Almost certainly. The circumference of the Earth had been known for nearly 2000 years before Newton was born. In about 250BC, the head librarian of the library at Alexandria (Egypt), Eratosthenes of Cyrene, came across an interesting account in one of the library's manuscripts.

It observed that in the distant southern city of Syene, at noon on the summer solstice vertical columns would cast no shadow, and the sun would shine all the way down a deep water well. That means the sun was directly overhead at that time, but no other. Eratosthenes had never observed such an occurrence in Alexandria, but set about to test it.

On the summer solstice, he placed a stick in the ground plumbed vertically, and watched to see if it would eventually cast no shadow. But it always cast a shadow, first getting shorter, then longer as the day wore on. The shortest shadow would have been cast at noon, when the sun was highest in the sky.

Eratosthenes was a mathematician and also knew the sun was very far away. He made the assumption that the sun's rays that struck the earth were largely parallel. If not, sharp shadows would not be cast. He knew that at noon in Syene, the difference in the angle between a vertical column and the sun was 0 degrees. Measuring the shortest shadow in Alexandria, he calculated the difference in the angle between the vertical shaft and the sun was 7.2 degrees (actually described as 1/50 of a circle).

If the Earth were flat, the column (or well) in Syene and the stick in Alexandria would have cast no shadows at noon. But if the surface of the Earth was curved, the sun could be directly overhead at one spot (Syene), but not another (Alexandria). Given the difference in angles (1/50th of a circle), and the distance between Alexandria and Syene, the actual circumference of the Earth could be calculated using simple trigonometry.

Apocryphally, Eratosthenes paid someone to measure the distance between Alexandria and Syene by walking there and back with a camel. However, the empire's cartographers tended to make annual measurements and that is most likely the metric Eratosthenes used. The distance between the two cities is about 800 km*. That gives the estimated circumference as 50 x 800 km = 40,000 km. The actual circumference of the Earth is about 40,800 km.

So why is the sun overhead one day a year in Syene, but never in Alexandria? Because of the 23.5 degree tilt of the Earth (the angle between the axis of rotation and the plane of revolution around the sun), the sun is only ever directly overhead between the Tropics of Cancer and Capricorn (23.5 degrees above and below the equator) and only directly overhead on the summer solstice at each of the Tropics. Outside that region, the sun can never be directly overhead, and Alexandria is outside that region, whereas Syene is located very near the Tropic of Cancer.

* At the time, Eratosthenes used a measure of distance that had not yet been fully standardized, stadia, and Alexandria is not directly north of Syene, so the original computed circumference may be off by as much as 17 percent.

Video of Carl Sagan on Cosmos describing this using a much better voice than mine.