15
152 CHAPTER - VII THE SCALES USED FOR MEASURMENTS IN VASTUSASTRA 7.1 PREAMBLE There are three types of angulas used in VSstusastra. They are {^)Manahgulam (2) Mathrahgulam (3) Dehalabdharigulam. MSthrahgulam is the length of the middle part of the middle finger on the right hand of the Acharya. The small measurements are 8 renu = 1 kesam 8 kesam = 1 liksa 8 liksa = I /"ukam 8 yukam = 1 yavam 8 yavam = 1 angula Relevant units of measurements are 1 purusa = 1 vyama = 5 aratnis =120 aiiguias^®^ This measure is manangulam. One tala is one part when an idol of Dasatala is divided by 10. 1/12 of this tala is 1 Dehalabdhangulam. Prasadas and mandapas are measured using manahgula and the instruments for Yajnas are measured using Mathrangulas and Pratimas are measured using Dehalaptangulas). Subhash C. Kak, -rhere old Indian values of K" IJHS 32 (4) 1997.

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152

CHAPTER - VII

THE SCALES USED FOR MEASURMENTS IN

VASTUSASTRA

7.1 PREAMBLE

There are three types of angulas used in VSstusastra. They are

{^)Manahgulam (2) Mathrahgulam (3) Dehalabdharigulam. MSthrahgulam

is the length of the middle part of the middle finger on the right hand of the

Acharya. The small measurements are

8 renu = 1 kesam

8 kesam = 1 liksa

8 liksa = I /"ukam

8 yukam = 1 yavam

8 yavam = 1 angula

Relevant units of measurements are

1 purusa = 1 vyama = 5 aratnis =120 aiiguias^®^

This measure is manangulam. One tala is one part when an idol of

Dasatala is divided by 10. 1/12 of this tala is 1 Dehalabdhangulam.

Prasadas and mandapas are measured using manahgula and the

instruments for Yajnas are measured using Mathrangulas and Pratimas are

measured using Dehalaptangulas).

Subhash C. Kak, -rhere old Indian values of K" IJHS 32 (4) 1997.

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There are 3 types of measures used in Vastuvidya. The first

measurement is based on the length of the body of the owner. Second

measurement is based on the length of the body of the sthapathy. The third

measurement is based on the measurement of Gramaksetra. In the scale

based on the measurement of the body, the smallest is angula which is the

length of the middle part of the middle finger of the right hand. The smallest

measurement in Vastuvidya is 'paramanu' which is 1/8'̂ of thrasarenu.

thrasarenu is the smallest particle flowing through the sunlight which can

be seen by the naked eye. Eight times of this irasarenu is one romagra and

eight times romagra is one liksa and eight liksa is one Yuka, eight times

yuka is one yava. Practical measurements started from yava. Jewellers,

weapons, crowns and idols are measured in Vastuvidya in angula: which is

eight times Yava. The first reference to angula is in Suioasutras. In

Sulbasutras angula is given as 4 14 Yava. Angula given in Baudha books is

7 Yavas and almost all other books give angula as 8 yavas.

7.2 ANGULA

Jaina books gives three types of angulas.^^^

1) Suchyangulam - Measure from lean fingers.

2) Pratharangulam - Measure from flat fingers.

3) Khanarigulam - Measure from fat fingers.

186

Dr. P.W.Ouseph, "yaslusaslram oru samagrapaJuncjnr Published by D.C Books, Kottayam. "' Ibid,

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154

Some books like Samaranganasutradhara and Aparajithaprcha give three

types of angulas.

1) Jyestangulam = 8 yavas, used for the measurement of towns.

2) Madhyahgulam = 7 yavas, used for the measurement of temples

and palaces.

3) Kanistahgulam = 6 yavas, used for construction of seats and

vehicles.

Some other types of angulas are given below.

Matrangulam:- Mai trangulam is given in the vastu texts Visvakarmiyam

and Mayamata. This is the length of the middle part of the middle finger.

Labdhapramanan'gulam:- This is half of the length of the idol oi; ihe grama

temple, the pratista should be made in Dasatala. * «

One ahgula is given as three Yavas in the Vastu text ' Viswakarmiyam'.

'Vinadandu' is the basic measurement given in the book

"Sangeetharatnakaram" of Sangadeva. This is given in 4 ways as 4>2

aiigula, 5 angula, 7 ahgula and 8 ahgula and ahgula is given as 9 yavas.

7.3 HASTA

There are different measurements for hasta. But the most commonly

used is kisku which is 24 angula. The length of this scale kisku is 71.5 cm

marked on the basement of the temple Harikanyakayur temple, Ariyannor,

very near to Guruvayoor. But the Mahabharata gives kisku as 48 angula

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155

and some other texts like Arthasastra of Koutilya and Samarangana

Sutradhara of Bhojaraja give hasta as 42 angulas.

7.4 PURUSAPRAMANA DANDA

There exists a method of taking the total length of the body as basic

measure. This measure is called Purusapramana danda. This is taken as

120 angula, 108 angula or 96 angula. First one is uttama, second one is

madhyama and the last is considered adhama. The height of Yajamana is

taken as the Pramana danda for the construction of Yagasala, height of

the owner is taken for the construction of houses, the length of the idol is

taken for the construction ofdevalaya and so on. One Danda for devalaya

iis the width of garbhagrha.

7.5 SOME OTHER SCALES

Another measurement referred to in V§stu texts is Krosam; which is

the distance of hearing the roaring of a healthy man. Koutilya gives this

distance as 100 Danda, Yojana is the largest measurement in Vastu sastra

which is the distance to which a good expert can send an arrow from the

bow. Koutilya gives one Yojana as 400 Danda, Mayamata gives 500

Danda, and Mahavira gives 2000 Danda etc.

Measurements

8 Paramanu = one Trasarenu

8 Thrasarenu = one Roniagra

8 Romagra = one Liksa

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8 Liksa

8 Yuka

one Yuka

one Yava

8 Yava = one Angula

7.6 NAMES OF DIFFERENT MULTIPLES OF ANGULAS^®®

1 angulas =

2 angulas =

3 angulas =

4 angulas =

5 angulas =

6 angulas =

7 anguISs =

8 angulas =

9 angulas =

10 angulas =

20 angulas =

30 angulas =

40 angulas =

50 angulas =

60 angulas =

70 angulas =

80 angulas =

90 angulas =

100 angulas =

Bindu

Kala, Kolaka, Padma, Aksi, Aswini r

Rudraksi, Agni, Guna, Sula, Vidya

Yaga, Bhaga, Veda, Turiya

Rudfasana, Indriya, Bhuta, Vana

Kamam, Anga, Anyatha, Rasa

Patala, Muni, Dhatu, Abdhi

Bhasu, Loka, Esa, Murty

Dvara, Sutra, Grha, Sakthy

Disa, N^di, Ayudha, Pradurbhava

Trista, Visku

Gathy

Trijagat

Sakuari

Ati Sakuari

Yasti

Ati yasti

Dhriti

Ati dtiriti

Ibid.,

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7.7 NAMES OF DIFFERENT TYPES OF HASTAS WITH RESPECT TO

THEIR LENGTHS

Name

24 angulas =

25 angulas =

26 angulas =

27 angulas =

28 angulas =

29 angulas =

30 angulas =

31 angulas =

Kisku 0

Prajapatyam

Dhanunriusti

Dhanurgrham

Prachyam

Videham

Vypulyam

Prakirnam

We see a beautiful arrangement in every creation whether it is man-

made or not. This is because of the proportionality of each part of the body.

Basically the Manusya praniana is used for the construction of houses and

used in the same proportionality also. Therefore it acquires strength

and beauty.

7.8 CONCEPTS OF SHAPES IN VASTUSASTRA

Any shape in nature is a rhythmic combination of triangles. It is

believed that triangles are the origin of fire 189

Any object in nature is a combination of pancabhutas; say earth,

water, fire, air and akas - space. Egyptians used the name for the three

Ihid.,

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158

dimensional figure of triangle as pyramid. Pira means fire and mid means

middle. They used this name because they have known that the pyramids

absorb Agni. The flat base and sharp top of the pyramid increase its

structural stability and natural calamities like earthquake do not affect

these types of constructions. Permanent constructions started from the

time of Budba. But from many years before this time, different types of

figures were used for the construction of Vedis. 'Hiranya Garbha' may be

used with the same meaning as that of pyramid.

The old icon is linga. Among different types of Lingas, the most

auspicious is 'Trilinga'. Three Murties Brahma, Vishnu, Maheswara were

composed on the same Linga. This is also called Mahalinga. Silpasastta

considers this as different combinations of triangles. A rectangle it̂ . a

combination of two triangles. This represents Brahma. Hexagon is obtained

by combining six triangles and this represents Vishnu. Rhythmic union of

infinite number of triangles gives a circle and this represents Siva

(Maheswara). There are some specialities for the pyramid in Egypt. Some

of them are given below.

The larger pyramid in Egypt is situated in a land of 13 acres. The

levelling of the land was done without a small declination. Now also there

is no change on the levelling. This pyramid is made using 2600000 stones

of weight varying from 2 tons to 70 tons. The space between any two

consecutive stones remains unaltered and the maximum space is less than

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159

1/5 inch. This pyramid is oriented towards the north. It is situated at the

geographical centre point of the earth.

7.9 SOME MATHEMATICAL TERMS USED IN VASTUVIDYA^^

Agram

r Adhikasesam

Antaracapam

Antaralam

Antyastanam

The extremity of a line or arc; remainder in

division

The positive remainder after division

The intervening arc between two points in the

circumference of the circle

Difference, the perpendicular distance from a

point to a straight line

The place of the digit of the highest

denomination, the ultimate place when

arranged in a column.

Anuparimanam

Annyonnyahamam :

Apavarthanam

Ayutam

Avarggastanam

Astasram

Asram

Asphutam •

Angulam

Ankam

Amsam

Infinitesimal

Mutual continued division

reducing a fraction or ratio to the lowest t<

10''

Even place counting from the unit's place

Octagon

Aside of a polygon, an edge

Rough in exact

Unit of length

Number, Digit

Part, Numerator of a fraction

'"* Dr. P.V. Ouseph, "Contribution to Kerala Vastusilpa with critical edition of Manusyalayacandrika", Unpublished Ph.D. Thesis, Department of Sanskrit, University of

Calicut.

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160

Adityamaddhyamam:

Adyakamam •

"Ayatacaturasram

Ayamam

Ayamavistaram

Ahati

Icha

Ichaphalam

Vistaram

Itaretarakodi

Hi t

Istapradesam

Upapaty f

Upadhyvasat

Upantyam

Urddhavam

Unasesam

Rnam m •

Ekam

Ojastanam

Ojam

Karnam

Kala

The mean longitude of the sun

One of the diagonals of a Quadnlateral taken for

reference. The other is known as dvitiyakamam

or itarakamam.

Rectangle

Length

Length and breadth.

Product

The desired antecedent

The desired consequent

Breadth

The ordinate of the other bhuja

A minute of Arc

The desired point

Proof

By Assumption

Penultimate, next to the digit of the highest

denomination

The topmost

The smallest number to be added to the

dividend to make it exactly divisible by the

given divisor

Negative

Unit, unit's place

Odd place counting from the unit's place

Odd

The diagonal of a quadrilateral, hypotenuse of a

right angled triangle, radiator

1/21600 of the circumference of the circle

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Kuttakaram

Kendram

Koti

Kotimulam

Kon

Khandam

Khandaguntindiv

Khandajya

Ganitam

Gatacapam

Gunam

Gunakaram

Gunanam

Gunnayam

Gurvaksaram

Golaprsthacaturasra-

ksetraphalam: *

Golaghanaksetra-

phalam

Golam

A special method of calculation employed in

Hindu astronomy involving the principles of rule

of three, indeterminate equations and continued

fractions.

Centre of a circle, the particular point on the

circumference from which the arc is measured.

Abscissa, adjacent side of a right angled

triangle,

corner rafters of a hipped roof, 10^

The point at which koti touches the circle is its

starting and the other end is its end.

Corner, direction.

Part

Multiplication by parts

The difference between two successive

ordinates, the first differential of Bhujaya.

Calculation; Science of calculation.

The arc already traversed.

Multiplication, multiplier.

Multiplier

Multiplication

Multiplicand

A unit of time

Surface area of a sphere

Volume of a sphere

Sphere

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Grasam

Grasonavyasam

grasam.

Ghanam

Ghanamulam

Ghanaksetraphalam:

Ghmam

Gh^taksetram 4

Cakrakala

Caturasram

CainrasrabhUmi

Capam

Capam, Koti

Chaya

Chedam

Jaladhi

Jyacapantaram

Tullyakaraksetrah

Thjya

Trisaradi

Tryasram

The maximum width of the overlap of two

intersecting circles.

The difference between the diameter and

Cube of a number

Cube root

Volume of a body

Product

Rectangle

The circumference of a circle is assumed to be

divided into 21600 equal parts and each part is

known as a Kala or Hi.

Quadrilateral

The base of a quadrilateral, the opposite side is

known as mukham

Arc of a circle

Complementary arc of bujacapam

Shadow

Denominator

lO '̂* (number and place)

Difference between an arc and the

corresponding Semi-chord

Similar figures

The ordinate of 3 rasis of arc, of a circle

i.e. % the circumference, the unit of

measurement being 1/21600 the part of the

whole circumference.

3, 5, 7 etc.

Triangle

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163

Dalam

Daksinottararekha :

Dikvyaparltyam

Diksamyam

Dvatrimsadasram

Dvadasamgulasamku:

Dvitiyasamkalitam

Dvitiyasamskara-

harakam

Dhanam

Dhanus

Nemi

Pankti

Pancarasikam

Padam

Parampara

Parikarmam

Paridhi

Pahbhramanam

Parsvam

Purvapararekha

Pratibhuja

Pramanam

Phalam

Bahu

Bhiajakam

Half

North-South line or direction

Perpendicularity

Same or parallel line or direction

A polygon of 32 sides

A gnomon 12 angulam long used by ancient

Hindu mathematicians in the measurement of

shadows.

Second integral

The divisor used to calculate a second

correction after a first correction

Positive

Arc

Circumference with reference to position

Column, ten, (number and place)

Compound proportion involving five terms.

A quadrant, number of terms in a series.

A series

Arithmetical processes or manipulations

Circumference with reference to magnitude.

A complete evolution of a planet^along the

Zodiac with reference to a fixed star.

Side, Surface

East-west line or direction.

Opposite side

The antecedent, the first term of a proportion

Result

Side of a triangle, a quadrilateral etc.

Divisor

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164

Bhinnasamkhya

Bhuja

Mandapam

Matsyam

Maham

MOIam

Yamyam

Yugmasthanam

Yogam

Rasi

RUpam

Rupavibhagam

Lamtia

Lambam

Lambanip'atam

Vargam

Vargamulam

Vargasthanam

Vargaksetram

Valli

Visamasamkhya

Vistaram

Fraction

Side of a triangular polygon; ordinate of an arc,

opposite side in a right angled triangle.

A square with a pyramidal roof usually found in

Kerala temples.

The overlapping portion of two interesting

circles.

An arbitrary unit of measurement

The starting point of a line or arc; square root;

cube root etc.

Southern

Even place counting from unit's place.

Sun; Contact; one of the elements of a

pancangam derived from the sun of the true

longitudes of the sun and moon nityayogam.

A number; one of the signs of the Zodiac a term

And ratio.

Unity

Division by magnitude

A chosen point on the equator

Perpendicular; Vertical.

Foot of the perpendicular.

Square

Square root

The odd place counting from the unit's place.

A square

A column or series

Odd number

Breadth

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I6.S

Vrttam

Vrttantargata-

Caturasram

Vyakti

Vyavakalitam

Vyastatriraslkam

Vyasam

Vyasarddham

Samku

/ r

Sarakhandham

Suddhi

Sunnyam

Sredi

Srediksetram «

e

Sadasram • Sodasasram • Samkalltam

1 Samacaturasram

Samacchedam

Samalambacaturasn

Samavitanam

Samasamkhya

Samasadasram •

Samahtararekha

Sutram

Saumyam

Circle

A cyclic quadrilateral

Unity

Subtraction

Inverse proportion.

Diameter

Radius

Gnomon; Style; Vertical post; 10

(number and place)

Parts of the height of an arc

Subtractive

Zero

A series

A figure corresponding to a series graphically

Hexagon

A polygon of 16 sides

Addition; summation of a series, sum of a

series.

A square

Same denominator

3m: Trapezium

Level

Even number

Regular Hexagon

Parallelo straight line

Line, direction, formula

Northern

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Sthanavibhagam

Sthaulyam

Sphutam

Haranam

Harakam

Harryam

Ksetram

Ksetraphalam

Division according to place

Difference from the correct value (Error)

Correct; True longitude of a planet

Division

Divisor

Dividend

A plane plot

Area