Pancha-siddhantika (IAST:Pañca-siddhāntikā) is a 6th-century CESanskrit-language text written byastrologer-astronomerVarāhamihira in present-dayUjjain, India. It summarizes the contents of the treatises of the five contemporary schools of astronomy (siddhantas) prevalent in India.
The text refers to theShaka year 427, which corresponds to 505 CE.[1]Indian writers onastrology andastronomy generally chose anepoch year close to the date of composition of their texts, in order to facilitate correct astronomical calculations.[2] Thus, 505 CE was most probably the year in whichVarāhamihira composedPancha-Siddhantaka or began planning it.[3] The writings of both Varāhamihira and his commentatorUtpala suggest that the text was Varāhamihira's first work.[4]
However, some scholars believe that 505 CE was the year of Varāhamihira's birth or of another important event in his life. This is because according to Amaraja, the author of a commentary onBrahmagupta'sKhanda-khadyaka, Varāhamihira died in 587 CE (Shaka year 509). If Varāhamihira wrotePancha-siddhantika in 505 CE even at the young age of 25, he must have been over 105 years old at the time of his death, which seems exceptionally high to these scholars.[5] Consequently, these scholars date Varāhamihira's lifespan to 505-587 CE.[6] Other scholars doubt the accuracy of Amaraja's statement, since he lived a thousand years after Varāhamihira.[5]
The text discusses five contemporary astronomical schools and their treatises, listed in order of importance, the last two regarded as inferior:[7][8][9]
Varāhamihira's text summarizes the contents of the astronomical treatises of these schools: these treatises, at least in their original form, are now lost. For example, the surviving version of theSurya Siddhanta can be dated to 1000 CE, although its original version may have been composed around 400 CE.[10] Similarly, thePaitamaha Siddhanta referred to by Varāhamihira was probably composed in the early 5th century (distinct from an even earlier work of the same name[11]), but the present-day text is a later work that survives as part of aPurana text.[12] Thus, Varāhamihira's text is the only source about these ancient treatises.[13] Varāhamihira mentions several rules from these texts, but sometimes, it is not clear which rule is from which text.[9]
Varāhamihira refers to hisPancha-siddhantika asKarana (a concise exposition of astronomy), but the text covers a wider range of topics that appear in the texts belonging to thekarana genre.[13]
Notable mathematical concepts in thePancha-siddhantika include:[7]
Like Brahma-gupta, Varāhamihira rejects Aryabhata's view (now universally accepted) that the earth revolves around the sun.[13]
Utpala suggests that Varāhamihira wrote an abridged version of thePancha-siddhantika, but that work is nowlost.[8] Shatananda based hisBhasvati-karana (c. 1098 CE) on theSurya Siddhanta section of thePancha-siddhantika.[14]
Printed editions of the text include:[15]
Varāhamihira, a mathematician born around 505 CE and died 587 CE, who was also known for innovation with Pascal's triangle.