From Wikipedia, the free encyclopedia
The
Br?hma-sphu?a-siddh?nta
("Correctly Established
Doctrine
of
Brahma
", abbreviated BSS)
is a main work of
Brahmagupta
, written c. 628.
[1]
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).
[2]
[3]
Positive and negative numbers
[
edit
]
Br?hmasphu?asiddh?nta
is one of the first books to provide concrete ideas on
positive numbers
,
negative numbers
, and zero.
[4]
For example, it notes that the sum of a positive number and a negative number is their difference or, if they are equal, zero; that subtracting a negative number is equivalent to adding a positive number; that the product of two negative numbers is positive. Some of the notions of fractions differ from the modern
rational number
system. For example, Brahmagupta allows
division by zero
resulting in a fraction with a
0
in the denominator, and defines
0/0 = 0
. In modern mathematics, division by zero is undefined for any
field
.
[5]
Influence
[
edit
]
Ashadhara, the son of Rihluka, wrote
Graha-jnana
with tables based on
Brahma-sphuta-siddhanta
in 1132. This work is also known by the names
Graha-ganita
,
Brahma-tulyanayana
,
Bhaumadi-panchagraha-nayana
,
Kshanika-grahanayana
, or simply
Ashadhara
. Harihara wrote an extended version of the
Graha-jnana
around 1575 CE.
[6]
References
[
edit
]
- ^
"Brahmagupta | Indian astronomer"
.
Encyclopedia Britannica
.
- ^
Bradley, Michael.
The Birth of Mathematics: Ancient Times to 1300
, p. 86 (Infobase Publishing 2006).
- ^
Mackenzie, Dana.
The Universe in Zero Words: The Story of Mathematics as Told through Equations
, p. 61 (Princeton University Press, 2012).
- ^
Henry Thomas Colebrooke
.
Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bhascara
, London 1817, p. 339 (
online
)
- ^
Kaplan, Robert (1999).
The Nothing that is: A Natural History of Zero
. New York: Oxford University Press. pp.
68?75
.
ISBN
0-19-514237-3
.
- ^
David Pingree
, ed. (1970).
Census of the Exact Sciences in Sanskrit Series A
. Vol. 1. American Philosophical Society. p. 54.
External links
[
edit
]
Sanskrit
Wikisource
has original text related to this article:
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