Hippocrates" concept of proportion and his astronomical theories are both related to the Pythagorean school of thought." .
Hippocrates of Chios is best known for his squaring of the circle and duplicating the cube. He wrote the first mathematical textbook, called the Elements of Geometry. His book was lost but many mathematicians were greatly influenced by his writing. .
Besides his book, Hippocrates major contribution to ancient mathematics was his quadrature of the lune. This is a figure bounded by two crescent-shaped arcs of unequal radii.
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In trying to square a lune, Hippocrates means to construct a square equal in area to the lune. In his research he showed that a cube can be doubled if two mean proportionals be determined between a number and its double. He used the method of reduction. He adjusted a difficult problem into simpler form, solving this simpler form of the problem, and then attempting to apply the form of the problem, and then attempting to apply the solution to the more difficult problem. .
Eudemus's work as he quoted the passage of the lunes of Hippocrates word for word is stated here to make the description clearer. The quadratures of lunes, which were considered to belong to an uncommon class of propositions on account of the close relation of lunes to the circle, were first investigated by Hippocrates, and his exposition was thought to be correct; we will therefore deal with them at length and describe them. He started out with, and laid down as first of the theorems useful for the purpose, the proposition that similar segments of circles have the same ration one to another as the squares on their bases. This he proved by first showing that the squares on the diameter have the same ratio as the circles. .
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After proving this, Hippcrates attempts to show what way it was possible to "square a lune the outer circumference of which that of a semicircle. This he affected by circumscribing a semicircle about an isosceles right-angled triangle and a segment of a circle similar to those cut off by the sides.
The Greeks view mathematics as a very important aspect of life, education and view it as a necessary tool to help assist in the forward progress of technology. To show how the Greeks view the concept of mathematics, dissect the word. The word mathema is a noun from the verb manthano meaning a subj...
