Pramāṇa · Search · About · API

The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t25: Chapter 12

The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t25

Language
English

Chapter 12

c8.t25.1

FIRE-ALTARS OF AREAS ONE-FOLD AND UPWARDS, AND FIRE-ALTARS IN THE FORM OF ISOSCELES TRIANGLE, RHOMBUS AND CHARIOT WHEEL

c8.t25.2

**12.1.** The side of an one-fold fire-altar of area 1 sq. *pu.* is 120 *aṅg*; that of a six-fold fire-altar is 293 *aṅg* 31 *tilas*. Baudhāyana (*Bśl.* 5.8-5.15) has discussed the question of fire-altars smaller than 7½ sq. *pu.* Here it is maintained that no fire-altar smaller than the seven-fold should be used, although some teachers uphold the legitimacy of fire-altars from 1½ to 6½ sq. *pu.* Such smaller fire-altars may be constructed but then only in the form of *praügas*, *rathacakras* etc.

c8.t25.3

**12.3.** The *kāmyas* (desires) are different forms of the seven-fold fire-altar. *Guṇas* (qualities) are six in number (Karavinda). For *guṇavikāra* see *Āśr.* 14.1, 1).

c8.t25.4

THE FIRE-ALTAR IN THE FORM OF AN ISOSCELES TRIANGLE (*PRAUGACITI*)

c8.t25.5

**12.4-12.6.** The fire-altars in the form of isosceles triangles (*prauga*) are discussed in these *sūtras*. The *prauga* has been likened to the fore part of a cart (*śakaṭa-mukha*). The method of transforming a square (or a rectangle) into an isosceles triangle has been discussed by Baudhāyana (*Bśl.* 1.7). The construction of a fire-altar in the form of an isosceles triangle and the various types of bricks employed are fully discussed in *Bśl.* 14.1-14.8. Baudhāyana advises the use of rectangular *bṛhatī* bricks and their triangular halves and quarters by cutting the *bṛhatīs* diagonally.

c8.t25.6

Āpastamba advises the use of isosceles triangular bricks of different sizes, as explained by his commentators. Since the isosceles triangle *ABC* formed out of the square *EBCD* is 15/2 sq. *pu.* we have (Fig. (13(a)): BC = AF = √15 pu = 120 √15 ang = 464 ang 22 ti (approx.) AB = 300 √3 ang = 519 ang 21 ti. ( = 4 pu. 39 ang. 21 ti, Karavinda)

c8.t25.8

Fig. 13 (a). An isosceles triangle from a square. (b) *dvādaśī* bricks and their sub-divisions. (c) *trayodaśī* bricks and their subdivisions.

c8.t25.9

The one-twelfth brick, *abc*, for the first layer has each of its two equal sides one-twelfth of *AB* or *AC* and the base one-twelfth of *BC* The half bricks are obtained by dividing *abc* vertically by *af*, and the quarter bricks by joining the mid-points *g*, *h*, *f* of the three sides (Fig. 13(b)). Sundararāja prescribes the use of one-ninth bricks by trisecting the three sides of the one-twelfth brick and joining them, as shown in Fig. 13 (c). For the second layer, one-thirteenth and their sub-divisions are used. The dimensions are: B₁ — one-twelfth (*dvādaśī*) isosceles triangular: side — 43 *aṅg* 10 *ti*, base — 38 *aṅg* 25 *ti* (Karavinda) ; B₂ — half of one-twelfth—43 *aṅg* 10 *ti*; 38 *aṅg* 25 *ti*; 19 *aṅg* 12½ *ti*.; B'₁ — one-thirteenth (*trayodaśī*) isosceles triangular: side—39 *aṅg* 33 *ti* (= 40 *aṅg*—1 *ti*) ; base—35 *aṅg* 25 *ti.* ; B'₂ = half of one-thirteenth—39 *aṅg* 33 *ti*; 35 *aṅg*. 25 *ti*; 17 *aṅg* 29½ *ti*. All these values agree with Karavinda's. Dimensions of quarter and one-ninth bricks are not given.

c8.t25.10

If for the first layer, the two sides and the base are divided into 12 equal parts and the dividing points joined parallel to the sides and the base, the whole area will be divided into 144 isosceles triangles, each to be fitted exactly by the one-twelfth brick. The number 144 can be computed by permutation because, starting with one triangle at the apex it increases to 23 at the 12th layer with a common difference 2. For the second layer, where the sides are to be divided into 13 equal parts, there are likewise 169 triangles, each to be exactly fitted by one-thirteenth brick. Thus Sundararāja says: *prathame prastāre catuścatvāriṁśaccatena dvādaśabhirudicyo dvādaśa rītayaḥ* |...*aparasmin prastāre trayodaśībhiḥ navaṣaṣṭiśatena trayodaśa rītayaḥ* | To complete the number of 200 bricks, in the first layer, 16 one-twelfth bricks in the middle four rows are replaced by 64 quarter bricks, and the apical brick is replaced by 9 one-ninth bricks, thus making up the deficit of 56 bricks. In the second layer, in place of 7 one-thirteenth bricks, 20 quarter and 18 one-ninth bricks are added to make good the deficit of 31 bricks.

c8.t25.11

THE FIRE-ALTAR IN THE FORM OF A RHOMBUS (*UBHAYATA PRAUGA*).

c8.t25.12

**12.7-12.8.** For the construction of a rhombus or two isosceles triangles on either side of the common base, Baudhyāyana’s rules, *BŚl.* 2.8 may be referred to. The seven-fold fire-altar in the form of a rhombus, with the types of bricks to be used, has been discussed by Baudhāyana (*BŚl.* 15.1-15.6). In the case of the rhombus fire-altar, the bricks are to be made as in the case of the *praugaciti*, and these should be in the form of a rhombus, as Karavinda explains (*karaṇāni cayanavidhiśca praugavat* | *viśeṣaḥtūbhayataḥ praugāḥ iṣṭakāḥ*|)

c8.t25.13

THE FIRE-ALTAR IN THE FORM OF A CHARIOT WHEEL (*RATHACAKRACIT*).

c8.t25.14

**12.9-12.10.** These two *sūtras* and the first three (13.1-13.3) of the next chapter deal with the construction of the fire-altar in the form of a chariot wheel. Āpastamba refers to the same type of *rathacakraciti*, as discussed in detail by Baudhāyana (*BŚl.* 16.1-16.5) and explained in the notes concerning these *sūtras*.

Linked texts (2)