Wednesday, April 16, 2014

Basic mathematical operations in Sanskrit


|| संस्कृतम ||


|| संस्कृत अध्ययन कार्ये स्वागतम् अस्तु ||

Welcome to learning learning Sanskrit



|| Sanskrit_Adhyayan || Sanskrit_Sanskruti || Bharatiya_Knowledge_Traditions || Sanskrit_Jagruti ||




सरल गणित-प्रक्रिया: -



१. योगे युति: स्यात् क्षययो: स्वयोर्वा धनर्णयोरन्तरमेवयोग:||



अन्वय - क्षययो: (राश्यो: -,-) योगे युति: स्यात्, (एवं) स्वयो: (+,+) (राश्यो: योगे युति:) वा| धन (+) ऋणयो: (-)

अन्तरं एव योग: स्यात्|



Meaning : Two positive or negative numbers will be added together but positive and negative number's difference is their addition.

Explanation : This algorithm explains very basic rule of addition of signed integers.



२. स्वयोरस्वयो स्‍वम् वध: स्वर्णघाते|

क्षयो भागहारे अपि चैवम् निरुक्तम्||



अन्वय - स्वयो: (+*+), अस्वयो: (-*-) वध: स्वम् (+) (भवति|) स्व-ऋण-घाते (+*-)

वध: क्षय: (-) (भवति)| भागहारे (/) अपि च एवम् निरुक्तम्|



Meaning : Multiplication of two positive or negative numbers is positive. Multiplication of positive and negative number is negative. Same in case of division.

Explanation : This algorithm explains rule for multiplication and division of signed integers.



३. योगान्तरं तेषु समानजात्योर्विभिन्नजात्योश्च पृथक् स्थितिश्च||



अन्वय - तेषु (अव्यक्तयोगान्तरेषु) समानजात्यो: योग: अन्तरं च (भवति) विभिन्नजात्यो: पृथक् स्थिति: च

(भवति)|



Meaning : (In case of variables' adition/subtraction) Their similar terms are added and subtracted, different terms remain separate.

Explanation : For example, in following addition of variables -

5a+3b+4c+7a+2b-c-2a+2c

adding/subtracting similar terms, it will give this result -

(5a+7a-2a)+(3b+2b)+(4c-c+2c) = 10a+5b+5c



४. अस्मिन् विकार: खहरे न राशावपि प्रविष्टेष्वपि निसृतेषु|

बहुष्वपिस्याल्लयसृष्टिकाले अनन्ते अच्युते भूतगणेषु यद्वद||



अन्वय - अस्मिन् खहरे राशौ बहुषु प्रविष्टेषु अपि (अथवा राशौ) निसृतेषु अपि विकार: न स्यात्|

यद्वत् सृष्टिलयकाले बहुषु अपि भूतगणेषु अनन्ते अच्युते (प्रविष्टेषु) विकार: न स्यात्|



Meaning : This infinite number does not change even after adding or subtracting any number from it. Like, the 'Brahmanda' (universe) is not altered when at the end of the world, many lives enter into it.

Explanation : This algorithm explains the concept of Infinity.