The Empire was established in 1336 by Harihara I and his brother Bukka Raya I of Sangama Dynasty. The empire rose to prominence as a culmination of attempts by the southern powers to ward off Islamic invasions by the end of the 13th century. The empire is named after its capital city of Vijayanagara, whose ruins surround present day Hampi, now a World Heritage Site in Karnataka, India. The empire's legacy includes many monuments spread over South India, the best known of which is the group at Hampi. The previous temple building traditions in South India came together in the Vijayanagara Architecture style. The mingling of all faiths and vernaculars inspired architectural innovation of Hindu temple construction, first in the Deccan and later in the Dravidian idioms using the local granite. South Indian mathematics flourished under the protection of the Vijayanagara Empire in Kerala. The south Indian mathematician Madhava of Sangamagrama founded the famous Kerala school of astronomy and mathematics in the 14th century which produced a lot of great south Indian mathematicians like Parameshvara, Nilakantha Somayaji and Jyesthadeva in medieval south India. Efficient administration and vigorous overseas trade brought new technologies such as water management systems for irrigation. The empire's patronage enabled fine arts and literature to reach new heights in Kannada, Telugu, Tamil and Sanskrit, while Carnatic music evolved into its current form. The Vijayanagara Empire created an epoch in South Indian history that transcended regionalism by promoting Hinduism as a unifying factor. The empire reached its peak during the rule of Sri Krishnadevaraya when Vijayanagara armies were consistently victorious. The empire annexed areas formerly under the Sultanates in the northern Deccan and the territories in the eastern Deccan, including Kalinga, while simultaneously maintaining control over all its subordinates in the south. Many important monuments were either completed or commissioned during the time of Krishna Deva Raya. Vijayanagara went into decline after the defeat in the Battle of Talikota (1565).
When was the Kerala school established?
14th century

The first satellite, BeiDou-1A, was launched on October 31, 2000. The second satellite, BeiDou-1B, was successfully launched on December 21, 2000. The last operational satellite of the constellation, BeiDou-1C, was launched on May 25, 2003.
What was the second satellite for the BeiDou-1 system called?
BeiDou-1B

When comparing different documents, or "witnesses", of a single, original text, the observed differences are called variant readings, or simply variants or readings. It is not always apparent which single variant represents the author's original work. The process of textual criticism seeks to explain how each variant may have entered the text, either by accident (duplication or omission) or intention (harmonization or censorship), as scribes or supervisors transmitted the original author's text by copying it. The textual critic's task, therefore, is to sort through the variants, eliminating those most likely to be un-original, hence establishing a "critical text", or critical edition, that is intended to best approximate the original. At the same time, the critical text should document variant readings, so the relation of extant witnesses to the reconstructed original is apparent to a reader of the critical edition. In establishing the critical text, the textual critic considers both "external" evidence (the age, provenance, and affiliation of each witness) and "internal" or "physical" considerations (what the author and scribes, or printers, were likely to have done).
Why is it important to document variations in witness texts when compiling a critical text?
so the relation of extant witnesses to the reconstructed original is apparent to a reader of the critical edition.