________________
REFERENCES AND NOTES 1. Smith, p.522.
Did the Jaina school of Indian mathematics use any name for 'index'? To reply this, the present author has found a clue. He proposes to study that clue in his future paper. 2. Singh, A.N., p.7.
The Egyptians often multiplied by continued doubling. So, to multiply 27 by 13, they would proceed thus -
27
2 4 8
54 108 216
AA
Since 13 = 8 + 4 + 1, the result is obtained by adding the marked numbers in the second column.
13351
Ct. Heath, pp.52-53, Hollongdale, pp.2-3 and Smith, p.34. 3. This is conceived according to the Sand Reckoner (Arenarius or Psammites) which
is an essay addressed by Archimedes to Gelon, King of Syracuse (now in Italy). In it, he made a plan to express very large numbers. His plan involved the counting
by octads (10") in which he proceeded as far as 1062 4. Gss, v.2.94 first half, p.29.
समदल विषमखरूपो गुणगुणितो वर्ग ताडितो गच्छः । vide also: PG,v.94, .134, example 108, p.134 and English Translation, pp.76-77 विषमे पदे निरेके गुणं समेऽर्धीकृते कृति न्यस्य। क्रमशो रुपस्योत्क्रमशो गुणकृतिफलमादिना गुणयेत्।। 94।। रूपत्रयं गृहीत्वा लाभार्थं निर्गतो वणिक कश्चित्। प्रतिमासं द्विगुणधनं तस्य भवेत् किं त्रिभिवषैः ।। 108 ।।
5. Sastri [1987] w.8.28-32, p.12.
द्विरद्धे।।2811 रूपे शून्यम्।। 29॥ द्वि शून्ये||3011 तावदः तद्गुणितम्।। 31।। द्वियनं तदन्तानाम्।। 32॥ 6. DVL - III, pp.19-21.
जहण्णमणताणत विरलेऊण एक्केक्कस्स रूवस्स जहण्णमणताणतं दाऊण वगिदसंवाग्गिदं काऊणुप्पण्णमहारासिं दप्पडिरासिं काऊण तथ्थेक्करासिं विरलेऊण अवरं महारासिपमाणं रूवं पडि दाऊण वगिदसंवम्गिद काऊण पुणो वि उद्विदमहारासिं दुप्पडिरासिं काऊण तत्थेक्करासिपमाणं विरलेऊण अवरमहारासिं विरलणरासिरूवं
पडि दाऊण अण्णोण्णब्भासे कदे तिण्णिवारं वग्गिदसंवग्गिदरासीणाम 7. Singh, A.N., p.7. For histroy of mediation', vide Smith, pp.34-35. 8. The fact that an index is simply a logarithm was known to the Jaina school of
Indian mathematics will be corroborated in the paper mentioned in ref. 1. प्राप्त : 15.11.02
Arhat Vacana, 15(4), 2003
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