The past simple form of 'believe' is 'believed.' Therefore, the complete sentence is 'People at that time believed that the Earth was the centre of the solar system.' This reflects the historical understanding of the cosmos prior to the Renaissance.
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To complete the sentence with the past simple tense of the verb provided in brackets, you need to change the verb 'believe' to its past simple form.
In English, forming the past simple tense for regular verbs involves adding '-ed' to the base form of the verb. Since 'believe' is a regular verb, you simply add '-ed' to get 'believed.'
Therefore, the completed sentence is:
'People at that time believed that the Earth was the centre of the solar system.'
This sentence refers to a historical belief known as the geocentric model, where, for a long time, people thought Earth was the center of the solar system. This belief was widely held until the heliocentric model, which correctly places the Sun at the center, was developed by astronomers like Nicolaus Copernicus and Galileo Galilei.