Archimedes and Ptolemy: Two of the Last Great Greeks

As we near the end of the most significant era of Ancient Greek innovation, there are at least two more Greek philosophers who must be discussed. Archimedes and Ptolemy made a huge impact on the world for centuries to come. Many of Archimedes’ ideas, principles, and inventions are still in use today. Ptolemy did not make many lasting contributions to science, but did make one significant contribution (which he is most known for) which shaped ideas of astronomy for centuries.

Archimedes (287 BC – 212 BC) was a Greek from Syracuse, Sicily. He is widely known for his contributions to physics and engineering, along with his additions to the fields of astronomy and mathematics. He is understood to be one of the greatest mathematicians of all time, and many consider him to be the first scientist. Archimedes was important in the hydrostatics branch of physics, and also created many machines and explained the principle of the lever.

Arguably Archimedes’ most lasting invention is what is today known as the Archimedes screw. Also known as a screwpump, it is used to transfer water from low-lying bodies to irrigation ditches. It is argued that other unknown Greek engineers may have invented it and it was just attributed to Archimedes. However, the story is that Archimedes was contracted by King Hiero II to design the largest ship in classical antiquity for Syracuse. Since the ship was so large and would begin to leak water through the hull, Archimedes supposedly developed the screw to remove this water. The Archimedes screw consists of a spiral around a center shaft encased in a hollow pipe. The screw is operated either manually or by a windmill. The lower part of the spiral picks up some of the water in the body of water it is inserted into, and the turning of the screw carries it up to the top of the screw, where it drops out into the irrigation ditch. Some have even said that this invention was used to irrigate the Hanging Gardens of Babylon. The screw is still used today in various machines, in its original form and in some variants. Also, using the screw in reverse by pouring water into it can power an electrical generator.

Archimedes has created other, more popularly-known inventions. For example, it is said (controversially) that he aligned an array of mirrors on a beach in such a manner as to combust the tar on the decks of enemy ships, burning them. However, the truth of this account is disputed due to the fact that the beach was facing a direction which would not have been optimal for this sort of feat, and that later attempts to recreate it have failed. Another invention of his was the Claw of Archimedes, which he designed in order to defend his home town of Syracuse. The Claw was a large crane with a grappling hook which would be dropped on a boat and then swung upwards, lifting it out of the water or sinking it.

The lever was explained much more thoroughly by Archimedes than any before him. His “Law of the Lever” is that “Magnitudes are in equilibrium at distances reciprocally proportional to their weights.” He is famous for stating “Give me a place to stand on, and I will move the Earth.”

One of his greatest contributions to physics was Archimedes’ principle. Upon his formulation of it, he is said to have shouted “Eureka!”, or “I have found it!”, immortalizing the phrase. The principle is that “Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. In mathematical terms, density/density of fluid = weight/weight of displaced fluid. With regard to floating objects, Archimedes stated that “Any floating object displaces its own weight of fluid.” It is said that Archimedes used his principle to determine if solid gold was more dense than a golden crown to be given to King Hiero II, but this story, too, is somewhat dubious due to the fact that Archimedes would probably have had to measure the displaced water extremely accurately.

There is much more that could be said about Archimedes, but it is also important to discuss Ptolemy. Ptolemy (90-168) is most known for his treatise known today as the Almagest. This treatise contains the great body of his theories which continued to survive for centuries afterwards. It was his Almagest which contained the geocentric Ptolemaic system of the cosmos. According to Ptolemy, the “celestial realm” is a sphere, similar to that described by Aristotle. It moves as a sphere, and the Earth is a sphere. The Earth is at the center of the cosmos and does not move. In relation to other stars, based on distance, the Earth has no appreciable size and must be treated as a geometric point. The order of the solar system was: Earth, the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and then the sphere of fixed and unmoving stars. This was followed by the sphere of the “prime mover” described by Aristotle. Each planet is moved by a system of its deferent sphere and its epicycles. The epicycles required an eccentric deferent and an equant point. The Ptolemaic system was widely accepted for centuries until Copernicus’ heliocentric model came to be more dominant.

In the next post, we will consider the contributions of medieval physicists, including Arabic scientists and the idea of impetus. These laid the foundations for the modern ideas of the Scientific Revolution which began towards the end of the Renaissance era and included Kepler, Copernicus, Galileo, Bacon, Newton, Leibniz, Descartes, and others.

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