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

Ch. I – Miśrakādhyāyaḥ 57
which is the mathematical formula of the base of a six cornered
plot of land in a circle as 2S = the total circumference of the
circle.]
195. For a sixteen cornered plot of land in a circle, the value of the
base in Bhuja (arc) is available by dividing the base of Six
cornered plot by sixteen into six. [Mathematically the base of a
sixteen cornered plot of land in a circle as 2S/16 where S is
the measurement of half circumference of the circle. [According
to the verse, base of the sixteen cornered plot of land = 2S/6 X
6/16=2S/16]. By joining the summation of the measurement
of each base, one will get the measurement of Vikarṇa (diameter,
the diagonal), generating thus the Mūla (centre) of the circle.
In other book:
196. Two arms (Bāhu) out of a right angle (Karṇa) inside a circle
joining two ends of a diameter of the circle having measurements
of 3 and 4 units will end up with a diameter of 5 units of
measurement.
Thus ends the methodology of measurement.
[In a right angle triangle, having two arms of dimensions, 3 units
and 4 units will result in 3² + 4² = 5²]*
Thus ends the definition of Kamvikā.
197. Multiply Kara (i. e Hasta=24 Aṅgulas ) with Kara to get (square)
Kara, also Aṅgulas with Karāṅgulas, and Aṅgula by dividing with
24(Jina) twice gives the result(of the area of rectangular or square
plot).
197. Multiply diameter by 3 and add 1/6 to it to get the circumfer-
ence of a circular (plot). To find the area of a circular plot,
multiply 1/4 of a diameter by the circumference (Paridhina)of
the circular (plot).
198 - 199. After the purification of the land, once again the Vāstu is to be
wor- shipped. Lord of the land (Kṣetrapāla), the lord of the
corners, (Diśādhīśa), Gaṇeśa, Grahacaṇḍī, should be worshipped
with offerings of Kṣīra, sweets, clarified butter(Ājya), various
types of cooked food, flowers, incense and according to the rule
of Śāstra.

• [Note :- These formulae were used to find out the measurement of plots
  of land, and the formula has been used by the architects of mediaeval days
  in western India.]