This recitation runs for about 61.5 seconds. The segments below divide it into eight equal listening intervals so the page can auto-scroll in sync with the audio.

Interval 1

Verse 1

गणनं प्रथमं तत्त्वं ततः योगः प्रजायते।
एकस्य खलु संवृद्ध्या सङ्ख्या-विस्तार उच्यते॥ १॥
Gaṇanaṃ prathamaṃ tattvaṃ, tataḥ yogaḥ prajāyate |
Ekasya khalu saṃvṛddhyā, saṅkhyā-vistāra ucyate || 1 ||

Translation: Counting is the first principle; from it, addition is born. By the continuous increment of one, the expansion of numbers is declared.</div> </div> </section>

Interval 2

Verse 2

पुनरावर्तिताद् योगात् गुणाकारो विधीयते।
गुणनस्य चावृत्त्या घातकर्म प्रदृश्यते॥ २॥
Punarāvartitād yogāt, guṇākāro vidhīyate |
Guṇanasya cāvṛttyā, ghātakarma pradṛśyate || 2 ||

Translation: From repeated addition, multiplication is defined. And by the repetition of multiplication, the operation of exponentiation is seen.</div> </div> </section>

Interval 3

Verse 3

विलोम-कर्म-जिज्ञासा ऋणं शून्यं प्रसूयते।
भागो मूलं च घाताङ्को विपरीतेन सिद्ध्यति॥ ३॥
Viloma-karma-jijñāsā, ṛṇaṃ śūnyaṃ prasūyate |
Bhāgo mūlaṃ ca ghātāṅko, viparītena siddhyati || 3 ||

Translation: The inquiry into inverse operations gives birth to negative numbers and zero. Division, roots and logarithms are established by this reversal.</div> </div> </section>

Interval 4

Verse 4

विस्तार्यन्ते च नियमा अज्ञातेऽपि पदे तथा।
काल्पनिक-पदैर्युक्ता निष्पत्तिः परमाद्भुता॥ ४॥
Vistāryante ca niyamā, ajñāte'pi pade tathā |
Kālpanika-padairyuktā, niṣpattiḥ paramādbhutā || 4 ||

Translation: These rules are generalized, even into unknown domains. Joined with imaginary terms, the resulting derivation is supremely astounding.</div> </div> </section>

Interval 5

Verse 5

ऋणमेकस्य यन्मूलं न शक्यं दृष्टभूमिषु।
कल्पितं तत्पदं नव्यं तिर्यग्रेखां प्रदर्शयेत्॥ ५॥
Ṛṇamekasya yanmūlaṃ, na śakyaṃ dṛṣṭabhūmiṣu |
Kalpitaṃ tatpadaṃ navyaṃ, tiryagrekhāṃ pradarśayet || 5 ||

Translation: The root of negative one is not possible in the visible grounds (the real number line). That newly imagined term reveals the transverse (perpendicular) line.</div> </div> </section>

Interval 6

Verse 6

बीजाङ्कानां हि घातेन वृत्तमानं प्रजायते।
ज्याकोटिज्यास्वरूपेण घातो भ्रमति मण्डले॥ ६॥
Bījāṅkānāṃ hi ghātena, vṛttamānaṃ prajāyate |
Jyākoṭijyāsvarūpeṇa, ghāto bhramati maṇḍale || 6 ||

Translation: Indeed, by the exponentiation of algebraic numbers, the measure of the circle is born. In the form of sine (jyā) and cosine (koṭijyā), the exponent rotates in a circle.</div> </div> </section>

Interval 7

Verse 7

सर्वं स्पन्दनरूपं यत् प्रकृत्या नटनं तथा।
अनेन सूत्रबन्धेन स्पष्टं भवति सर्वथा॥ ७॥
Sarvaṃ spandanarūpaṃ yat, prakṛtyā naṭanaṃ tathā |
Anena sūtrabandhena, spaṣṭaṃ bhavati sarvathā || 7 ||

Translation: Everything that is in the form of vibration and the very dance of nature - by this binding mathematical formula, it becomes entirely clear.</div> </div> </section>

Interval 8

Verse 8

शून्यमेकं तथा वृत्तं मूलघातोऽपि कल्पितः।
पञ्चतत्त्वसमायोगात् पूर्णं ज्ञानं प्रकाशते॥ ८॥
Śūnyamekaṃ tathā vṛttaṃ, mūlaghāto'pi kalpitaḥ |
Pañcatattvasamāyogāt, pūrṇaṃ jñānaṃ prakāśate || 8 ||

Translation: Zero, one, the circle (π), the base of growth (e) and the imagined unit (i) - from the union of these five elements, complete knowledge shines forth.</div> </div> </section>