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Geometry According to Sulba Sutra
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Geometry According to Sulba Sutra
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Preface

 

In the following pages, information about the state of knowledge of geometry at the Srautasutra pariod (B. C. 700 to B. C. 200) is presented. A chapter on knowledge of geometry of the people of Indus Civilization is included as a historical background. Every Srautasutra of Yajurveda recension has an appendix or a question, generally dealt with as a last part of it, called Sulbasutra. These Sulbasutras give information on the methods of layout of different parts, like vedi, citi, mandapa and others, which are required for performing different sacrifical rituals. In order to obtain layouts of these vedis accurately, the science of geometry was developed. There is every likelihood that this geometrical knowledge was developed at the time of Brahmanas and found expression at the time of Srauta-sutras. Sulbasutra is not a book of geometry and the information of geometry given in it is limited as a utilitarian material for the accurate layout of vedis etc. It is, therefore, obvious that the Sulbasutrakaras had given only the necessary formulae and statements of theorems and not the derivations or proofs of them. The proofs and derivations as might have been arrived at by them for these theorems, formulae etc., as given in Sulbasutras is a conjectural part of this study. Many a mathematician has tried to give these derivations and proofs, I have assimilated almost all of these and added my own little contribution.

 

When I have started studying different Sulbasutras I have approached Prof. C. G. Kashikar, Editor, Sanskrit dictionary section, Deccan College, Poona, the authority on this subject, for solving the difficulties. I am grateful to him for his continuous encouragement and advice given by him through out the preparation. I am thankful to Prof. A. M. Ghatge, Director, Deccan College, Postgraudate and Research Institute, Pune, tor giving all the library facilities. I also wish to thank Prof. R. N. Dandekar, and University of Poona for giving me the research grant and for giving permission to ,publish the report. My thanks are also due to the Editor, Indian Journal of History of Science, Calcutta, for allowing me to reproduce my two papers, which are included as Chapter one and part of Chapter eleven.

 

I wish to thank Dr. T. N. Dharmadhikari and Mrs., N. M. Dhadphale, for taking pains for faultless printing of this book. I also thank the Secretary Shri H. N. Joshi, and the Executive Council of the Vaidika Samsodhana Mandala for accepting this dissertation as the publication of the Mandala

 

Contents

 

 

Preface

 

1.

Geometry. as known to the people of Indus Civilization

1

2.

Geometry as known before Sulba-sutras

9

3.

The arithmetic back ground of geometry of Sulba-sutras

19

4.

Units of length measures according to Sulba-sutras

30

5.

Constructions given in Sulba-sutras

39.

6.

Area and volume of rectilinear figures and circle as given in Sulba-sutras

68

7.

Calculations for the location of Daksinagni

74

8.

Similar figures

19

9.

The theorem of the squre of the Diagonal

85

10.

Rational right angle triangles

91

11.

Derivation of formulae for the magnitude of ⱱ2 and π

99

12.

Summary and Conclusions

119

Appendix I :

Geometrical terms:-

 

 

from literature before Srauta Sutra period

121

 

in Baudhayana Sulba Sutra

121

 

in Apastamba Sulba Sutra

126

 

in Mauava Sulba Sutra

126

II :

Requirements of bircks of different fire. altars according to Baudhayana Sulba Sutra

127

 

References

137

 

Sample Page


Geometry According to Sulba Sutra

Item Code:
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1983
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Preface

 

In the following pages, information about the state of knowledge of geometry at the Srautasutra pariod (B. C. 700 to B. C. 200) is presented. A chapter on knowledge of geometry of the people of Indus Civilization is included as a historical background. Every Srautasutra of Yajurveda recension has an appendix or a question, generally dealt with as a last part of it, called Sulbasutra. These Sulbasutras give information on the methods of layout of different parts, like vedi, citi, mandapa and others, which are required for performing different sacrifical rituals. In order to obtain layouts of these vedis accurately, the science of geometry was developed. There is every likelihood that this geometrical knowledge was developed at the time of Brahmanas and found expression at the time of Srauta-sutras. Sulbasutra is not a book of geometry and the information of geometry given in it is limited as a utilitarian material for the accurate layout of vedis etc. It is, therefore, obvious that the Sulbasutrakaras had given only the necessary formulae and statements of theorems and not the derivations or proofs of them. The proofs and derivations as might have been arrived at by them for these theorems, formulae etc., as given in Sulbasutras is a conjectural part of this study. Many a mathematician has tried to give these derivations and proofs, I have assimilated almost all of these and added my own little contribution.

 

When I have started studying different Sulbasutras I have approached Prof. C. G. Kashikar, Editor, Sanskrit dictionary section, Deccan College, Poona, the authority on this subject, for solving the difficulties. I am grateful to him for his continuous encouragement and advice given by him through out the preparation. I am thankful to Prof. A. M. Ghatge, Director, Deccan College, Postgraudate and Research Institute, Pune, tor giving all the library facilities. I also wish to thank Prof. R. N. Dandekar, and University of Poona for giving me the research grant and for giving permission to ,publish the report. My thanks are also due to the Editor, Indian Journal of History of Science, Calcutta, for allowing me to reproduce my two papers, which are included as Chapter one and part of Chapter eleven.

 

I wish to thank Dr. T. N. Dharmadhikari and Mrs., N. M. Dhadphale, for taking pains for faultless printing of this book. I also thank the Secretary Shri H. N. Joshi, and the Executive Council of the Vaidika Samsodhana Mandala for accepting this dissertation as the publication of the Mandala

 

Contents

 

 

Preface

 

1.

Geometry. as known to the people of Indus Civilization

1

2.

Geometry as known before Sulba-sutras

9

3.

The arithmetic back ground of geometry of Sulba-sutras

19

4.

Units of length measures according to Sulba-sutras

30

5.

Constructions given in Sulba-sutras

39.

6.

Area and volume of rectilinear figures and circle as given in Sulba-sutras

68

7.

Calculations for the location of Daksinagni

74

8.

Similar figures

19

9.

The theorem of the squre of the Diagonal

85

10.

Rational right angle triangles

91

11.

Derivation of formulae for the magnitude of ⱱ2 and π

99

12.

Summary and Conclusions

119

Appendix I :

Geometrical terms:-

 

 

from literature before Srauta Sutra period

121

 

in Baudhayana Sulba Sutra

121

 

in Apastamba Sulba Sutra

126

 

in Mauava Sulba Sutra

126

II :

Requirements of bircks of different fire. altars according to Baudhayana Sulba Sutra

127

 

References

137

 

Sample Page


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