Major Greek contributions include astronomy, optics, and acoustics, along with major advances in mathematics. Science in ancient Greece was based on logical thinking and mathematics. The Greeks were very interested to know about the world, the heavens, and themselves. Greek geniuses were articulate thinkers. (Pg. 55, Society and Technological Change)
The Greek philosophers were very much drawn to mathematics. They invented its generality, analyzed its premises, and made notable discoveries of theorems by a rigid adherence to deductive reasoning. Geometry became the basic instrument for measuring all things. (Weinkopf, http://www.perseus.tufts.edu/GreekScience/Students/Chris/GreekMath.html)
Plato examined the difference between the untrustworthy and changing world of the senses and that of the permanent truths that could only be found through rational thought. The unchanging elements of geometry were the measures of this ideal, permanent thought-world. This union of logic with geometry laid the foundations of the Western way of life. (Pg.17, The Day The Universe Changed)
Pythagoras studied geometry, and discovered the general proof of the theorem about right-angled triangles. He insisted on generality in reasoning. He is said to have taught that the mathematical entities, such as numbers and shapes, were the ultimate stuff out of which the real entities that we perceive are constructed. He discovered the importance of dealing with abstractions; and in particular directed the attention of number as characterizing the periodicity of notes of music. His followers made important contributions to medicine and astronomy and were among the first to teach that the earth was a spherical planet, revolving about a fixed point. (Pythagoras, http://www.tmth.edu.gr/en/aet/1.html)
Archimedes is famous for his works on buoyancy, or floating bodies. The famous 'Eureka' incident where water overflowed in his bath led him to discover the principle of displacement. His works showed how the behavior of objects in various media might be shown to follow rules of behavior, which could be measured using geometric means. Archimedes shifted the emphasis from mysterious "qualities" which objects were thought to possess to quantifiable matters such as weight, centers of gravity, balance, and so on. He invented ingenious machines of war, calculated the value of fà, and devised a mathematical exponential system to express extremely large numbers. His best-known invention was a machine for raising water called Archimedes screw. (Rorres, http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html)
Greek philosophers and scientists developed a number of important astronomical ideas. Thales is credited with introducing geometrical ideas into astronomy. Thales taught that everything in nature is composed of one basic thing, which he believed to be water. He and two generations of followers are credited with the invention of philosophy. ...