Adyamadyena-Antyamantyena

      The Sutra ' Adyamadyena-Antyamantyena' means 'the first by the first and the last by the last'.

    Suppose we are asked to find out the area of a rectangular card board whose length and breadth are respectively 6ft . 4 inches and 5 ft. 8 inches. Generally we continue the problem like this.


Area = Length X Breath

By Vedic principles we proceed in the way "the first by first and the last by last"

i.e. 6’ 4" can be treated as 6x + 4 and 5’ 8" as 5x + 8,

Where x= 1ft. = 12 in; x2 is sq. ft.

Now ( 6x + 4 )(5x + 8 )



It is interesting to know that a mathematically untrained and even uneducated carpenter simply works in this way by mental argumentation. It goes in his mind like this

    6’     4"

    5’     8"

First by first i.e. 6’ X 5’ = 30 sq. ft.

Last by last i.e. 4" X 8" = 32 sq. in.

Now cross wise 6 X 8 + 5 x 4 = 48 +20 = 68.

Adjust as many '12' s as possible towards left as 'units' i.e. 68 = 5 X 12 +8 , 5 twelve's as 5 square feet make the first 30+5 = 35 sq. ft ; 8 left becomes 8 x 12 square inches and go towards right i.e. 8 x 12 = 96 sq. in. towards right ives 96+32 = 128sq.in.

Thus he got area in some sort of 35 squints and another sort of 128 sq. units.
i.e. 35 sq. ft 128 sq. in



Another Example:


Now 12 + 2 = 14, 10 x 12 + 24 = 120 + 24 = 144

Thus 4′ 6″ x 3′ 4″ = 14 Sq. ft. 144 Sq. inches.

Since 144 sq. in = 12 X 12 = 1 sq. ft .

The answer is 15 sq. ft.