The Siddhant Shiromani & Yasti Yantra of Bhaskaracharya (1072 AD)
Bhaskaracharya was one of the promonent Indian mathematician and astronomer, who wrote a book ‘Sidhantshiromani’. In his book he has documented valuable ancient liturature and given the references of many of the instruments used by the astronomers before him. Similarly he has documented the various methods for the use of these instruments.
Yasti means a stick. Yasti Yantra was developed by Bhaskaracharya and has also been refered to as Dhi Yantra. The same type of instrument has also been described by ancient sages and astronomers, but Bhaskaracharya has developed this Yantra as unique methods to calculate the height of terrestrial objects like trees and mountains. The usage and principles have been described in the ‘Shidhantashiromani’ of Bhaskaracharya.
The concept of this Yantra is to mount a stick on a pivot at a height d above the ground, and take sightings of the top and bottom of the object such as a tree using the stick.
The projected length of the stick on a horizontal line at the two sightings, L1 and L2, and the heights to which the stick is raised, h1 and h2, can be marked on an adjoining board. If the overall height of the object is H, and the horizontal line at the height at which the stick is mounted splits it into H1 and H2, the lengths form similar triangles, and we can write
h1/L1 = H1/L and h2/L2 = H2/L,
where L is the distance to the object. Eliminating L from the equations using L = H2 (L2/h2), and since H2=d, we get
H = H1 + H2 = (h1/L1) L + H2 == ( (h1/L1) (L2/h2) + 1 ) d .
