anyonya hārābhihata

 Anyonya hārābhihata means “mutually multiplied by their denominators,” a technical Sanskrit term used in mathematics for reducing two fractions to a common denominator.

Core meaning

The expression appears in Sanskrit mathematical terminology as anyonyahārābhihata (अन्योन्यहाराभिहत), defined as:

• “(two quantities) mutually multiplied by their denominators”

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This describes the standard arithmetic procedure in which, to compare or combine two fractions, each numerator and denominator is multiplied by the other fraction’s denominator.

Breakdown of the compound

• anyonya — “mutual, reciprocal”

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• hāra — “denominator”
• abhihata — “struck, multiplied”
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Thus the compound literally means:
“struck/multiplied reciprocally by (each other’s) denominators.”

Technical explanation

The dictionary gives an example of its use:

• anyonya-hārābhihatau harāṃśau rāśyoḥ samacchedavidhānam evam —
  “The denominator and numerator of two quantities, being reciprocally multiplied by their denominators, are thus reduced to the same denominator.”

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In modern mathematical terms, this is the process of obtaining a common denominator for two fractions:

$\frac{a}{b}\text{and}\frac{c}{d}$

become

$\frac{a\cdot d}{b\cdot d}\text{and}\frac{c\cdot b}{d\cdot b}$

Relation to anyonya

The base word anyonya (“mutual, reciprocal”) is widely used in Sanskrit literature, philosophy, and poetics to indicate reciprocal action or relationship

Wisdom Library

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In anyonya hārābhihata, it specifically describes the reciprocal multiplication of denominators.

Summary

• anyonya hārābhihata = “reciprocally multiplied by the denominators”
• A mathematical term used when reducing fractions to a common denominator
• Built from anyonya (mutual) + hāra (denominator) + abhihata (multiplied)