Narada Purana — Purva Bhaga, Shloka 45

Jyotiṣa-śāstra Saṅgraha: Threefold Division, Gaṇita Methods, Muhūrta, and Planetary Reckoning

Devanagari script

विंवरात्तत्कर्णपदं क्षेत्रे त्रिचतुरस्रके । राश्योरंतरवर्गेण द्विघ्ने घाते युते तयोः ॥ ४५ ॥

Transliteration

viṃvarāttatkarṇapadaṃ kṣetre tricaturasrake | rāśyoraṃtaravargeṇa dvighne ghāte yute tayoḥ || 45 ||

Translation

在三角形或四边形的区域中，与“迦尔那”(karṇa，斜线/对角)相应的量，当依“毗ṃ伐罗”(viṃvara)之法求得：取两分量之平方相加；并于需要时，以其差之平方乘二，成就所算之果。

Word by Word

• विंवरात्: from the circle/diagram (contextual technical term)
• विंवरात्: Apadana (अपादान)
• Type: Noun
• Root: विंवर (प्रातिपदिक)
• Form: नपुंसकलिङ्ग/पुंलिङ्ग (प्रयोगानुसार), पञ्चमी (5th case), एकवचन

• तत्: that
• तत्: Visheshana (विशेषण)
• Type: Adjective
• Root: तद् (सर्वनाम-प्रातिपदिक)
• Form: नपुंसकलिङ्ग, द्वितीया (2nd case), एकवचन; विशेषण (demonstrative)

• कर्ण-पदम्: the hypotenuse-term/diagonal value
• कर्ण-पदम्: Karma (कर्म)
• Type: Noun
• Root: कर्ण (प्रातिपदिक) + पद (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, द्वितीया (2nd case), एकवचन; समासः—तत्पुरुष

• क्षेत्रे: in the figure/field
• क्षेत्रे: Adhikarana (अधिकरण)
• Type: Noun
• Root: क्षेत्र (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, सप्तमी (7th case), एकवचन

• त्रि-चतुरस्रके: in the triangular/quadrilateral (three-/four-sided) figure
• त्रि-चतुरस्रके: Visheshana (विशेषण)
• Type: Adjective
• Root: त्रि (संख्या-प्रातिपदिक) + चतुरस्रक (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, सप्तमी (7th case), एकवचन; द्विगुसमास (numerical compound)

• राश्योः: of the two quantities
• राश्योः: Sambandha (सम्बन्ध/षष्ठी)
• Type: Noun
• Root: राशि (प्रातिपदिक)
• Form: पुंलिङ्ग, षष्ठी (6th case), द्विवचन

• अन्तर-वर्गेण: by the square of the difference
• अन्तर-वर्गेण: Karana (करण)
• Type: Noun
• Root: अन्तर (प्रातिपदिक) + वर्ग (प्रातिपदिक)
• Form: पुंलिङ्ग, तृतीया (3rd case), एकवचन; समासः—तत्पुरुष

• द्विघ्ने: in the doubled (quantity)
• द्विघ्ने: Visheshana (विशेषण)
• Type: Adjective
• Root: द्वि (संख्या-प्रातिपदिक) + घ्न (कृदन्त-प्रातिपदिक, हन् धातोः)
• Form: पुंलिङ्ग/नपुंसकलिङ्ग, सप्तमी (7th case), एकवचन; कृदन्त-विशेषण (multiplied by two)

• घाते: in the product/multiplication
• घाते: Adhikarana (अधिकरण)
• Type: Noun
• Root: घात (प्रातिपदिक)
• Form: पुंलिङ्ग, सप्तमी (7th case), एकवचन

• युते: when added/combined
• युते: Visheshana (विशेषण)
• Type: Adjective
• Root: युत (कृदन्त-प्रातिपदिक, युज् धातोः)
• Form: पुंलिङ्ग/नपुंसकलिङ्ग, सप्तमी (7th case), एकवचन; भूतकृदन्त (past participle)

• तयोः: of those two
• तयोः: Sambandha (सम्बन्ध/षष्ठी)
• Type: Noun
• Root: तद् (सर्वनाम-प्रातिपदिक)
• Form: पुं/नपुंसकलिङ्ग, षष्ठी (6th case), द्विवचन

Speaker

Sanatkumara (in instruction to Narada, within Vedanga/technical exposition embedded in Moksha Dharma context)

Vrata Kalpa

Vrata: none

Verse Rasa

Primary Rasa: shanta

Secondary Rasa: adbhuta

FAQs

What is the spiritual significance of this verse in Narada Purana?

It highlights that Dharma is supported by precision: correct measurement and right procedure safeguard the integrity of sacred works, aligning practical action with higher order.

How does this verse explain the path of devotion (Bhakti)?

Indirectly: it teaches that devotion is not only emotion but also disciplined correctness in actions done for sacred purposes—careful execution becomes an offering.

What practical Vedic knowledge (Vedanga) is highlighted here?

A Śulba/gaṇita-style rule for computing a diagonal (karṇa) in triangular or quadrilateral plots using squares, sums, and (in some cases) twice the square of the difference—useful for altar/field layouts.