Narada Purana — Purva Bhaga, Shloka 109

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

Devanagari script

त्रिज्याभ्यस्तं भुजफलं मकरादौ धनं स्मृतम् । संशोध्यं तु त्रिजीवायां कर्कादौ कोटिजं फलम् ॥ १०९ ॥

Transliteration

trijyābhyastaṃ bhujaphalaṃ makarādau dhanaṃ smṛtam | saṃśodhyaṃ tu trijīvāyāṃ karkādau koṭijaṃ phalam || 109 ||

Translation

当弧段/星宫自摩羯（Makara，摩羯座）起算时，bhujā（正弦）与 trijyā（半径）相乘之值称为“dhana”。但依半径作必要校正后，自巨蟹（Karka）起则成为 koṭi（余弦）的结果。

Word by Word

• त्रिज्या-अभ्यस्तम्: multiplied by the radius
• त्रिज्या-अभ्यस्तम्: विशेषण (Adjectival modifier/विशेषण)
• Type: Adjective
• Root: त्रिज्या (प्रातिपदिक) + अभ्यस्त (कृदन्त; √अस्/√अभ्यस् धातु)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन; कृदन्त-भूतकृदन्त (past participle) ‘अभ्यस्त’ = multiplied/iterated; विशेषणम्

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

• मकर-आदौ: in Makara etc. (signs)
• मकर-आदौ: अधिकरण (Locative/अधिकरण)
• Type: Indeclinable
• Root: मकर (प्रातिपदिक) + आदि (प्रातिपदिक)
• Form: अव्ययीभावसमास; ‘आदौ’ = सप्तमी-एकवचन-रूपेण अव्ययवत् (locative used adverbially): ‘in/at the beginning of Makara etc.’

• धनम्: positive quantity / ‘wealth’ (here: positive value)
• धनम्: कर्म (Object/कर्म)
• Type: Noun
• Root: धन (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन

• स्मृतम्: is stated/considered
• स्मृतम्: क्रिया (Predicate/क्रिया)
• Type: Verb
• Root: √स्मृ (धातु) → स्मृत (कृदन्त)
• Form: कृदन्त-भूतकृदन्त (past passive participle); नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन; भावे/कर्मणि प्रयोगः: ‘is said/considered’

• संशोध्यम्: to be corrected/adjusted
• संशोध्यम्: विशेषण (Adjectival modifier/विशेषण)
• Type: Adjective
• Root: √शुध्/√शोध् (धातु) → संशोध्य (कृदन्त)
• Form: कृदन्त-तव्यत्/यत्-प्रत्ययार्थक (gerundive: ‘to be corrected/adjusted’); नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन; विशेषणम्

• तु: but/indeed
• तु: सम्बन्ध (Discourse particle/निपात)
• Type: Indeclinable
• Root: तु (अव्यय)
• Form: अव्यय; निपात (particle)

• त्रिजीवायाम्: in Tri-jīvā (a region/segment)
• त्रिजीवायाम्: अधिकरण (Locative/अधिकरण)
• Type: Noun
• Root: त्रिजीवा (प्रातिपदिक)
• Form: स्त्रीलिङ्ग, सप्तमी एकवचन; अधिकरणे (locative)

• कर्क-आदौ: in Karka etc. (signs)
• कर्क-आदौ: अधिकरण (Locative/अधिकरण)
• Type: Indeclinable
• Root: कर्क (प्रातिपदिक) + आदि (प्रातिपदिक)
• Form: अव्ययीभावसमास; ‘आदौ’ locative-form used adverbially: ‘in/at the beginning of Karka etc.’

• कोटि-जम्: arising from the complement (koṭi)
• कोटि-जम्: विशेषण (Adjectival modifier/विशेषण)
• Type: Adjective
• Root: कोटि (प्रातिपदिक) + ज (कृदन्त; √जन् धातु)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन; तत्पुरुष: ‘कोट्या जातम्’ = arising from the complement (koṭi)

• फलम्: result/value
• फलम्: कर्म (Object/कर्म)
• Type: Noun
• Root: फल (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया एकवचन

Speaker

Sanatkumara (teaching Narada in a technical/śāstra context)

Vrata Kalpa

Vrata: none

Verse Rasa

Primary Rasa: shanta

Secondary Rasa: adbhuta

Characters & Entities

• Narada
• Sanatkumara
• Makara
• Karka

FAQs

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

It shows that the Purana preserves śāstric precision alongside dharma—accurate Jyotiṣa/gaṇita supports correct timing and understanding of sacred duties, which in turn aids disciplined living oriented toward mokṣa.

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

Indirectly: by grounding religious life in accurate computation (for calendrical and astronomical determinations), it safeguards proper observance of vrata and worship schedules that support steady Vishnu-bhakti in practice.

What practical Vedic knowledge (Vedanga) is highlighted here?

Jyotiṣa (Vedāṅga) with gaṇita: the relationship between jīvā/bhujā (sine), koṭi (cosine), and trijyā (radius), including sign/quarter-based usage from Makara and Karka.