Narada Purana — Purva Bhaga, Shloka 46

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

Devanagari script

वर्गयोगोथ योगांतहंतिर्वर्गांतरं भवेत् । व्यास आकृतिसंक्षण्णोव्यासास्यात्परिधिर्मुने ॥ ४६ ॥

Transliteration

vargayogotha yogāṃtahaṃtirvargāṃtaraṃ bhavet | vyāsa ākṛtisaṃkṣaṇṇovyāsāsyātparidhirmune || 46 ||

Translation

得“平方之和”(varga-yoga)，而对其积作“末端减除”，则成“平方之差”。噢牟尼，直径(vyāsa)随所观形相而定；由直径便可得周长/圆周(paridhi)。

Word by Word

• वर्ग-योगः: the sum of squares
• वर्ग-योगः: Karta (कर्ता)
• Type: Noun
• Root: वर्ग (प्रातिपदिक) + योग (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रथमा (1st case), एकवचन; समासः—तत्पुरुष

• अथ: then/now
• अथ: Sambandha (सम्बन्ध/connector)
• Type: Indeclinable
• Root: अथ (अव्यय)
• Form: अनन्तरबोधक अव्यय (sequencing particle)

• योग-अन्त-हन्तिः: the subtraction at the end of the sum (terminal subtraction)
• योग-अन्त-हन्तिः: Karta (कर्ता)
• Type: Noun
• Root: योग (प्रातिपदिक) + अन्त (प्रातिपदिक) + हन्ति (प्रातिपदिक/स्त्री)
• Form: स्त्रीलिङ्ग, प्रथमा (1st case), एकवचन; समासः—तत्पुरुष

• वर्ग-अन्तरम्: the difference of squares
• वर्ग-अन्तरम्: Karma (कर्म)
• Type: Noun
• Root: वर्ग (प्रातिपदिक) + अन्तर (प्रातिपदिक)
• Form: नपुंसकलिङ्ग, प्रथमा/द्वितीया (1st/2nd case), एकवचन; समासः—तत्पुरुष

• भवेत्: should be/becomes
• भवेत्: Kriya (क्रिया)
• Type: Verb
• Root: भू (धातु)
• Form: विधिलिङ् (optative), प्रथमपुरुष (3rd person), एकवचन; परस्मैपद

• व्यासः: the diameter
• व्यासः: Karta (कर्ता)
• Type: Noun
• Root: व्यास (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रथमा (1st case), एकवचन

• आकृति-संक्षण्णः: well-determined by the figure/shape
• आकृति-संक्षण्णः: Visheshana (विशेषण)
• Type: Adjective
• Root: आकृति (प्रातिपदिक) + संक्षण्ण (कृदन्त-प्रातिपदिक, क्षण्/क्षण्?; here ‘संक्षुण्ण’ sense: well-determined)
• Form: पुंलिङ्ग, प्रथमा (1st case), एकवचन; भूतकृदन्त विशेषण

• व्यासः: the diameter
• व्यासः: Karta (कर्ता)
• Type: Noun
• Root: व्यास (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रथमा (1st case), एकवचन

• स्यात्: should be
• स्यात्: Kriya (क्रिया)
• Type: Verb
• Root: अस् (धातु)
• Form: विधिलिङ् (optative), प्रथमपुरुष (3rd person), एकवचन; परस्मैपद

• परिधिः: circumference
• परिधिः: Karma (कर्म)
• Type: Noun
• Root: परिधि (प्रातिपदिक)
• Form: पुंलिङ्ग, प्रथमा (1st case), एकवचन

• मुने: O sage
• मुने: Sambodhana (सम्बोधन)
• Type: Noun
• Root: मुनि (प्रातिपदिक)
• Form: पुंलिङ्ग, सम्बोधन (8th case), एकवचन

Speaker

Sanatkumara (teaching Narada)

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 instruction in the Narada Purana includes disciplined, precise knowledge (śāstric pramāṇa)—training the mind toward clarity, order, and truthfulness, which supports higher contemplation.

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

Indirectly: by valuing correct knowledge and careful method, it supports the devotee’s disciplined life—so that worship, vows, and recitation are performed with accuracy and steadiness of mind.

What practical Vedic knowledge (Vedanga) is highlighted here?

A practical computational/measurement principle (gaṇita and māna): operations involving squares and the relation of diameter (vyāsa) to circumference/perimeter (paridhi) for figures.