The Greek mathematician, Eratosthenes, found the circumference of the Earth by using logic and reasoning. On one midsummer's day in Syene, Eratosthenes found that the reflection of the sun could be seen at the bottom of a deep well. The rays pointed to the center of the Earth and the sun was overhead. This means it was basically 0° of circle. Remembering this, the next midsummer's day in Alexandria, he measured the shadow cast by an obelisk(a stone pillar, found in Ancient Egypt). Eratosthenes knew sun beams travel in parallel lines, so he infered that the difference between the angle had to result from the curvature of the Earth. The angle was 1/50 of a circle, so the distance around the world must be 50x the distance from Alexandria to Syene. Eratosthenes made an extremely close estimate of the circumference on the Earth; he got 25,000 miles, and the actual circumference is 24,901 miles.

Many Greek astronomers looked at the skies to make observations on the movement of the stars, the planets, the Sun, and the moon. They saw how the Sun moved across the sky and how the moon got bigger and smaller. This was how many of them reasoned that the Earth was NOT the center of the universe.

The Law of Buoyancy, or Archimedes' Principle, states that for something to float, the weight of the item floating must be equivalent of less than the amount of water displaced by it, otherwise it will sink. The story of Archimedes' Eureka! moment says that Archimedes was in a bathtub when the crown fell in. It floated because the bottom half displaced more water than the top half weighed. Archimedes knew that the mass of the crown was definitely more than that of the water and that the bottom half displaced more water than the top half. So, he used logic and reasoning to figure WHY it stayed afloat, thus creating Archimedes' Principle, or the Law of Buoyancy.