By the fourth century BC the Greek philosophers and astronomers were largely unanimous that the earth was a small stationary sphere located in the center of a larger rotating spherical shell that contained the stars. This concept has been labelled the “two-sphere universe”.[1] The sun, moon and planets were thought to be moving in the expanse between the spheres. The word planet, meaning “wanderer”, fitted the observed movement of these bodies across the sky in relation to the relatively fixed position of the stars. The ancient Greeks believed that the sun and moon were planets.[2] These beliefs were incorrect, but some of their other ideas were remarkably accurate. Eratosthenes (276–195 BC), head of the library of Alexandria, famously estimated the circumference of the earth at 252,000 stadia, potentially about 29,000 miles (depending on which stadion length is used), a slight overestimate of the correct value of roughly 25,000 miles.[3]
About AD 150, Ptolemy made a major contribution to astronomy when he published what was later called the Almagest. This was an attempt to explain the motion of the seven known planets (including the sun and moon) which the “two-sphere” model could not do. Some progress had been made by Greek mathematicians, who developed systems of extra-circular planetary motions, called epicycles. Ptolemy’s was the greatest of these attempts. His system on the motions of the planets and stars formed the foundation for further developments for roughly 1300 years in the Christian West. One of the benefits of the two-sphere model and the subsequent Ptolemaic systems were that they encouraged attempts at accurate measurement of the planetary motions to fine tune the various theories.[4] In fact, the Ptolemaic system could be made as accurate as needed by adding extra epicycles.[5] This was useful descriptive model science.
Advancements in mathematics permitted further developments in astronomy. Drawing on the foundation of Babylonian mathematics, the Greeks added formulation and proof of theorems as a central part of the discipline, which has remained to this day.[6] Pythagoras showed how to calculate the length of the hypotenuse of a right-angled triangle and developed a proof for his theorem. Equally well known is Euclid’s geometry, dating from the third century BC. Euclid, a mathematician and logician, composed a short treatise on geometry, titled Elements, which took a presuppositional, or axiomatic approach based on earlier Babylonian work.[7] From numerous postulates and five basic axioms, Euclid reasoned his way to a substantial theory of geometry, all supported by proofs. Euclid’s geometry was considered a work of genius—his text remained a core part of Western education for more than 2000 years. His acclaimed fifth axiom, also known as the parallel postulate, stated that given a line and a point not on it (in the plane), there exists exactly one line through the point parallel to the original line.[8] This implies that two distinct parallel lines never intersect. From his work we have the term “Euclidean geometry” which today indicates a three-dimensional coordinate system with each straight-line axis at right angles to the other two.
[1] Kuhn, 1957, p. 27.
[2] Ibid., p. 45.
[3] American Council of Learned Societies, 1991, pp. 681–684.
[4] Kuhn, 1957, pp. 64–72.
[5] McElreath, 2020, p. 71.
[6] Aaboe, 1964, p. 33.
[7] Blacker & Loewe, 1975, p. 42.
[8] Aleksandrov, Kolmogorov, & Lavrent’ev, 1999, p. 98 (Vol 3).