Here is a chronological list of the major ancient Greek scientists that focuses on the inventions or discoveries attributed to them, rightly or wrongly, especially in the areas of astronomy, geography, and mathematics. N.B.: Some of the scientists were contemporaries, so inventions of, for instance, Aristotle, might pre-date those of Eudoxus.
Be sure to read the whole article on the scientist of interest by clicking on the link for "more info."
References are at the end of the list.
What We Owe to the Ancient Greeks in the Field of Science
The Greeks developed philosophy as a way of understanding the world around them, without resorting to religion, myth, or magic. Early Greek philosophers, some influenced by (or even importing and exporting ideas from and to) nearby Babylonians and Egyptians, were also scientists who observed and studied the known world, the earth, seas, and mountains here below, and the solar system, planetary motion, and astral phenomena, above.
Astronomy, which began with the organization of the stars into constellations, was used, for practical purposes, to fix the calendar. The Greeks estimated the size of the earth, they figured out how a pulley and levers work, they studied refracted and reflected light, as well as sound. In medicine, they looked at how the organs worked, and studied how a disease progresses. They learned to make inferences from observations. Their contributions in the field of mathematics went beyond the practical purposes of their neighbors.
Many of the ancient Greeks' discoveries and inventions are still used today, although some of their ideas have been overturned. At least one, the discovery that the sun is the center of the solar system, was ignored and then rediscovered.
The earliest philosophers are little more than legend, but this is a list of inventions and discoveries attributed through the ages to these thinkers, not an examination of how factual such attributions may be. Our knowledge of the Pre-Socratic philosophers comes from fragments of their works included in the writing of others. The Presocratic Philosophers: A Critical History with a Selection of Texts, by G.S. Kirk and J.E. Raven provides these fragments in English. Diogenes Laertius provides biographies of the Pre-Socratic philosophers: Lives of Eminent Philosophers, Loeb Classical Library. DK=Die Fragmente der Vorsokratiker, by H. Diels and W. Kranz, is the standard edition on the Pre-socratics.
Thales was a geometer, military engineer, astronomer, and logician. Probably influenced by Babylonians and Egyptians, Thales discovered the solstice and equinox, and is credited with predicting a battle*-stopping eclipse thought to be on 8 May 585 B.C. ["How Thales Was Able to "Predict" a Solar Eclipse without the Help of Alleged Mesopotamian Wisdom," by Dirk L. Couprie; Early Science and Medicine (2004), pp. 321-337]. He invented abstract geometry, including the notion that a circle is bisected by its diameter, and that the base angles of isosceles triangles are equal.
See: "Chaldaean Astronomy of the Last Three Centuries B.C.," by George Sarton; Journal of the American Oriental Society, Vol. 75, No. 3 (Jul. - Sep., 1955), pp. 166-173.
*The Battle of Halys (a river) between Medes and Lydians.
Pythagoras realized that the earth and sea are not static: where once was land is now sea and where once was sea is now land; valleys are formed by running water and hills are eroded by water. He stretched string to produce specific notes in octaves after having discovered the numerical relations between the notes of the scale.
In the field of astronomy, Pythagoras may have thought of the universe as rotating daily around an axis corresponding with the axis of the earth. He may have thought of the sun, moon, planets, and even the earth as spheres. He is credited with being the first to realize the Morning Star and Evening Star were the same.
Presaging the heliocentric concept, a follower of Pythagoras, Philolaus, said the earth revolved around the "'central fire' of the universe," according to "A Chinese Eratosthenes of the Flat Earth: A Study of a Fragment of Cosmology in Huai Nan tzu 淮 南 子," by C. Cullen; Bulletin of the School of Oriental and African Studies, 1976.
Previously, illness had been thought to be a punishment from the gods. Medical practitioners were priests of the god Asclepius (Asculapius). Hippocrates studied the human body and discovered there were scientific reasons for ailments. He told physicians to watch especially when fever peaked. He made diagnoses and prescribed simple treatments like diet, hygiene, and sleep.
Eudoxus improved the sundial (called an arachne or spider), made a map of the known stars, devised a theory of proportion, which allowed for irrational numbers, a concept of magnitude, and developed a method for finding areas and volumes of curvilinear objects. Eudoxus used deductive mathematics to explain astronomical phenomena, turning astronomy into a science. He developed a model in which the earth is a fixed sphere inside a larger sphere of the fixed stars which rotate around the earth in circular orbits.
Goldstein and Bowen; Chandler, Meyer and Rose
Democritus thought (realized) the Milky Way was composed of millions of stars. He was the author of one of the earliest parapegmata (sg. παράπηγμα) tables of astronomical calculations. He is said to have written a geographical survey, as well. Goldstein and Bowen say that Democritus thought of the earth as disc-shaped and slightly concave. Burch ["Counter-Earth,' by George Bosworth Burch; Osiris (1954), pp. 267-294] says Democritus thought the sun was made of stone.
Aristotle decided the earth must be a globe. The concept of a sphere for the earth appears in Plato's Phaedo, but Aristotle elaborates and estimates the size. [Source: "The Ancient Measurements of the Earth," by Aubrey Diller; Isis 1949.]
Aristotle classified animals and is the father of zoology. He saw a chain of life running from the simple to more complex, from plant through animals.
Theophrastus was the first botanist we know of. He described about 500 different types of plants and divided them into trees herbs and shrubs.
Aristarchus is held to be the original author of the heliocentric hypothesis. He thought the sun was immovable, like the fixed stars. He knew that day and night were caused by the earth turning around on its axis. There were no instruments to verify his hypothesis, and evidence of the senses -- that the earth is stable -- testified to the contrary. He was not believed by many. Chi'en and Ricci ("Matteo Ricci's Contribution to, and Influence on, Geographical Knowledge in China, by Kenneth Ch'en and Matteo Ricci; Journal of the American Oriental Society, Vol. 59, No. 3 (Sep., 1939), pp. 325-359) say that even a millennium and a half later, Copernicus was afraid to reveal his heliocentric vision until he was dying. One person who did follow Aristarchus was the Babylonian Seleucos (fl. mid 2nd C B.C.).
Archimedes discovered the usefulness of the fulcrum and lever. He began the measurement of the specific gravity of objects. He is credited with having invented what is called the screw of Archimedes for pumping up water or so they say, as well as an engine to throw heavy stones at the enemy. A work attributed to Archimedes called The Sand-Reckoner, which Copernicus probably knew, contains a passage discussing Aristarchus' heliocentric theory.
During the Renaissance, Petrarch and Leonardo credited Archimedes with creating the cannon. ["Archimedes and the Invention of Artillery and Gunpowder," by D. L. Simms; Technology and Culture, (Jan., 1987), pp. 67-79.]