What was the main belief of the Universal Zetetic Society?

That the Earth is flat!

Contrary to the popular belief that the Earth was generally believed to be flat until a few hundred years ago, Earth's sphericity has been widely accepted in the Western world (and universally by scholars) since at least the Hellenistic period (323 BCE-31 BCE). It was not until the 19th century that the Flat Earth concept had a resurgence.

https://en.wikipedia.org/wiki/Modern_flat_Earth_beliefs

Samuel Rowbotham (1816-1884) published a pamphlet in 1849 called "Zetetic Astronomy." The Universal Zetetic Society was the forerunner of the Flat Earth Society. Using pseudo-science principles, people "proved" that the Earth was flat. Interested readers are advised to consult the Wiki article for further information.