वास्तु मण्डन (मण्डन सूत्रधार - गृह, राजप्रासाद, दुर्ग एवं नगर-वास्तु सटीक)

Ch. I – Miśrakādhyāyaḥ 55
[1/4 d x circumference = πd x d/4 = πd²/4 = mathematical
formula for the area of a circle.
192ab After getting the measurement of the diameter of the circle, half
of the cubic value of the diameter has to be divided into 21 parts.
The remaining first half of the cube of the diameter is then to be
added to one twenty first part of the previous half. The result of
the summation will give the volume of the Gola.
[If d is the diameter of the Gola, cubic half of the diameter
when broken into twenty-one parts and one part is then added
to the remaining cubic half of the diameter, this results in a
summation as d³/2 (1 +1/21) =d³/6(3+1/7) = d³/6(3.142)
say πd³/6 i.e. the mathematical formula for the volume of a
sphere]
192cd Add sine (Jyā) to verse sine (Śara) and half of the summation
be multiplied by verse sine again. Adding one eighteenth of it
further to itself, the measurement of dhanu (part of a circle) would
be established.
193. With the above formulae one can draw the east-west as well as
the north-south line of the land with the depiction of a fish. A
quadrangular square can be drawn with the same formula, by
lay- ing on four corners.
194. A wise man will determine half of the circumference of a circle
with one's own desired Hasta measurement (out of three desired
types). One Bhuja (base) will be one-sixth of the value of half
circumference by Hasta measurement; this formula was being
used for the measurement of a plot of land.
A six cornered plot of land would have 1/6 of half circumference
measured by Hasta and added with 1/6 of the other half circum-
ference would give the base of the 6 cornered plot of land in
Bhuja i.e. 2 bhuja.
[Let us take S = the measurement in Hasta of half circumference
of a circle. Bhuja is then = S/6. The base of a six cornered plot of
land according to the verse is equal to S/6 + S/6 = 2S/6