The 'Principia Mathematica' book written in 1687 was described by theoretical physicist Albert Einstein as "perhaps the greatest intellectual stride that has ever been granted to any man to make."
Auction house Christie's that handled the sale expected the goat-skin-covered book to fetch between USD one million and USD 1.5 million.
An unnamed bidder bought it for nearly four times that value at USD 3,719,500.
The crimson book measures about 9x7 inches and contains 252 leaves - some with woodcut diagrams - and a folding plate, according to Christie's.
Only one other original leather-bound copy of Newton's Principia has been sold at auction in the past 47 years.
That copy was presented to King James II (1633-1701) and bought at Christie's New York for about USD 2.5 million in December 2013.