Shloka 3

Prastāra–Naṣṭa Procedures and Enumeration of Chandas

Laghu–Guru Computation

Devanagari script

संख्या द्विरर्धे रूपे तु शून्यं शून्ये द्विरीरितम् / तावदर्धे तद्गुणितं द्विर्द्व्यूनन्तु तदन्ततः

Transliteration

saṃkhyā dvirardhe rūpe tu śūnyaṃ śūnye dvirīritam / tāvadardhe tadguṇitaṃ dvirdvyūnantu tadantataḥ

Translation

സംഖ്യയെ രണ്ടുതവണ പകുതിയാക്കിയപ്പോൾ ഒരു ശേഷിപ്പുണ്ടെങ്കിൽ അത് ശൂന്യമായി കണക്കാക്കണം; സംഖ്യ തന്നെ ശൂന്യമെങ്കിൽ അത് ദ്വിഗുണമെന്ന് പറയുന്നു. തുടർന്ന് ആ പകുതിയെ വിധിപ്രകാരം ഗുണിക്കണം; അവസാനം ഫലം ഇരട്ടിയാക്കി അതിൽ നിന്ന് രണ്ട് കുറയ്ക്കണം।

Word by Word

संख्याthe number

द्विःtwice

अर्धेin the half

रूपेin the form/figure

तुbut/indeed

शून्यम्zero/void

शून्येin/at zero

द्विःtwice

ईरितम्is said/declared

तावत्so much/as many

अर्धेin the half

तत्that

गुणितम्multiplied

द्विःtwice

द्विtwo

ऊनम्less/deficient

तुand/but

तत्of that

अन्ततःfinally/at the end

Speaker

Lord Vishnu (in dialogue instruction to Garuda/Vinata-putra, within an explanatory section)

Philosophical Teaching

Concept: Rule-based transformation of numbers (halving, remainder handling, doubling) to derive a final computed value.

Vedantic Theme: Buddhi-niścaya (determinacy of intellect) and order (ṛta) reflected in structured enumeration; knowledge as precise method.

Application: When applying a metrical/ritual enumeration algorithm: perform successive halving; treat remainder-one as zero in that step; if the base is zero, double per rule; multiply the half as directed; finalize as ‘twice minus two’ of the computed value.

Verse Rasa

Primary Rasa: shanta

Secondary Rasa: adbhuta

Cross References

Related Themes: Garuda Purana chandas/saṅkhyā passages around 1.212: algorithmic rules for lagas/vṛttas/prastāra (contextual linkage)

Characters & Entities

Vishnu

Garuda

FAQs

What is the importance of numerical rules like this in the Garuda Purana?

This verse preserves a procedural rule for handling halves, doubling, and adjustments, which can support precise counting or structured computations used in traditional instructions and observances.

How does this verse relate to Garuda Purana teachings on dharma and ritual order?

Even when the Purana discusses philosophy and the afterlife, it also transmits practical ‘how-to’ methods; this shloka reflects the text’s emphasis on correct procedure (vidhi) and orderly execution.

Practical application of this wisdom today?

It encourages careful, step-by-step thinking: define edge-cases (like remainder/zero), follow a consistent method, and verify the final adjustment—useful for study, record-keeping, and disciplined practice.