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Brāhmasphuṭasiddhānta
The ''Brāhma-sphuṭa-siddhānta'' ("Correctly Established Doctrine of Brahma", abbreviated BSS) is a main work of Brahmagupta, written c. 628. This text of mathematical astronomy contains significant mathematical content, including the first good understanding of the role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and Brahmagupta theorem. The book was written completely in verse and does not contain any kind of mathematical notation. Nevertheless, it contained the first clear description of the quadratic formula (the solution of the quadratic equation).Bradley, Michael. ''The Birth of Mathematics: Ancient Times to 1300'', p. 86 (Infobase Publishing 2006). Positive and negative numbers ''Brāhmasphuṭasiddhānta'' is one of the first books to provide concrete ideas on positive numbers, negative numbers, and zer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brahmagupta
Brahmagupta ( – ) was an Indian Indian mathematics, mathematician and Indian astronomy, astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established Siddhanta, doctrine of Brahma", dated 628), a theoretical treatise, and the ''Khandakhadyaka'' ("edible bite", dated 665), a more practical text. In 628 CE, Brahmagupta first described gravity as an attractive force, and used the term "gurutvākarṣaṇam (गुरुत्वाकर्षणम्)" in Sanskrit to describe it. He is also credited with the first clear description of the quadratic formula (the solution of the quadratic equation)Bradley, Michael. ''The Birth of Mathematics: Ancient Times to 1300'', p. 86 (Infobase Publishing 2006) in his main work, the ''Brāhma-sphuṭa-siddhānta''. Life and career Brahmagupta, according to his own statement, was born in 598 CE. Born in ''Bhillamāla'' in Gurjaradesa (modern Bhinmal in Rajasthan, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equation
In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where the variable (mathematics), variable represents an unknown number, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant coefficient'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the quadratic function on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Formula
In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations, such as completing the square, yield the same solutions. Given a general quadratic equation of the form , with representing an unknown, and coefficients , , and representing known real number, real or complex number, complex numbers with , the values of satisfying the equation, called the Zero of a function, ''roots'' or ''zeros'', can be found using the quadratic formula, x = \frac, where the plus–minus sign, plus–minus symbol "" indicates that the equation has two roots. Written separately, these are: x_1 = \frac, \qquad x_2 = \frac. The quantity is known as the discriminant of the quadratic equation. If the coefficients , , and are real numbers then when , the equation has two distinct real number, real roots; when , the equation has one repeated root, repeated real root; and when , the equation h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero
0 (zero) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently division by zero has no meaning in arithmetic. As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya. Common name ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Division By Zero
In mathematics, division by zero, division (mathematics), division where the divisor (denominator) is 0, zero, is a unique and problematic special case. Using fraction notation, the general example can be written as \tfrac a0, where a is the dividend (numerator). The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplication, multiplied by the divisor. That is, c = \tfrac ab is equivalent to c \cdot b = a. By this definition, the quotient q = \tfrac is nonsensical, as the product q \cdot 0 is always 0 rather than some other number a. Following the ordinary rules of elementary algebra while allowing division by zero can create a mathematical fallacy, a subtle mistake leading to absurd results. To prevent this, the arithmetic of real numbers and more general numerical structures called field (mathematics), fields leaves division by zero undefined (mathematics), undefined, and situations where division by zero might occur m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Thomas Colebrooke
Henry Thomas Colebrooke FRS FRSE FLS (15 June 1765 – 10 March 1837) was an English orientalist and botanist. He has been described as "the first great Sanskrit scholar in Europe". Biography Henry Thomas Colebrooke was born on 15 June 1765. His parents were Sir George Colebrooke, 2nd Baronet, MP for Arundel and Chairman of the East India Company from 1769, and Mary Gaynor, daughter and heir of Patrick Gaynor of Antigua. He was educated at home, and from the age of twelve to sixteen he lived in France. In 1782 Colebrooke was appointed through his father's influence to a writership with the East India Company in Calcutta. In 1786 and three years later he was appointed assistant collector in the revenue department at Tirhut. He wrote ''Remarks on the Husbandry and Commerce of Bengal'', which was privately published in 1795, by which time he had transferred to Purnia. This opposed the East India Company's monopoly on Indian trade, advocating instead for free trade be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Treatises
A treatise is a Formality, formal and systematic written discourse on some subject concerned with investigating or exposing the main principles of the subject and its conclusions."mwod:treatise, Treatise." Merriam-Webster Online Dictionary. Accessed September 12, 2020. A ''monograph'' is a treatise on a specialized topic. Etymology The word "treatise" has its origins in the early 14th century, derived from the Anglo-French term ''tretiz'', which itself comes from the Old French ''traitis'', meaning "treatise" or "account." This Old French term is rooted in the verb ''traitier'', which means "to deal with" or "to set forth in speech or writing". The etymological lineage can be traced further back to the Latin word ''tractatus'', which is a form of the verb ''tractare'', meaning "to handle," "to manage," or "to deal with". The Latin roots suggest a connotation of engaging with or discussing a subject in depth, which aligns with the modern understanding of a treatise as a formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Algebra
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers, which is not an algebraic property). This article describes the history of the theory of equations, referred to in this article as "algebra", from the origins to the emergence of algebra as a separate area of mathematics. Etymology The word "algebra" is derived from the Arabic language, Arabic word , and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Muhammad ibn Musa al-Khwarizmi, Al-Khwārizmī, whose Arabic title, ''Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala'', can be translated as Al-Jab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
7th-century Manuscripts
The 7th century is the period from 601 through 700 in accordance with the Julian calendar in the Christian Era. The spread of Islam and the Muslim conquests began with the unification of Arabia by the Islamic prophet Muhammad starting in 622. After Muhammad's death in 632, Islam expanded beyond the Arabian Peninsula under the Rashidun Caliphate (632–661) and the Umayyad Caliphate (661–750). The Muslim conquest of Persia in the 7th century led to the downfall of the Sasanian Empire. Also conquered during the 7th century were Syria, Palestine, Armenia, Egypt, and North Africa. The Byzantine Empire suffered setbacks during the rapid expansion of the Caliphate and a mass incursion of Slavs in the Balkans which reduced its territorial limits. The decisive victory at the Siege of Constantinople in the 670s led the empire to retain Asia Minor, which ensured the existence of the empire. In the Iberian Peninsula, the 7th century was known as the ''Siglo de Concilios'' (century o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
7th-century Sanskrit Literature
The 7th century is the period from 601 through 700 in accordance with the Julian calendar in the Christian Era. The spread of Islam and the Early Muslim conquests, Muslim conquests began with the unification of Arabia by the Islamic prophet Muhammad starting in 622. After Muhammad's death in 632, Islam expanded beyond the Arabian Peninsula under the Rashidun Caliphate (632–661) and the Umayyad Caliphate (661–750). The Muslim conquest of Persia in the 7th century led to the downfall of the Sasanian Empire. Also conquered during the 7th century were Muslim conquest of Syria, Syria, Palestine (region), Palestine, Muslim conquest of Armenia, Armenia, Muslim conquest of Egypt, Egypt, and Muslim conquest of the Maghreb, North Africa. The Byzantine Empire suffered setbacks during the rapid expansion of the Caliphate and a mass incursion of Slavs in the Balkans which reduced its territorial limits. The decisive victory at the Siege of Constantinople (674–678), Siege of Constantin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava of Sangamagrama, Madhava. The Decimal, decimal number system in use today: "The measure of the genius of Indian civilisation, to which we owe our modern (number) system, is all the greater in that it was the only one in all history to have achieved this triumph. Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat. But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own." was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of 0 (number), ze ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GRETIL
The Göttingen Register of Electronic Texts in Indian Languages (GRETIL) is a comprehensive repository of e-texts in Sanskrit and other Indian languages. It contains several texts related to Indology Indology, also known as South Asian studies, is the academic study of the history and cultures, languages, and literature of the Indian subcontinent, and as such is a subset of Asian studies. The term ''Indology'' (in German, ''Indologie'') is ..., such as philosophical texts. Rather than scanned books or typeset PDF files, these texts are in plain text, in a variety of encodings, and are machine-readable, so that (for instance) word search can be performed on them. It was started by Reinhold Grünendahl, with the intention of being a "cumulative register of the numerous download sites for electronic texts in Indian languages". It is used by many scholars; for instance David Smith writes: "Sanskritists are enormously indebted to this incomparably useful site and to those who have co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
