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The Hindu Temple v1.c5.s1: Square and Circle: Vedic Origins

The Hindu Temple v1.c5.s1

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Square and Circle: Vedic Origins

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“The shape of the Vāstu for gods and Brāhmaṇas is prescribed as square” (‘Mayamata’, III. 1).² The square is literally the fundamental form of Indian architecture. Baudhāyana’s prescription how to make a square (caturaśrīkaraṇa) requires a cord (sūtra) of the desired length of the square, its division in half, fixing of poles in the middle of the east-west line and at the cardinal points, and the drawing of circles from these points with the length, and half the length of the cord respectively as radius. The exterior points of intersection of the four circles about the eastern, southern, western and northern poles with a diameter equal to the length of the cord are the four corners of the required square field.³ The square is the essential and perfect form of Indian architecture. It presupposes the circle and results from it. Expanding energy shapes the circle from the centre; it is established in the shape of the square. The circle and curve belong to life in its growth and movement. The square is the mark of order, of finality to the expanding life, its form; and of perfection beyond life and death.

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² Also ‘Vāstuvidhāna’ of Nārada (Ms. 1602, Adyar Library), VIII. See Appendix.

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³ ‘Baudhāyana Śulva Sūtra’, I. 22-28. The very same method of constructing the square with the help of circles is prescribed in later texts with reference to the square of the Vāstupuruṣa (for instance, ‘Śaradātilaka’, III. 6; VI. 3-7), it is similar to the method prescribed in the ‘Āpastamba Śulva Sūtra’, VIII. 8-10; XI. 1. where a bamboo rod is rotated. The construction of the square by, rotation, of rod or cord, is however not the only one. Three further methods are prescribed in the ‘Śulva Sūtras’ (‘Āpastamba Śulva Sūtra’, I. 7; ‘Baudhāyana Śulva Sūtra’, I. 29-35 and ‘Āpastamba Śulva Sūtra’, I. 2) where the square is constructed by the stretching of the cord only, and without rotation (B. B. Datta, ‘The Science of the Śulba’, pp. 55-62). See also Part VII.

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Square and circle are co-ordinated in the architecture of India from the Vedic Fire altar, Agni. The Fire (Agni) and its support, the altar, are one in name. The ‘Śatapatha Brāhmaṇa’ and the ‘Śulva Sūtras’ give the rules for piling up these hearths or altars. In the sacrificial shed (prācīna-vaṃśa-śālā) are three altars, two of them on the east-west line in the middle, the ‘easterly spine’ (prācīnavamśa), and one to the south of the line. Of the two altars on the east-west line, the one at its eastern end is square, the other at its western end is circular. The square one, on which burns the Āhavanīya fire, denotes the heaven (dyau) world; from this celestial fire all other fires are subsequently lighted.⁴ The circular one, the Gārhapatya hearth, denotes this terrestrial world. The third hearth, which is that of the Southern fire, Dakṣiṇāgni, denotes the air-world (Ś. B. XII. 4. 1. 3).⁵

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⁴ The fire is first lighted by friction of wood on the Gārhapatya hearth. From the Gārhapatya the fire is transferred to the Āhavanīya hearth.

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⁵ The rules and meaning of the Agni and the Vedi are given in the Brāhmaṇas (c. 2000 B.C.). They form part of the Karmavidhi, the rules for the performance of the sacrificial rites. The Śrauta-Sūtras (2000-1500 B.C.) contain the rules for the rites ordained by the Veda. Each Śrauta-Sūtra seems to have had its Sulva-Sūtra, or section dealing with the measurements and the ‘geometry’ of the altar.—The Vedi is the sacred ground measured out for the sacrifices (yajña); RV. VIII. 19. 18. In the ‘Śatapatha-Brāhmaṇa’, VII. I. I. 37; VII. 2. 2. ff. are explicit descriptions of the Gārhapatya and Āhavanīya hearths.

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The square Āhavanīya hearth at the eastern end of the sacrificial shed is in the middle of an area, one fathom (vyāma) square. In the Soma sacrifice, the highest of all sacrifices, after the initiation of the sacrificer, the square Āhavanīya hearth makes way on the first Upasad day⁶ for the new brick-built Śālādvārya Gārhapatya which has one fathom square for its area (Ś.B. VII. 1. 1. 37)⁷ and is round in shape.

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⁶ The Upasad days are counted from the commencement to the completion of the altar (Agni).

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⁷ S.B.E., Vol. XLIII, p. 307. Vyāma, a fathom, is the distance between the tips of the middle fingers when the arms are stretched out horizontally. This length of a fathom is also the height of man, from the soles to the root of the hair on the forehead, and remains throughout Indian art and symbolism the perfect proportion; cf. Weber, ‘Indische Studien’, XIII, p. 242.

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Outside, to the east of the sacrificial shed, at a given distance a plot is demarcated; this is called the Mahāvedi.⁸ The square High altar, Uttara Vedi, is on its eastern side.⁹ The Uttara Vedi, too, symbolizes the heavenly world (Ś.B. VII. 3. 1. 27). In the centre of the Uttara Vedi is a small square, its ‘navel’ (nābhi), one span (vitasti) square (Āp.Ś.S. VII. 5. 1).

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⁸ The Mahāvedi is a trapezium, its ‘prācī’ or middle line in the E-W direction measures 36 units (‘prakrama’ or ‘pada’, the east side 24 units, the west side 30 units. 1 prakrama = 3 pada: 1 pada=10 aṅgulas or 15 aṅg. or also 12 aṅg. (‘Taitt. Saṃh.’, VI. 2. 4. 5; ‘Mānava Sulva Sūtra’, ch. IV). The Mahāvedi is also called Saumikī Vedi and is situated in the open to the east of the sacrificial shed (prācīnavamśaśālā) for the purpose of the Soma sacrifice. The Vedi in the shed, between the three hearths, is rectangular with concave, curved sides (cf. the drawing in S.B.E., vol. XXVI, p. 475 and W. Caland-V. Henry ‘L’Agniṣṭoma’, I. Pl. IV). Neither of these Vedis is square.

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⁹ The Uttara Vedi is the principal—and primary—Vedi.

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The square is the shape of the Uttara Vedi, the High altar; it is also the shape of the hearth of the celestial Fire, the Āhavanīya Agni; it is the shape of the centre, the Nābhi, of the Uttara Vedi, and also of the Ukhā, the pan in which the celestial fire is carried from the Āhavanīya Agni.

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The Ukhā, the earthen fire pan (Ś.B. VI. 5. 2. 8), has the shape of a cube. It is the earthen 'womb' of the Fire (Agni; Ś.B. VI. 5. 2. 21).¹⁰ In the Soma sacrifice, the celestial sacrificial fire is transferred daily from the Āhavanīya hearth to a seat of Udumbara wood by the sacrificer in an initiation of one year's duration; the fire is transferred in the pan, the Ukhā (Ukhya Agni) serving as Āhavanīya Agni. On the first day after the initiation, a new round Gārhapatya hearth is built. Its new site is the space of a fathom square in the centre of which was the original square Āhavanīya hearth. The new Gārhapatya hearth (śālādvārya), near the eastern entrance of the sacrificial shed, is built of brick. Its area is equal to one fathom square. It preserves its identity in its name, Gārhapatya, and in its round shape. The domestic fire (Gārhapatya) of the sacrificer has now been transferred to the place of the celestial fire (Āhavanīya) not only by its position but also by its extent. The circle of the Gārhapatya, now situated in the east of the sacrificial shed is equal to a square of one fathom. Its nucleus in the centre is also square.

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¹⁰ The Ukhā is burnt with fire of the Dakṣiṇāgni, or with newly made fire. Weber, op. cit., vol. XIII, p. 225 f.

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The Purāṇa Gārhapatya, the old Gārhapatya hearth, was of terrestrial nature. This now, at the completion of the initiation, is commuted in the Śālādvārya Gārhapatya, to its celestial nature and destination.

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The centre of the new Gārhapatya hearth is laid out in the shape of a cross: four large rectangular (2 'pada' by 1 'pada' each; double square) bricks, in one line from North to South, to which are added two bricks at the back and two in front (1 square pada each), that is West and East; these four bricks are half the size of those North to South. To these are added further bricks which fill the corners in the intermediate directions of the square area inside the round Gārhapatya hearth. To these, further bricks are added; they fill the round periphery with its 21 enclosing bricks (Ś.B. VII. 1. 1. 17-19). The new Gārhapatya hearth has the shape of a circle in area to a square fathom (vyāma = a man's length).

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Each kind of sacrifice requires an Agni (altar) of prescribed shape (and size). Sacrifices are (1) obligatory, daily or seasonal and (2) undertaken for the purpose of wish fulfilment.

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The main altars for the daily (nitya) sacrifices are the Āhavanīya, Gārhapatya and Dakṣiṇa. Amongst the seasonal or recurrent sacrifices, the Soma sacrifice necessitates a Vedi = altar-ground, outside the sacrificial shed, the Mahāvedi or Saumiki Vedi, and on it, the Uttara Vedi, and a Fire Altar (Agni). Their construction, form and meaning as well as those of the abovementioned hearths, are fundamentally important to the Hindu temple. The Soma sacrifice entails the building of the Agni, the Fire Altar, which is piled above the Uttara Vedi on the Mahāvedi. This rite is called Agnicayana, the piling of the Fire Altar. The 'Śatapatha Brāhmaṇa' gives its rules and meaning. This big sacrifice must be performed in a Vedic Hindu family at least once in three generations.

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The brick-built Gārhapatya altar is proper to the Soma-sacrifice. Weber, l.c. Vol. XIII, p. 242.

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About the Kāmya Agnis, the fire altars of different shapes for sacrifices performed with the purpose of attaining definite objects, see Thibaut, 'On the Śulva Sūtras', JASB., 1875; and N. K. Majumder, 'Sacrificial Altars: Vedis and Agnis', JISOA, Vols. VII and VIII; the one of falcon shape (caturaśra-śyena citi) is the most relevant. The Kāmya Agnis are not directly related to the Hindu Temple.

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"The Gārhapatya is this (terrestrial world) and this world is circular" (Ś.B. VII. 1. 1. 37). The earth as the terrestrial world, in Vedic tradition, is symbolised by the circle, and by the round Gārhapatya hearth in contradistinction to the square of the Āhavanīya hearth which stands for the heaven world. During the year of initiation the round hearth of the earthly fire is re-built, at the place of the celestial fire and to the extent of its square site. In this architectural rite it is transferred to another place where it is identical, by measure and position, though not outwardly by shape, to the site of the altar of the celestial fire. Agni is the name of the Fire wherever it burns and the altar, Agni, is its support, terrestrial or celestial, according to its shape.

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The Vedi, in Vedic tradition, represents the extent of the earth. It is an area for sacrificial purposes. The shape of the Vedi varies. It is symbolical as a delimited area and not as a definite figure. The Uttaravedi is square and it is said: "the Vedi is the earth, the Uttaravedi the heaven world" (Ś.B. VII. 3. 1. 27). This is its symbolic value by virtue of its squareness.

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In the Hindu temple, it is the square Vedi which makes the sacred ground. The circular aspect of the earth is left behind, it belongs to the world of appearance and its movement; the earth is beheld itself under the perfection of the heavenly world and, knowing this perfection, is drawn as a square.¹¹

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¹¹ Under this aspect the earth is known in RV. X. 58. 3 (caturbhṛṣṭi) ; VII. 99. 1 (catussrakti) ; Ś. B. VI. 1. 2. 29 (catussrakti). On this knowledge are based the square maṇḍala of the earth, Pṛthivīmaṇḍala, and the square Vāstupuruṣamaṇḍala of the Hindu temple (see Part I).

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On the last day of the initiation (dīkṣā), the Mahāvedi is measured and demarcated and on it the area of the Fire altar which is to be built, so that the fire in the Ukhā can finally be deposited on it, having been brought from the new Gārhapatya (śālādvārya). Of the Agni now to be built, first the body (ātman) is thrown up on the Mahāvedi, the altar ground, which has been ploughed and sown during the introductory sacrifice (prāyaṇīyam) on the day following the last day of the initiation. The Agni lies symmetrically on the East-West line, the middle line or spine of the Mahāvedi, close to its east side ('Kātyāyana Śrauta Sūtra' XVI. 7. 31). The body (ātman) of the altar is laid out square. "Agni piled up for the first time should be without wings and tail and measure one square 'puruṣa'. A bamboo rod is the measure; it measures the length of the sacrificer when he stretches up his arms". (Āp.Ś.S. XVI. 17. 8-10). It is also laid down that the body (ātman) of the bird-shaped Agni has an area of 40 square feet (pada) or 4 men's length (puruṣa) square in an area of 7 men's length square (sapta-puruṣa).¹² "With man's measure he (the sacrificer) metes out. Man is commensurate with the sacrifice." (Taitt. Saṃh. V. 2. 5. 1). "As much as a man with arms extended, with so much a bamboo rod (the Fire altar) is meted out" ('Maitrāyaṇīya S.' III. 2. 4). He metes it out with (the measure of) man (puruṣa) with arms extended. "Verily the sacrifice is a 'puruṣa' and hence by it, all these are measured, and that is its best measure inasmuch as with arms extended he (man) has his maximum measure" (Ś.B. X. 2. 2. 6.). Man in his maximum measure is the standard of measuring the Agnikṣetra, the square field of the Agni.

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¹² Of the bird-shaped Agni it is said (Ś. B. VI. 1. 2. 36). "For what object is this fire (altar) built? 'Having become a bird, he (Agni) shall bear me to the sky', so say some; but let him not think so; for by assuming that form, the seven breaths [(prāṇa) in the sense of the Greek 'pneuma'] became Prajāpati" (cf. VI. 1. 1. 5-6); "by assuming that form Prajāpati created the gods; by assuming that form the gods became immortal: and what thereby the immanent breaths and Prajāpati, and the gods became, that indeed he (the sacrificer) thereby becomes" (trans. Eggeling, S.B.E. XLI). One 'puruṣa' is the length of man standing on tiptoe (or not) with raised arms; it measures 5 'aratni' (the length from the elbow to the tip of the little finger, an ell) or 'hasta', the distance between the elbow and the tip of the middle finger, or 10 'padavitasti' (span) ;

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The square Ātman within the Agnikṣetra has two spines (vaṃśa, pṛṣṭhva); the main one, in the East-West direction coincides with the middle line of the Mahāvedi; the other cuts across it at a right angle.¹³ Where the middle lines meet the sides of the square 'body' an earthen brick (logeṣṭakā) is laid down on each side. From the point, which is to be the centre of the Ātman and of the Agnikṣetra and where a bundle of Kuśa grass has been placed, the Uttara-Vedi is now thrown up, a square mound or platform.¹⁴ The earth for it has been taken from a square pit (cātvāla) of the same content. Its height is made equal to that of the earth bricks in the middle of the sides of the body (ātman) of the Fire altar. The remaining area of the Ātman is then filled up (with sand) to the same height. The Uttara-Vedi, the High altar, is made part of the first layer (citi) of the Fire altar. The 4 earth-bricks and the Kuśa grass bundle in the centre are counted as 5 'bricks' of the first layer (Ś. B. X. 4. 3. 14).

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¹³ The Agnikṣetra, the complete extent of the Fire altar, has 95 increasing sizes, the area of each being increased by one-seventh of the original size (1 square puruṣa); Weber, l.c. p. 240.

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¹⁴ The measurement of the Uttara-Vedi is given in Ś. B. VII. 3. 1. 27; cf. also 'L'Agniṣṭoma', op. cit., I. p. 75.

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The Navel (nābhi) in the centre of the Uttara-Vedi, the High altar, is square and measures a span;¹⁵ it is the centre of the sacrifice. There, originally, the fire was laid and it is here that the symbolism of the square has its root in the Vedic rites.¹⁶ The Ukhā, the fire-pan made of clay, in which the Fire (Agni) is carried from the Āhavanīya hearth, to the Agni, the Fire altar, piled above the Uttara-

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¹⁵ Prādeśa, or it has the length of a bull's foot or a horse's foot ('Āpastamba Ś. S.' VII. 5. 1).

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¹⁶ K. F. Johansson, 'Die Altindische Göttin Dhiṣaṇā', p. 51, speaks of the Uttara Vedi as more ancient than the Vedi of the Prācīnavaṃśa.—The sacrifice itself is called 'bhuvanasya nābhiḥ', RV. I. 164. 34.

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Weber, l.c. p. 239. These are relative measures; they vary with the height of the sacrificer. The cubit 'hasta' = 2 'padas' = 24 aṅgulas is the generally accepted unit in Hindu architecture.

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A 'puruṣa' is the measure of man with arms raised. Vyāma, the measure of man from the soles to the root of the hair on the forehead, is equal to one fathom. The latter is the standard of measure for the altars of the daily sacrifices. The Agni of the Soma-sacrifice is measured with man's greatest measure.

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The length of a 'puruṣa' is standardised as 120 aṅgulas. Aṅgula is the width of a finger, i.e., the thumb (see Part V). A Vyāma has 120 or else 96 aṅgulas. Generally however 'puruṣa' and Vyāma denote a length of 120 aṅgulas. This explanation is given in the commentary by Bhaṭṭabhāskara Miśra of the 'Taittirīya Saṃhitā' (Mysore Oriental Library series, Bibl. Sanskr., No. 15, pp. 134-136). The 'Samarāṅgaṇasūtradhāra', IX. 45, however, gives 84 aṅgulas as equal to 'vyāma = puruṣa'. Re: the different types of aṅgula, see Part V.

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Vedi, is necessarily square in section; it measures a span as does the Nābhi. It is spoken of as the womb, and its cube holds the entire manifested universe, its under surface being this world; the lower part of its sides is the air; the upper portion is the sky (Ś. B. VI. 5. 2. 22). This womb of Agni survives its name and retains its function and to some extent its form in the shape of the Phelā, which is the ‘womb’ of the temple (Pt. IV), and also in the Garbhagṛha, the ‘womb chamber’ of the Embryo, or innermost sanctuary of the temple. It also is generally built on a square plan and is cubical. The navel and womb as places of generation and continuity are images which endure. They are fitted into the square, not in any way as visual symbols, but in virtue of their function, the one accommodating the celestial Fire and the other the Garbhagṛha with the image or symbol of God.

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The square, as fundamental figure of sacrificial symbolism and temple architecture, lends itself to many variations. Baudhāyana prescribes the construction of the Sārārathacakracit and the commentator explains how to form at first a small square with 4 bricks in the middle of the Agnikṣetra then to enlarge this square, to one of 16, etc. This method has become known in the West, through Aristotle, as the Pythagorean ‘gnomon’.” It is in this way too, that the various types of the Vāstumaṇḍala are enumerated in Vāstuśāstra in a progressive series of 1, 2, 3, 4 units square, etc., the most sacred being the plan of 64 squares, preserving the meaning of 64 which is exemplified in “64 bricks form the spokes of the wheel, 64 the Vedi.¹⁸

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¹⁸ G. Thibaut, l.c. quoting ‘Baudhāyana Śulva Sūtra’, III, with reference to the Sārārathacakracit. In this particular instance, three consecutive squares are constructed. The central one of 16 squares for the nave, that of 64 squares for the interior edge of the felloe, and the third square as its outer edge. These squares are then turned into circles. The Vāstumaṇḍala of 64 squares is, according to Varāhamihira, prescribed for the temple (‘Bṛhat Saṃhitā’, LV. 10; cf. Part I). It is its original plan. Utpala, however, commenting on LII, 73, admits the Vāstumaṇḍala of 81 squares for all kinds of temples, regulating the rhythmical disposition of their ground-plan (adhaśchanda, talacchanda), etc., whereas palaces, etc., must have a Vāstumaṇḍala of 81 squares.—The royal maṇḍala, it appears, is thus admitted and established in the sacerdotal field.

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In general a brick in the Brāhmaṇas is one foot square, or its multiple or sub-multiple.¹⁹ It is a natural unit and its name ‘iṣṭakā’, which denotes a brick, has remained the name of any building ‘stone’.

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¹⁹ Ś.B. VIII. 7. 2. 17. prescribes one foot square. The bricks are classified as ‘padya, ardhapadya, padabhāga’ according to their side length of one foot, a half and, a quarter foot respectively (Weber, l.c.) ; the 4 bricks which form the ‘body’ of the Gārhapatya hearth are rectangular, twice the length of the square bricks laid at the front and back, east and west ; Ś.B. VII. I. 1. 18. This makes the centre of the round Gārhapatya hearth a square (p. 253). According to Āp. Ś.S., XVI. 13. 6. bricks may also measure one ‘aratni’ or ell, or the length of the thigh or the upper spine. The unit of the measure of the sacrificial body which the sacrificer builds up for himself is always taken from his physical body.

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The description of the Gārhapatya (śālādvārya) as a circle equal in area to the square of one fathom is given in the ‘Śatapatha Brāhmaṇa’ (VII. I. I. 37).²⁰

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¹⁷ G. Thibaut, ‘On the Śulva Sūtras’, JASB., 1875, p. 200 f. ; T. L. Heath, ‘History of Greek Mathematics’, Vol. I. p. 77.

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²⁰ In the ‘Śulva Sūtras’ various (approximate) methods are given for the circling of the square and the squaring of the circle. That for circling the square is identical in the various

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The square shape of the Āhavanīya hearth, of the Uttara Vedi and the other sacred centres and objects cannot as an alternative be circular; whereas the Gārhapatya, fundamentally circular, may be set up on a square or circular area according to one or the other school.²¹ That is, the ‘earth’ may be thought of as round, in its own shape or square in its figure ordered by the law of the ‘heaven world’.

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²¹ Āp. Ś.S. XVI. 14. 1, and elsewhere. Similarly too, the Dhiṣṇya hearths are piled on a square or circular (base); Āp. Ś.S. XVII. 21. 5.—Analogously, the funeral mound (śmaśāna) is either square or round. Ś.B. XIII ; 8. 1. 5. See also Caland, ‘Die Altindischen Todten und Bestattungsgebräuche’, p. 141.

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Because it is the perfect shape the square is sacred in the hierarchy of Indian architectural symbolism; the square is of greater significance than the circle.

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Sūtras; whereas alternative methods are given in the Sūtras for squaring the circle. The circling of the square is described and its various methods are given in translation by B. B. Datta, op. cit. pp. 140-149, from the Sulva Sūtras of Āpastamba, Kātyāyana, and Baudhāyana.

Cites (14)