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ब्राह्...
ब्राह्मस्फुट सिद्धान्त (Brahmasphuta Theory)
गणित एवं कुट्टक गणित (अंकगणित, ज्यामिति एवं बीजगणित (Mathematics and Kuttaka Mathematics (Arithmetic, Geometry and Algebra) by: Kedar Nath Shukla₹288.00
ISBN: 9788124612965
Year Of Publication: 2024
Edition: 1 st
Pages : viii,162
Bibliographic Details : Bibliography; Index
Language : Hindi
Binding : Paperback
Publisher: D.K. Printworld Pvt. Ltd.
Size: 21 cm
Weight: 260
ब्राह्मस्फुट सिद्धान्त भारत के महान् ज्योतिर्विद् एवम् गणितज्ञ, आचार्य ब्रह्मगुप्त की सातवीं शताब्दी की प्रथम रचना है। आर्य छन्दों में वर्णित ब्राह्मस्फुट सिद्धान्त के दो अध्याय (18 एवं 24) गणित एवं कुट्टक गणित के सूाें को स्थापित करते हैं। गणित की संख्या प्रणाली में ब्रह्मगुप्त का योगदान अद्वितीय है। किसी संख्या को उसी से घटाने पर शून्य प्राप्त होता है। शून्य की इस अवधारणा के साथ उन्होंने धनात्मक, ऋणात्मक एवं शून्य, इन तीनों प्रकार की संख्याओं के साथ गणितीय संक्रियायों (परिक्रम) की व्याख्या की है। आज की मान्यता के विपरीत उनका मानना था कि शून्य से शून्य को विभाजित करने पर शून्य प्राप्त होता है। गणितीय अध्याय में आचार्य ने बीस गणितीय संक्रियाओं (परिक्रम), यथा संकलित (योग) आदि एवं छाया की माप जैसे नित्य-प्रति के आठ व्यवहारों का उल्लेख किया है। तत्कालीन आवश्यकता के अनुरूप आचार्य ने मिश्रक, श्रेढ़ी, क्षेम् (ज्यामिति), चिति, क्राकचिक (काष्ठकला), राशि (अनाज का ढेर), छाया से सम्बन्धित 8 व्यवहार गणित के सू स्थापित किए। मिश्रक में वर्णित मिश्रधन से ब्याज की गणना हेतु वर्ग समीकरण के हल की विधि पहली बार स्पष्ट की गई है। ब्रह्मगुप्त ने समानान्तर, ज्यामितीय श्रेणियों, प्राकृत संख्याओं एवं उनके वर्गों तथा घनों के n पदों के योग का सू स्थापित किया है। कुट्टक गणित (बीजगणित) में रैखिक अनिर्धार्य समीकरणों, ax−by = c का हल प्रस्तुत है। ब्रह्मगुप्त ने द्विघातीय अनिर्धार्य समीकरणों, Nx2 + 1 = y2 के हल की विधि भी प्रस्तुत की है।
प्राक्कथन v
भूमिका 1
ब्राह्मस्फुटसिद्धान्तो गणिताध्याय:
अध्याय 1: गणित
अंकगणित 11
व्यवहारः (निर्धारण) — व्यवहार गणित 42
श्रेढीव्यवहार: (श्रेढी व्यवहार : समानान्तर एवम् ज्यामितीय श्रेणियाँ) 50
क्षेत्रव्यवहार: (ज्यामिति) 58
वृत्तक्षेत्रगणितम् (वृत्त) 75
खात व्यवहार: (उत्खनन) 79
चितिव्यवहार: (चिति व्यवहार) 82
क्राकचिक व्यवहार: (काष्ठकला) 83
राशिव्यवहार: (राशिव्यवहार) 85
छायाव्यवहार: (छाया गणित) 87
गुणन विधि 90
श्रीब्राह्मस्फुटसिद्धान्तो कुट्टकाध्याय:
अध्याय 2: बीजगणित
कुट्टक गणित 101
धन, ऋण राशियों और शून्य के योग के सूत्र 113
अथैकवर्ण समीकरण बीजम् (अज्ञात पदाें के समीकरण) 119
भावितबीजम् (अज्ञात राशियों के गुणनफल से युक्त समीकरण) 128
वर्ग प्रकृति: (अनिर्धार्य वर्ग समीकरण) 131
सन्दर्भ-ग्रन्थ/लेख सूची 151
श्लाेकानुक्रमणिका 153
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