Narada Purana — Purva Bhaga, Shloka 135

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

Devanagari script

शंकुच्छायाकृतियुतेर्मूलं कंर्णोऽय वर्गतः । प्रोह्य शंकुकृते मूलं छाया शेकुविपर्ययात् ॥ १३५ ॥

Transliteration

śaṃkucchāyākṛtiyutermūlaṃ kaṃrṇo'ya vargataḥ | prohya śaṃkukṛte mūlaṃ chāyā śekuviparyayāt || 135 ||

Translation

Trong hình vuông góc do śaṅku (cọc đo) và bóng của nó tạo thành, đường chéo (karṇa) được suy ra từ tổng các bình phương. Ngược lại, khi đã biết đường chéo, có thể tìm bóng bằng cách trừ đi bình phương của śaṅku—tức đảo ngược phép tính theo śaṅku.

Word by Word

• शंकु: gnomon/pole
• शंकु: Sambandha (सम्बन्ध)
• Type: Noun
• Root: शंकु (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रातिपदिक (compound-member)

• छाया: shadow
• छाया: Sambandha (सम्बन्ध)
• Type: Noun
• Root: छाया (प्रातिपदिक)
• Form: स्त्रीलिङ्ग, प्रातिपदिक (compound-member)

• आकृति: shape/form
• आकृति: Sambandha (सम्बन्ध)
• Type: Noun
• Root: आकृति (प्रातिपदिक)
• Form: स्त्रीलिङ्ग, प्रातिपदिक (compound-member)

• युतेः: of the sum/combination
• युतेः: Sambandha (षष्ठी-सम्बन्ध)
• Type: Noun
• Root: युति (प्रातिपदिक)
• Form: स्त्रीलिङ्ग, षष्ठी (6th/Genitive), एकवचन

• मूलम्: the root/base value
• मूलम्: Karma (कर्म/Object)
• Type: Noun
• Root: मूल (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया (1st/2nd), एकवचन

• कर्णः: the hypotenuse/diagonal
• कर्णः: Karta (कर्ता/Subject)
• Type: Noun
• Root: कर्ण (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रथमा (1st), एकवचन

• अयम्: this
• अयम्: Karta-anvaya (कर्तृसम्बन्ध/Deictic)
• Type: Noun
• Root: इदम् (सर्वनाम-प्रातिपदिक)
• Form: पुंलिङ्ग, प्रथमा (1st), एकवचन; सर्वनाम (pronoun)

• वर्गतः: from the square (i.e., by squaring)
• वर्गतः: Sambandha (सम्बन्ध/Adverbial)
• Type: Indeclinable
• Root: वर्ग (प्रातिपदिक)
• Form: तसिल्-प्रत्ययान्त अव्यय (ablatival adverb)

• प्रोह्य: having removed/setting aside
• प्रोह्य: Purvakala (पूर्वकाल/Preceding action)
• Type: Indeclinable
• Root: प्र + √ऊह्/√वह् (धातु)
• Form: क्त्वा-प्रत्ययान्त अव्यय (gerund/absolutive)

• शंकु: gnomon
• शंकु: Sambandha (सम्बन्ध)
• Type: Noun
• Root: शंकु (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रातिपदिक (compound-member)

• कृते: when (it is) made/done
• कृते: Adhikarana (अधिकरण/Condition)
• Type: Noun
• Root: कृत (कृदन्त; √कृ + क्त)
• Form: नपुंसकलिङ्ग, सप्तमी (7th/Locative), एकवचन; ‘कृते’ = in the case of/when done (idiomatic)

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

• छाया: the shadow
• छाया: Karta (कर्ता/Subject)
• Type: Noun
• Root: छाया (प्रातिपदिक)
• Form: स्त्रीलिङ्ग, प्रथमा (1st), एकवचन

• शंकु: gnomon
• शंकु: Sambandha (सम्बन्ध)
• Type: Noun
• Root: शंकु (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रातिपदिक (implied in compound)

• विपर्ययात्: by reversal/inversion
• विपर्ययात्: Hetu (हेतु/Cause)
• Type: Noun
• Root: विपर्यय (प्रातिपदिक)
• Form: पुंलिङ्ग, पञ्चमी (5th/Ablative), एकवचन

Speaker

Sanatkumara (in instruction to Narada on technical/practical knowledge supporting dharma and moksha)

Vrata Kalpa

Vrata: none

Verse Rasa

Primary Rasa: shanta

Secondary Rasa: adbhuta

Characters & Entities

• Narada
• Sanatkumara

FAQs

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

It shows that Moksha Dharma in the Narada Purana also values disciplined, accurate knowledge—using precise methods (like measurement and calculation) to uphold dharma in practice, such as correct timing and orientation for sacred acts.

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

While not directly preaching bhakti, it supports devotional life indirectly: correct Jyotiṣa-based timing and procedural accuracy help a devotee perform vows, worship, and daily disciplines steadily—making devotion consistent and well-ordered.

What practical Vedic knowledge (Vedanga) is highlighted here?

Jyotiṣa (Vedāṅga astronomy/astrology) and gaṇita (calculation): it describes a Pythagorean-style relation for the śaṅku (gnomon), its chāyā (shadow), and the karṇa (diagonal), including the reverse computation by subtraction.