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Shulbasutras (शुल्बसूत्राणि) (view source)

Revision as of 23:25, 28 March 2020

4,104 bytes added ,  23:25, 28 March 2020
added Units of Measurement Table and reference
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* 1/8 = Shapha (शफः)
 
* 1/8 = Shapha (शफः)
 
* 1/4 = Pada (पदा)
 
* 1/4 = Pada (पदा)
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These names of fractions referred in context with bargaining for a price of material (Soma) to be purchased. The price of the material is increased step by step. <blockquote>वसो ह्येष विन्दते यः सोमं क्रीणाति ॥ सोमविक्रयिन्सोतिमं ते क्रीणानि महान्तं बह्वर्हं बहु शोभमानं , कलया ते क्रीणानि, कुष्टया ते क्रीणानि, शफेन ते क्रीणानि, पदा ते क्रीणानि ॥ (Mait. Samh. 3.7.7)<ref>Maitrayani Samhita ([https://sa.wikisource.org/wiki/%E0%A4%AE%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%AF%E0%A4%A3%E0%A5%80%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%82_%E0%A5%A9/%E0%A4%AA%E0%A5%8D%E0%A Kanda 3 Prapathaka 7])</ref></blockquote>Thus we see naming of fractions and operations like sum, subtractions and fractions were quite common at those times.<ref>Jayashankara, K. (2007) Ph. D. Thesis: ''Sulba sutra, A Critical Analysis.'' Mangalore University ([http://hdl.handle.net/10603/132298 Chapter 8 Page 8])</ref>
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These names of fractions referred in context with bargaining for a price of material (Soma) to be purchased. The price of the material is increased step by step. <blockquote>वसो ह्येष विन्दते यः सोमं क्रीणाति ॥ सोमविक्रयिन्सोतिमं ते क्रीणानि महान्तं बह्वर्हं बहु शोभमानं , कलया ते क्रीणानि, कुष्टया ते क्रीणानि, शफेन ते क्रीणानि, पदा ते क्रीणानि ॥ (Mait. Samh. 3.7.7)<ref>Maitrayani Samhita ([https://sa.wikisource.org/wiki/%E0%A4%AE%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%AF%E0%A4%A3%E0%A5%80%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%82_%E0%A5%A9/%E0%A4%AA%E0%A5%8D%E0%A Kanda 3 Prapathaka 7])</ref></blockquote>Thus we see naming of fractions and operations like sum, subtractions and fractions were quite common at those times.<ref name=":3">Jayashankara, K. (2007) Ph. D. Thesis: ''Sulba sutra, A Critical Analysis.'' Mangalore University ([http://hdl.handle.net/10603/132298 Chapter 8] )</ref>
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=== Concentric Circles ===
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Evidence shows that the knowledge of geometry was developed during the vedic period itself. Mantras in Rigveda, for example in Mandala 1 (त्रय: पवयो मधुवाहने रथे । 34.2 and त्रिवन्धुरेण त्रिवृता रथेन त्रिचक्रेण सुवृता । 118.2) there is a mention of three (solid) wheeled, triangular, tricolumnar well-constructed chariot of Ashvini devatas on which they travel. At another instance a wheel formed of hub, spokes and metallic rim are also described. Thus we see that knowledge of construction of drawing concentric circles of desired diameters had developed in the Rigvedic period. The names of Rathakaras that occur in Rigveda are Bhrgu (एवेदिन्द्राय वृषभाय वृष्णे ब्रह्माकर्म भृगवो न रथम् । 4.16.20), Rbhus, Tvastr and others. In Yajurveda the rathakaras are given special importance for their skill.
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The knowledge of geometry is also evident from the preparedness to cover wells of different shapes and dimensions.<ref name=":3" />
    
== Components of Yajna Vedis ==
 
== Components of Yajna Vedis ==
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The chitis had rich symbolic significance and their designs were often intricate. For instance, the Syenacit has the shape of a falcon in flight (a symbolic representation of the aspiration of soaring upward); the Kurmachit is shaped as a tortoise, with extended head and legs, the rathacakracit as a chariot wheel with spokes, and so on.<ref>A. K. Dutta and M. S. Sriram. ''[https://pdfs.semanticscholar.org/bb84/9b5ff23bc22e2056f0aab069c92c05f7af0c.pdf Mathematics and Astronomy in India before 300 BCE.]'' </ref>
 
The chitis had rich symbolic significance and their designs were often intricate. For instance, the Syenacit has the shape of a falcon in flight (a symbolic representation of the aspiration of soaring upward); the Kurmachit is shaped as a tortoise, with extended head and legs, the rathacakracit as a chariot wheel with spokes, and so on.<ref>A. K. Dutta and M. S. Sriram. ''[https://pdfs.semanticscholar.org/bb84/9b5ff23bc22e2056f0aab069c92c05f7af0c.pdf Mathematics and Astronomy in India before 300 BCE.]'' </ref>
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Units and Measurements
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=== Units of Measurements ===
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The units of measurement occur commonly in the three vedas themselves; Angula, Gavyuti, Aratni, and Yojana are mentioned in Rigveda, Yojana in Yajurveda and Aratni and Vyama in Atharvaveda. However the length is not clearly mentioned in the samhitas.
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'Angula' seems to be the standard unit for measuring lengths of different vedis, whereas 'purusha' is the standard unit for measuring length of chitis like Syena and others. All other units are derived from Angula. Baudhayana Shulbasutras (1.3-4) while giving the names and definitions of different units begins with the definition of 'Angula'.<blockquote>अथाङ्गुलप्रमाणं चतुर्दशाणवः चतुस्त्रिंशत्तिलाः पृथु संश्लिष्टा इत्यपरम् । (Baud. Shul. Sutr. 1.3)<ref>Baudhayana Shulbasutras ([https://sa.wikisource.org/wiki/%E0%A4%AC%E0%A5%8C%E0%A4%A7%E0%A4%BE%E0%A4%AF%E0%A4%A8%E0%A4%B6%E0%A5%81%E0%A4%B2%E0%A5%8D%E0%A4%AC%E0%A4%B8%E0%A5%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%8D#%E0%A5%A7 Full text])</ref></blockquote>
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'''1 Angula (अङ्गुलम्) = 14 Grains of Anu or 34 grains of Tila'''
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'''1 Purusha (पुरुषः) = 121 Angulas'''
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{| class="wikitable"
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|+Derived Units of Measurement in Shulbasutras<ref>Jayashankara, K. (2007) Ph. D. Thesis: ''Sulba sutra, A Critical Analysis.'' Mangalore University ([https://shodhganga.inflibnet.ac.in/bitstream/10603/132298/10/10_chapter%204.pdf Chapter 3] )</ref>
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!Reference
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!Name
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!Measure
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|-
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|दशाङ्गुलं क्षुद्रपदम् ।
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|1 Kshudrapada
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|10 Angulas
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|-
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|द्वादश प्रादेशः ।
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|1 Pradesha
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|12 Angula
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|-
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| rowspan="2" |पृथोत्तरयुगेत्रयोदशिके।
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|1 Prth
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| rowspan="2" |13 Angula
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|-
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|1 Uttarayayuga
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|-
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|पदं पञ्चदश ।
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|1 Pada
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|15 Angula
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|-
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|द्विपदः प्रक्रमः ।
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|1 Prakrama (2 Padas)
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|30 Angula
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|-
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|द्वौ प्रादेशावरत्निः ।
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|1 Aratni (2 Pradesha)
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|24 Angula
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|-
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|द्वात्रिंश्ज्जानुः ।
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|1 Janu
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|32 Angula
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|-
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| rowspan="2" |षटि्त्रंशच्छम्याबाहू ।
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|1 Shamya
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| rowspan="2" |36 Angula
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|-
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|1 Bahu
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|-
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| rowspan="2" |पञ्चारत्निः पुरुषो व्यामश्च ।
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|1 Purusha (5 Aratni)
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| rowspan="2" |121 Angula
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|-
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|1 Vyama (5 Aratni)
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|-
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|चतुररत्निव्व्या यामः।
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|1 Yama
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|98 Angula
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|-
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|अष्टाशीतिशतमीषा ।
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|1 Isha
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|188 Angula
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|-
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|चतुःशतमक्षः ।
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|1 Aksha
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|104 Angula
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|-
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|षडशीतिर्युगम् ।
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|1 Yuga
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|86 Angula
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|}
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It should be remembered that the Shulbasutras of different Sutrakaras have slight variations thus we see versions of the above angula measures.
    
== Subject-matter of Shulbasutras ==
 
== Subject-matter of Shulbasutras ==
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