The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c6.s3: Kātyāyana-śulbasūtra

The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c6.s3

Language: English

Kātyāyana-śulbasūtra

**1.2** *same śaṅkuṁ nikhāya śaṅkusammitayā rajyvā maṇḍalaṁ parilikhya yatra lekhayoḥ śaṅkvagracchāyā nipatati tatra śaṅkū*¹ *nihanti sā prācī* | *tadantaraṁ rajyvābhyasya pāśau kṛtvā śaṅkvoḥ pāśau pratimucya dakṣiṇāyamya madhye śaṅku*²*mevamuttarataḥ sodīcī* |

c6.s3.3

¹ *śaṅkuṁ*, P.

c6.s3.4

² *śaṅkurevam*, P.

c6.s3.5

c6.s3.6

³ *śroṇyamsayo*, P.

c6.s3.7

**1.4** *pramāṇamabhyasyābhyāsacaturthe lakṣṇaṁ karoti tannirañchanam* | *akṣṇayā tiryaṅmānīśeṣa* |

c6.s3.8

**1.5** *pramāṇārdhaṁ vābhyasyābhyāsaṣaṣṭhe*⁴ *lakṣaṇaṁ karoti tannirañchanam* | *akṣṇayā tiryaṅmānīśeṣaḥ* |

c6.s3.9

⁴ *vābhyāsaṣaṣṭhe*, P.

c6.s3.10

**1.6** *pramāṇārdhe samacaturasrasya śaṅkuḥ* | *śāstravadardhe dīrghacaturasrasya* | *śakaṭamukhasya caivam* |

c6.s3.11

**1.7** *etena prāgvaṁśavedimānāni vyākhyātāni* | *śālāmānaṁ ca* | *tatrodīcī prācīvat* | *sadasaścaivam* |

c6.s3.12

**1.8** *aparimitaṁ pramāṇādbhūyaḥ* |

c6.s3.13

**1.9** *pramāṇe śāstraṁ pramāṇaṁ nirhāsavivṛddhyoḥ*⁵ | *yogaśca* |

c6.s3.14

⁵ *-vivṛdhyoḥ*, K.

c6.s3.15

**1.10** *itarasyavitṛtīye dakṣiṇata ityetadvakṣyāmaḥ* | *gārhapatyāhavanīyayorantarālaṁ ṣaḍhdhā saptadhā vāgantusamaṁ tredhā vibhajyāparavitṛtīyalakṣaṇena dakṣiṇāyamya tasminnagniḥ* | *viparyasyottarata utkaraḥ* |

c6.s3.16

**1.11** *apivāntaratribhāgo' nayā rajyvā purvārdhe samacaturasraṁ kṛtvā śroṇyāmagniḥ* | *viparyasyottarāṁsa utkaraḥ* |

c6.s3.17

c6.s3.18

**2.1** *aṅgulai rathasammitāyāḥ pramāṇam* | *tatrāṣṭāśītiśatamīṣā* | *catuḥśatamakṣaḥ* | *ṣaḍaśītiryugam* | *catvāro' ṣṭakāḥ śamyā* | producers of the *śulba*-texts. Baudhāyana and Āpastamba whose *śulbasūtras* are fully discussed in this book belonged to the Taittirīya school, the Maitrāyaṇī school is represented by Mānava, while we have in Kātyāyana the sole representative of the White Yajurvedins in this ancient mathematical effort. Apart from basic geometry and arithmetic we have in these works a fairly detailed glimpse of the Vedic sacrificial cult built around various types of altars designed in the likeness of birds and other familiar objects,—the falcon, the kite, the chariot wheel, the funeral pyre, and geometrical figures like isosceles triangle, rhombus and trapezium. Man's eternal craving for wish fulfilment was supposed to be achieved through sacrifices over such fire-altars aptly called the *kāmya agni*, whose philosophical importance need hardly be overestimated.

c6.s3.19

*rtvā karaṇīmadhye śaṅkavaḥ sa*

*akṣṇayā ceti rajjavaḥ* |
*syākṣṇyā rajjurdaśakaraṇī* |
*mānī tasyākṣṇayā rajjuścatvār-*

*ṇ ca darśanāt* |
*īnī pārśvamānī ca yatpṛthag-*
|

*enātmacatustriṃśonena saviśeṣa*

*ṣṇayā rajjustrikaraṇī* |
*bhāgastu navadhā karaṇītṛtīyaṃ*

*aṇī samāsārthā* |
*taḥ samāsaḥ* | *nānāpramāṇa-*
*hindyāttasyākṣṇayā rajjurubhe*

*jihīrṣettāvadubhayato' pacchidya*
*sammitāmakṣṇayāṃ tatropasaṃ-*
*hrāsaḥ* |
*n madhye tiryagapacchidyānyata-*
*ccheṣamāgantunā purayettasyokto*

*dyaikasamāsena samasya śeṣaṃ*

*ṣan madhye' kṣṇayā' pacchidya*
*dhyādviṣamam cedyathāyogamu-*

*avakaraṇī catuḥpramāṇā ṣoḍa-*

*nto vargā bhavanti tānsamasyet* |

c6.s3.20

P. V. Kane placed Baudhāyana, Āpastamba and Kātyāyana between 800 b.c. and 400 b.c. Ramgopal also concluded that the principal *sūtras* by the above-mentioned *sūtrakāras* were composed between 800 b.c. and 500 b.c. These dates are discussed. But there can hardly be any doubt that what Baudhāyana, Āpastamba, Mānava, Kātyāyana and others tried to codify in a systematic manner in their *śulbasūtra* manuals must have for a long time formed the common property of all *adhvaryus* and priests specialized in the performance of sacrificial rites. The origin of mathematics in India clearly lies embedded in these ancient priestly practices.

c6.s3.21

**1.1** *rajjusama*... *yatra* **1.2** *same śaṅ*... *aram* *lekhayoḥ śaṅku*... *adhye* *rajjvābhyasya* ... *śaṅku*²*mevamut*...

c6.s3.22

² *śaṅkurevam*, P.

c6.s3.23

**1.3** *rajjvanta*... *igeṣu* *lakṣaṇāni* | *prā*... *āśau* *pratimucya nir*... *itaḥ*| *viparyasyetara*...

c6.s3.24

**1.4** *pramāṇā*... *m* | *akṣṇayā tiryaṅ*...

c6.s3.25

**1.5** *pramāṇā*... *ham* | *akṣṇayā tiryaṅ*...

c6.s3.26

**1.6** *pramāṇā*... *uras*- *rasya* | *śakaṭan*...

c6.s3.27

**1.7** *etena prā*... *rodīcī* *prācīvat* | *sadas*...

c6.s3.28

**1.8** *aparimita*...

c6.s3.29

**1.9** *pramāṇe* ...

c6.s3.30

**1.10** *itarasyai*... *oran*- *tarālam ṣaḍh*... *akṣa*- *ṇena dakṣiṇāy*...

c6.s3.31

**1.11** *apivāni*... *śroṇ*- *yāmagnih* | *vipi*...

c6.s3.32

**2.1** *aṅgulai r*... *hśata*- *makṣaḥ* | *ṣaḍaś*...

c6.s3.33

¹ *śaṅkum*, P.

c6.s3.34

³ *śroṇyaṁsayo*, P.

c6.s3.35

⁴ *vābhyāsaṣaṣṭhe*, P.

c6.s3.36

⁵ *-vivṛdhyoḥ*, K.

c6.s3.37

*2.2 paitṛkyāṃ dvipuruṣaṃ samacaturaśraṃ kṛtvā karaṇīmadhye śaṅkavaḥ sa samādhiḥ |* *2.3 karaṇī tatkaraṇī tiryaṅmānī pārśvamānyakṣṇayā ceti rajjavaḥ |* *2.4 padaṃ tiryaṅmānī tripadā pārśvamānī tasyākṣṇyā rajjurdaśakaraṇī |* *2.5 evaṃ dvipadā tiryaṅmānī ṣaṭpadā pārśvamānī tasyākṣṇayā rajjuścatvāriṃśatkaraṇī |* *2.6 upadiṣṭaṃ yugapramāṇaṃ śamyāpramāṇaṃ ca darśanāt |* *2.7 dīrgha*⁶*caturaśrasyākṣṇayā rajjustiryaṅmānī pārśvamānī ca yatpṛthagbhūte kurutastadubhayaṃ karotīti kṣetrajñānam |* *2.⁸ samacaturaśrasyākṣṇayā rajjurdvikaraṇī |* *2.⁹ karaṇīṃ tṛtīyena vardhayettacca svacaturthenātmacatustriṃśonena saviśeṣa iti viśeṣaḥ*⁷ *|* *2.10 pramāṇaṃ tiryak dvikaraṇyāyāmastasyākṣṇayā rajjustrikaraṇī |* *2.11 tṛtīyakaraṇyetena vyākhyātā | pramāṇavibhāgastu navadhā karaṇītṛtīyaṃ navabhāgaḥ | navabhāgāstrayastṛtīyakaraṇī |* *2.12 sautrāmaṇyāṃ prakramārthā | tṛtīyakaraṇī samāsārthā |* *2.13 tulyapramāṇānāṃ samacaturasrāṇāmuktaḥ samāsaḥ | nānāpramāṇasamāse hrasīyasaḥ karaṇyā varṣīyaso'pacchindyāttasyākṣṇayā rajjurubhe samasyatīti samāsaḥ |*

c6.s3.38

c6.s3.39

*3.1 caturaśrāccaturaśraṃ nirjihīrṣan yāvannirjihīrṣettāvadubhayato' pacchidya śaṅkū*⁸ *nikhāya pārśvamānīṃ kṛtvā pārśvamānīsammitāmakṣṇayāṃ tatropasaṃharati, sa samāse' pacchedaḥ, sā karaṇyeṣa nirhrāsaḥ |* *3.2 dīrghacaturaśraṃ samacaturaśraṃ cikīrṣan madhye tiryagapacchidyānyataradvibhajyetaratpurastāddakṣiṇataścopadadhyāccheṣamāgantunā purayettasyokto nirhrāsaḥ |* *3.3 atidīrghaṃ cettiryaṅmānyāpacchidyāpacchidyaikasamāsena samasya śeṣaṃ yathāyogamupasaṃharedityekaḥ samāsaḥ |* *3.4 samacaturaśraṃ dīrghacaturaśraṃ*⁹ *cikīrṣan madhye' kṣṇayā' pacchidya tacca vibhajyānyataratpurastāduttarataścopadadhyādviṣamaṃ cedyathāyogamupasaṃharediti vyāsaḥ |* *3.5 pramāṇaṃ caturaśramādeśādanyat |* *3.⁶ dvipramāṇā catuḥkaraṇī tripramāṇa navakaraṇī catuḥpramāṇā ṣoḍaśakaraṇī |* *3.⁷ yāvatpramāṇā rajjurbhavati tāvantastāvanto vargā bhavanti tānsamasyet |*

c6.s3.40

⁶ *caturasrasyākṣṇayā*, P.

c6.s3.41

⁷ *iti viśeṣaḥ*, P omits.

c6.s3.42

⁸ *śaṅkum*, P.

c6.s3.43

⁹ P omits.

c6.s3.44

**3.8** *ardhapramāṇena pādapramāṇaṁ vidhīyate* | *tṛtīyena navamo’ mśaḥ* | *caturthena*¹⁰*ṣoḍaśī kalā* |

c6.s3.45

¹⁰ *śaturthena*, P.

c6.s3.46

**3.9** *eṣa nirhrāsastasya purastāduktam śāstram* |

c6.s3.47

**3.10** *yāvatpramāṇā rajjurbhavatīti vivṛddhe hrāso bhavati* |

c6.s3.48

**3.11** *caturaśraṁ maṇḍalaṁ cikīrṣanmadhyādamse nipātya pārśvataḥ parilikhya tatra yadatiriktam bhavati tasya tṛtīyena saha maṇḍalam parilikhet sa samādhiḥ* |

c6.s3.49

**3.12** *maṇḍalam caturaśram cikīrṣan viṣkambhaṁ pañcadaśabhāgān kṛtvā dvāvuddhāreccheṣaḥ karaṇī* |

c6.s3.50

c6.s3.51

**4.1** *droṇacidrathacakracitkaṅkacitpraugacidubhayataḥ praugaḥ samuhya-purīṣa ityagnayaḥ* |

c6.s3.52

**4.2** *droṇe yāvānagniḥ sapakṣapucchaviśeṣastāvaccaturaśraṁ kṛtvā droṇadaśa-mavibhāgo vṛnt*¹¹*amityeke* | *taddaśamenāpacchidyāpacchidyaikasamāsena samasya nirhṛtya sarvamagniṁ tathākṛtiṁ kṛtvā purastātpaścādvopadadhyāt| maṇḍale’ pyevam* |

c6.s3.53

¹¹ *vṛtta*, P.

c6.s3.54

**4.3** *prauge yāvānagniḥ sapakṣapucchaviśeṣastāvaddviguṇaṁ caturaśraṁ kṛtvā yaḥ purastātkaraṇīmadhye śaṅkuryau ca śroṇyoḥ so ’gniḥ* |

c6.s3.55

**4.4** *ubhayataḥ prauge tāvadeva dīrghacaturaśraṁ kṛtvā karaṇīmadhyeṣu*¹² *śaṅkavaḥ sa samādhiḥ* |

c6.s3.56

¹² *-madhye*, P.

c6.s3.57

**4.5** *praugaṁ caturaśram cikīrṣanmadhye prāñcamapacchidya viparyasye*¹³*tarata upadhāya dīrghacaturaśrasamāsena samasyet sa samādhiḥ* |

c6.s3.58

¹³ *viparyasyotarat*, P.

c6.s3.59

**4.6** *ubhayataḥ praugaṁ cenmadhye tiryagapacchidya pūrvavatsamasyet* |

c6.s3.60

**4.7** *etenaiva trikarṇasamāso vyākhyātaḥ* | *pañcakarṇānām ca* | *prauge’ pacchi-dyaikakarṇānām*¹⁴ | *dvikarṇānāṁ samacaturaśre ’pacchidya*¹⁵ |

c6.s3.61

¹⁴ *-ekakarṇānām*, P omits.

c6.s3.62

¹⁵ P. omits *dvikarṇānāṁ samacaturasre’ pacchidya*.

c6.s3.63

c6.s3.64

**5.1** *uttareṣu puruṣoccayenaikaśatavidhādityetadvakṣyāmaḥ* |

c6.s3.65

**5.2** *ādyo ’gnirdviguṇastriguṇo bhavatīti sarvasamāsaḥ* |

c6.s3.66

**5.3** *ekaviṁśatividho bhavatīti puruṣābhyāsaḥ*¹⁶ |

c6.s3.67

¹⁶ *puruṣobhyāsaḥ*, P.

c6.s3.68

**5.4** *puruṣābhyāse yāvānagniḥ sapakṣapucchaviśeṣastāvaccaturaśraṁ kṛtvā tas-minpuruṣapramāṇamavadadhyāt*¹⁷ | 5.5 *samastaṃ pañcadaśabhāgānkṛtvā dvāvekasamāsena samasyet sa puruṣaḥ* | 5.6 *pañcavibhāgena bṛhatī tasya daśamavibhāgena pādamātrī bhavati*¹⁸ | 5.7 *puruṣaṃ vā pañcamenobhayato 'pacchidya pañcavibhāgan samasya tṛtīyaṃ nirhṛtya tasmin puruṣapramāṇe 'vadadhyādityaparam* | 5.8 *pañcadaśavibhāgo 'ṣṭāṅgulam* | 5.9 *pañcāratnirdaśavitastirviṃśatiśatāṅgulaḥ puruṣa ityetasmād*¹⁹ *dvādaśāṅgulaṃ padamiti*²⁰ *ca*²¹ | 5.10 *puruṣaṃ vā sapta*²²*menobhayato 'pacchidya saptabhāgān samasya sasaptamabhāgamāṅgulaṃ nirhṛtya puruṣapramāṇe 'vadadhyādityaparam* | 5.11 *nāralnivitastīnām samāso vidyate saṃkhyāyogāditi śruteḥ* |

c6.s3.69

¹⁷ *upadadhyāt*, P.

c6.s3.70

¹⁸ P. omits *tasya daśamavibhāgena pādamātrī bhavati*.

c6.s3.71

¹⁹ P. omits *ityetasmād*.

c6.s3.72

²⁰ P gives after *padam, puruṣamityetasmātpuruṣādvijñeyam*.

c6.s3.73

²¹ P. omits *ca*.

c6.s3.74

²² *pañcamena*, P.

c6.s3.75

c6.s3.76

6.1 *yathāgni vediṣṭakāpramāṇaṃ varddhata ityetadvakṣyāmaḥ* | 6.2 *yā karaṇī caturdaśaprakramānsaṅkṣipati triṃśca prakramasaptamabhāgān sa ekaśatavidhe prakramaḥ* | 6.3 *dvitīye vā saptasu prakrameṣu prakramamavadhāya tasya saptamabhāgena prakramārthaḥ* | 6.4 *prakrameṇa vā saptamabhāgena prakramārthaḥ*²³ | 6.5 *evam*²⁴*aikaśatavidhāt* | 6.6 *nāntaḥpātyagārhapatyayorvṛddhirbhavati tāvadeva yonirbhavati na vai jātam garbhaṃ yoniranuvardhata iti śrutervṛddheratyantaṃ pratiṣedhaḥ* | 6.7 *yāvatpramāṇāni samacaturuśrāṇyekīkartuṃ cikirṣedekonāni tāni bhavanti tiryagdviguṇānyekata ekādhikāni tryasrirbhavati tasyeṣustatkaroti* | 6.8 *yathāyūpaṃ vedivarddhanamityetadvakṣyāmaḥ* | 6.9 *yā rajjurekādaśoparavān saṅkṣipati daśa ca rathākṣāṃstasyā yaścaturviṃśo bhāgaḥ sa prakramaḥ* | 6.10 *tena vediṃ nirmāya*²⁵ *dvādaśāṅgulaṃ purastādapacchidya tadyūpāvaṭyācchaṅkoḥ purastātprāñcamavadhāya tasmin yūpānminoti* | 6.11 *pārśvayorvā 'rdhamantarvedīti śruterarddhakānīti* | 6.12 *eke prathamottamau prakṛtivat* | 6.13 *saiṣā śikhaṇḍinī vediḥ*²⁶ |