Narada Purana — Purva Bhaga, Shloka 106

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

Devanagari script

युग्मवृत्तेधनर्णश्यादोजादूनेऽधिके स्फुटम् । तद्गुणे भुजकोटिज्येभगणांशविभाजिते ॥ १०६ ॥

Transliteration

yugmavṛttedhanarṇaśyādojādūne'dhike sphuṭam | tadguṇe bhujakoṭijyebhagaṇāṃśavibhājite || 106 ||

Translation

In einem geraden (yugma) Kreis ist das Ergebnis als positiv oder negativ zu behandeln: ist der ungerade Anteil zu gering, wird er erhöht; ist er zu groß, wird er vermindert, sodass ein klares (korrigiertes) Maß entsteht. Multipliziert man damit und teilt durch den passenden Bruchteil der Tierkreis-Umläufe (bhagaṇa-aṃśa), erhält man die bhujajyā (Sinus der Basis) und die koṭijyā (Sinus der Senkrechten).

Word by Word

• युग्मवृत्ते: in the even (paired) circle/cycle
• युग्मवृत्ते: Adhikarana (अधिकरण/Locative)
• Type: Noun
• Root: युग्म + वृत्त (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, सप्तमी (7th/Locative), एकवचन

• धन: sine / धन (technical)
• धन: Karma (कर्म/Object)
• Type: Noun
• Root: धन (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया (Nom/Acc), एकवचन

• ऋण: negative (value) / ऋण (technical)
• ऋण: Karma (कर्म/Object)
• Type: Noun
• Root: ऋण (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया (Nom/Acc), एकवचन

• श्यात्: should be / would be
• श्यात्: Kriya (क्रिया/Verb)
• Type: Verb
• Root: अस् (धातु)
• Form: विधिलिङ् (Optative), प्रथमपुरुष (3rd person), एकवचन

• ओजात्: from ojas (value)
• ओजात्: Apadana (अपादान/Ablative source)
• Type: Noun
• Root: ओजस् (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, पञ्चमी (5th/Ablative), एकवचन

• ऊने: when deficient / in deficiency
• ऊने: Adhikarana (अधिकरण/Locative)
• Type: Adjective
• Root: ऊन (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, सप्तमी (7th/Locative), एकवचन; विशेषण

• अधिके: when in excess
• अधिके: Adhikarana (अधिकरण/Locative)
• Type: Adjective
• Root: अधिक (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, सप्तमी (7th/Locative), एकवचन; विशेषण

• स्फुटम्: clearly, explicitly
• स्फुटम्: Kriya-visheshana (क्रियाविशेषण/Adverbial)
• Type: Indeclinable
• Root: स्फुट (प्रातिपदिक)
• Form: अव्यय; क्रियाविशेषण (adverb)

• तत्: that
• तत्: Sambandha (सम्बन्ध/Genitive-like)
• Type: Noun
• Root: तद् (प्रातिपदिक/सर्वनाम)
• Form: सर्वनाम, नपुंसकलिङ्ग, सप्तमी (7th/Locative), एकवचन (तद्गुणे इत्यत्र पूर्वपद)

• गुणे: in the multiplier/factor
• गुणे: Adhikarana (अधिकरण/Locative)
• Type: Noun
• Root: गुण (प्रातिपदिक)
• Form: पुंलिङ्ग, सप्तमी (7th/Locative), एकवचन

• भुजकोटिज्ये: in the sine and cosine
• भुजकोटिज्ये: Adhikarana (अधिकरण/Locative)
• Type: Noun
• Root: भुजज्या + कोटिज्या (प्रातिपदिक)
• Form: स्त्रीलिङ्ग, सप्तमी (7th/Locative), एकवचन; द्वन्द्व (भुजज्या-कोटिज्या)

• भगणांशविभाजिते: when divided by the bhagaṇa-fraction/portion
• भगणांशविभाजिते: Adhikarana (अधिकरण/Locative)
• Type: Adjective
• Root: भगण + अंश + वि-भज् (धातु) + क्त (कृदन्त)
• Form: भूतकर्मणि कृदन्त (P.P.P.), नपुंसकलिङ्ग, सप्तमी (7th/Locative), एकवचन; विशेषण

Speaker

Sanatkumara (in instruction to Narada on technical/Vedanga-style computation)

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 frames precise calculation (sphuṭa—true value) as part of dharmic knowledge: correct measures and truthful computation support right ritual timing and disciplined practice, which in turn aids the pursuit of mokṣa.

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

Indirectly: by emphasizing accurate determination of values used in calendrical/astronomical contexts, it supports proper observance of vows and sacred timings (which are often dedicated to Viṣṇu-bhakti), ensuring devotion is practiced with correctness and steadiness.

What practical Vedic knowledge (Vedanga) is highlighted here?

Vedāṅga Jyotiṣa/Gaṇita: handling positive/negative results (dhana/ṛṇa), applying correction to obtain sphuṭa values, and computing bhujajyā and koṭijyā (sine components) via division by a bhagaṇa-aṃśa factor.