
Pañcasiddhāntikā of Varāhamihira Chapter Two: Vasishtha Siddhanta – Planetary Computations, etc.
2018
This translation contains Chapter Two of the Panchasiddhantika, a famous East Indian astrology text by Varahamihira (circa 6th century). The text is a compilation of five astronomical texts known to Varahamihira: the Paulisha, Romaka, Vasishtha, Saura, and Paitamaha. There are a total of 18 chapters in the Panchasiddhantika. The other chapters will be added as I complete them. My translation includes an outline of the major concepts for each chapter, a word for word translation from Sanskrit to English with parts of speech annotations. Chapter Two covers various calculations from the Vasishtha Siddhanta including the true position of the sun, true position of the moon, locating the nakshatra and tithi from the true positions of the sun and moon, duration of day and night time in the zodiac signs throughout the year, the twelve gnomonic shadow digits based on the position of the sun by tropical zodiac sign, position of the sun by tropical zodiac sign based on the twelve gnomonic shadow digits, position of the lagna from the shadow before noon and afternoon, and the position of the shadow from the lagna before noon and afternoon. I welcome any feedback. Thank you for your attention and support.