The Twelve Yantras of Lalla

Lalla (720–790 CE) was an Indian astronomer and mathematician who followed the tradition of Āryabhaṭa, Brahmagupta, and Bhāskara I.Lalla was known as being one of the leading Indian astronomers during the eighth century. Only two of Lalla's works are currently thought to be extant.Lalla’s most famous work was entitled Shishyadhividdhidatantra(Treatise which expands the intellect of students). He was well known because of twelve instruments which he brought into practice.

Lalla describes the 12 Instruments as follows:

Sphere, ring, dial, bow, time measuring water vessel, Gnomon, divider, scissor. Circular seat with central stick, semicircle with stick, combination of sticks, are the twelve instuments along with a stick.

The 12 instruments are as follows:

1)The Gola yantra is a type of armilliary sphere used to locate planetary positions.
2)Bhangana is a ring with angular graduations alonge its circumference, it is a type of protractor.
3)Chakra is a circular disk with angular graduations; it is also a type of protractor.
4)Dhanu is a semicircular disk with angular graduations and a stick pivoted at the center, it is a type of protractor with a plumb bob arrangement.
5)Ghati is a small vessel with a hole at the bottom. It was used to measure time.
6)Shanku is a type of gnomon, a long vertical cone used to identify East-West-North-South direction based on shadow of its tip.
7)A special geometrical construction known a ‘Matsya‘ was used for the above purpose. Altitude of sun and day time was also measured with this instrument based on the shadow.
8)Shakata consists of two ‘V’ shaped sticks, pivoted at the end.
9)Kartari means a seizer. This instrument is made up of two sticks both pivoted together. It was used like a caliper, and also to measure angle with the help of protractor.
10)Pitha is a horizontal disk with a vertical stick at its center. It was used to measure local time based on its shadow, it was used to measure the height with the help of special geometrical contruction.
11)Shalaka is combination of two sticks with a string.
12)Yasti is just a long stick having standard dimensions; it was used to measure height and distances. Special geometrical constructions were framed to facilitate the use of this stick. These proposed geometrical constructions were to construct the proportionate triangles with the help of which heights of terrestrial objects could be calculated.