Guest guest Posted April 25, 2003 Report Share Posted April 25, 2003 Positive and Negative numbers and their calculations > > Compiled by > Indian Institute of Scientific Heritage > Ushus, Estate Road, Pappanamcode, > Thiruvananthapuram, 695 018, Kerala,India. > > Ph. 0471-490149, www.iish.org > > > In ancient India knowledge of fundamental rules on > +ve and -ve numbers were at par with that of present > day. Brahmagupta and Bhaskaracharya-II have given > these aspects as early as 6th century AD. > > > > Brahmagupta has given 3 rules on +ve and -ve numbers > in Brahmasphuta Siddhanta. > > > > "Runamrunayordhanayorghatho > > Dhanamrunayordhanavadho dhanam bhavati". > > > > When two -ve numbers are multiplied , the resulting > number is +ve. When +ve and -ve numbers are > multiplied the result is -ve. When two +ve numbers > are multiplied the result is +ve. > > > > Sripathi(1039 AD) in Siddhanta Sekhara(14-6) gives > explanation for the operation with zero as follows. > > "Nothing happens to the +ve or -ve number when it is > added with 0.When +ve and -ve numbers are subtracted > from 0, the +ve numbers become -ve and -ve numbers > become +ve. When multiplied with zero, the values of > both +ve and -ve numbers become 0.When divided by > zero it becomes infinity." > > > > Later in 1150 AD BhaskaracharyaII has given the > rules for +ve and - ve in Beejaganitham which is a > chapter incorporated in his famous astronomical > treatise Siddhanta Siromani. > > > > Rule 1.2 > > Swayorasvayo: swam vadha: swarunaghate Kshaya: > > > > Among +ve and - ve numbers when multiplied each > other ,the result is -ve. > > > > Rule 2.2 > > Dhanam dhanenarnamrunena nighnam dvayam dhanam > > > When +ve number is multiplied with a +ve number and > -ve number with a -ve number the results are +ve > numbers. > > > > Rule3.2 > > Bhaajya bhaajakayorubhayorapi > > Dhanathve runathve kalabdhirdhanameva > > > > When +ve and - ve numbers are divided among > themselves the results are +ve. > > > > Bhaskaracharya had, not only given the calculations > with +ve and - ve numbers among themselves, but also > had given rules for determining the squares and > square roots of +ve and - ve numbers. > > > > Rule 1.4 > > Kruthisvaraunayo: swam swamoole dhanarne > > na moolakshayasyaasthi thasyaakruthithwaath > > > > For +ve and - ve numbers square is always +ve. > Because of the nature of the -ve numbers there is no > square root for _ve numbers. > > > > Please send this document to everyone you know. > Remember, it is your, mine and our duty, privilege > and responsibility to learn, teach and spread our > Heritage. > > > > Compiled by > Indian Institute of Scientific Heritage > Ushus, Estate Road, Pappanamcode, > Thiruvananthapuram, 695 018, Kerala,India. > > Ph. 0471-490149, www.iish.org > > > > > The New Search - Faster. Easier. Bingo http://search. Quote Link to comment Share on other sites More sharing options...
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