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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.
153
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,
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
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
156
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.,
157
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.,
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
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.
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
161
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
162
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
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
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
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
166
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