Contribution of Mahaviracharya in the

Author(s): R S Lal
Publisher: Z_Deshbhushanji_Maharaj_Abhinandan_Granth_012045.pdf

Page 8

"The square of the number of layers is diminished by one, divided by three, and (then) multiplied by the number of layers. On adding (to quantity so obtained) the product, obtained by multiplying the arbitrarily chosen number (representing) the bricks in (the topmost layer) by the sum of the (natural numbers beginning with one and going upto the given) number of layers, the required answer is obtained".
Symbolically, if n be the number of layers, and a number arbitrarily chosen representing the bricks in the topmost layer, then
Example:
Total number of bricks = 2=1
n2-1 3
"There is constructed an equilateral quadrilateral structure consisting of 5 layers. The topmost layer is made up of one brick. O' you, who know the calculation tell me how many bricks there are (in all)". Solution :
n = 5, a= 52-1 3
So total number of bricks
25-1 3
40+15 = 55 bricks.
1. GSS 2. GSS
:●o
पञ्चतरंकेनाग्रं व्यवघटित। गणितविन्मिश्रे । समचतुरश्रश्र ढी कतीष्टकाः स्युर्ममाचक्ष्व ॥
=
=
Xn+ax
6
2
= 1.
X 5 + 1 x
Now we shall consider the work of Mahavira on Geometrical progressions. In the following sutra is given the rule for finding gunadhana (T) and the sum of a G. P. if the first term, common ratio and the number of terms of the series are known :2
× 5+
The product of the first term with the common ratio multiplied to itself as many times as the number of terms gives the gunadhana. It be known that the gunadhana lessened by the first term and divided by one less than the number of terms gives the gunasankalita.
Symbolically, if n = the number of terms
a = first term
common ratio then
and gunadhana
ar" = (n+1)th term.
and gunasankalita (sum of the series) =S=
177
28
5 × 6 2
n (n+1) 2
पदमितगुणहृतमितप्रभवः स्वाद्गुणधनं तदाचूनम् । एकोनगुणविभक्तं गुणसङ्कलित विजानीयात् ॥
5 (5+1)
2
3311
93
ar"-a 7-1
आचार्य रत्न श्री वेशभूषण जी महाराज अभिनन्दन ग्रन्थ