The ‘usual’ example of the ‘Barbara’ syllogism: All men are mortal, Socrates is a man, therefore Socrates is mortal. Another (inference) form: All men are mortal, All Greeks are men, therefore All Greeks are mortal. The same, in the form of an implication: If all men are mortal and all Greeks are men, then all […]
Four Element & Humor Theory
Great Chain of Being & Cosmos
Ancient Greek Numerals
Hellenistic Astronomy
Apollonius’ Derivation of Planetary Stations
The computation of the stations of the planets in the epicyclic theory was reduced by Apollonius to the geometrical problem of drawing a line intersecting the epicycle such that the sections have a definite ratio. Through the revolution of the entire epicycle towards the left side, the planet situated on its circumference moves from point […]
Eratosthenes’ Determination of the Circumference of Earth
Result: Circumference of Earth = 24,662 miles (252,000 stades). Therefore, the diameter of the Earth = 7,850 miles (actual mean polar diameter = 7,900 miles!) NOTE: This is on the assumption that 1 stade = 516.73 feet, following Pliny’s metrology.
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Aristarchus’ Derivation of the Sun’s Distance
Aristarchus’ seventh proposition is his most important, since there the essential numerical result is derived. The demonstration is reproduced here in brief. In the figure below, A represents the position of the sun, B the earth, C the moon when seen halved. Hence angle EBD = angle BAC = 3 degrees. Let the angle FBE […]