Narada Purana — Purva Bhaga, Shloka 110

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

Devanagari script

तद्बाहुफलवर्गैक्यान्मूलं कर्णश्चलाभिधः । त्रिज्याभघ्यस्तं भुजफलं पलकर्णविभाजितम् ॥ ११० ॥

Transliteration

tadbāhuphalavargaikyānmūlaṃ karṇaścalābhidhaḥ | trijyābhaghyastaṃ bhujaphalaṃ palakarṇavibhājitam || 110 ||

Translation

The square root of the sum of the squares of those two side-results is called the hypotenuse (karṇa), also termed calā. The desired side-result (bhujaphala) is obtained by multiplying by the radius (trijyā) and then dividing by the hypotenuse (here called pala-karṇa).

Word by Word

• तत्-बाहु-फल-वर्ग-ऐक्यात्: from the sum/unity of the square of that sine-value
• तत्-बाहु-फल-वर्ग-ऐक्यात्: अपादान (Source/Ablative/अपादान)
• Type: Noun
• Root: तत् (सर्वनाम-प्रातिपदिक) + बाहु (प्रातिपदिक) + फल (प्रातिपदिक) + वर्ग (प्रातिपदिक) + ऐक्य (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, पञ्चमी एकवचन; समासः (बहुपद-तत्पुरुष): ‘तत् बाहुफलस्य वर्गस्य ऐक्यात्’ = from the unity/sum of the square of that sine-value; अपादानार्थे (ablative)

• मूलम्: the square root
• मूलम्: कर्म (Object/कर्म)
• Type: Noun
• Root: मूल (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन

• कर्णः: the hypotenuse (karṇa)
• कर्णः: कर्ता (Subject/कर्ता)
• Type: Noun
• Root: कर्ण (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रथमा एकवचन

• चल-अभिधः: called ‘cala’
• चल-अभिधः: विशेषण (Adjectival modifier/विशेषण)
• Type: Adjective
• Root: चल (प्रातिपदिक) + अभिध (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रथमा एकवचन; तत्पुरुष: ‘चल इति अभिधीयते’ = called ‘cala’; विशेषणम्

• त्रिज्या-अभ-घ्यस्तम्: multiplied by the radius
• त्रिज्या-अभ-घ्यस्तम्: विशेषण (Adjectival modifier/विशेषण)
• Type: Adjective
• Root: त्रिज्या (प्रातिपदिक) + अभ (प्रातिपदिक/उपसर्गवत्) + घ्यस्त (कृदन्त; √घस्/√हन्? पाठभेद; here intended ‘अभ्यस्त’ = multiplied)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन; पाठभेदः ‘अभघ्यस्त’ सम्भवतः ‘अभ्यस्त’; अर्थतः ‘त्रिज्यया अभ्यस्तम्’ = multiplied by radius; विशेषणम्

• भुज-फलम्: sine value
• भुज-फलम्: कर्म (Object/कर्म)
• Type: Noun
• Root: भुज (प्रातिपदिक) + फल (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन; षष्ठी-तत्पुरुष

• पल-कर्ण-विभाजितम्: divided by palakarṇa
• पल-कर्ण-विभाजितम्: विशेषण (Adjectival modifier/विशेषण)
• Type: Adjective
• Root: पल (प्रातिपदिक) + कर्ण (प्रातिपदिक) + विभाजित (कृदन्त; √भज् धातु)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन; कृदन्त-भूतकृदन्त (PPP) ‘विभाजित’ = divided; तत्पुरुष: ‘पलकर्णेन विभाजितम्’ = divided by palakarṇa; विशेषणम्

Speaker

Sanatkumara (teaching Narada in a technical passage)

Vrata Kalpa

Vrata: none

Verse Rasa

Primary Rasa: shanta

Secondary Rasa: none

Characters & Entities

• Narada
• Sanatkumara

FAQs

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

It shows that Moksha Dharma is supported by disciplined śāstric knowledge—precise calculation and right understanding (pramāṇa) are treated as aids to clarity, which ultimately supports dharma and inner steadiness.

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

Indirectly: by valuing exact śāstra-based methods used in dharma (such as timing and measurement), it supports orderly practice; such orderliness becomes a practical support for steady Vishnu-bhakti rather than replacing devotion itself.

What practical Vedic knowledge (Vedanga) is highlighted here?

Vedāṅga Jyotiṣa/gaṇita-style computation: a rule akin to the Pythagorean relation for determining the karṇa (hypotenuse) and deriving a side value via multiplication by trijyā (radius) and division by the computed karṇa.