Ancient Mathematics (Sciences of Antiquity Series) by Serafina Cuomo

By Serafina Cuomo

The concept of Pythagoras, Euclid's "Elements", Archimedes' approach to locate the quantity of a sphere: all components of the helpful legacy of old arithmetic. yet old arithmetic was once additionally approximately counting and measuring, surveying land and attributing mystical importance to the quantity six.
This quantity bargains the 1st obtainable survey of the self-discipline in all its type and variety of practices. The interval lined levels from the 5th century BC to the 6th century advert, with the focal point at the Mediterranean area. issues include:
* arithmetic and politics in classical Greece
* the formation of mathematical traditions
* the self-image of mathematicians within the Graeco-Roman period
* arithmetic and Christianity
* and using the mathematical earlier in overdue antiquity.

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Again, I will focus on the latter rather than the former, and again, I am aware that no such distinction is really possible. There seems to be a consensus, however, that Plato was more of a mathematician than Aristotle, that he got more involved and participated more directly in the subject. Consequently, what Aristotle says about mathematics, even in his capacity as a philosopher, would seem to reflect historical circumstances to a greater degree than Plato. But we will be cautious anyway. Like Plato, Aristotle was very interested in the mathematicians’ method, and it is on mathematical procedures that some of his philosophical discussions concentrate.

B. Yes. S. The eight-foot figure, on how long a line should it be based? ] The four-foot figure is on this half line here, is it not? B. Yes. S. Very well. Is the eight-foot figure not double this and half that? Will it not be on a line greater than this and lesser than that? Is that not so? B. I think that it is so. S. Good, you answer what you think. And tell me, was one not two feet, and the other four feet? B. Yes. S. Therefore the side of the eight-foot figure must be greater than this one of the two-feet figure, and lesser than that of the four-feet figure?

B. Yes. S. The sophists call this diagonal; so that if diagonal is its name, do you say, o Meno’s boy, that the double figure would be based on the diagonal? B. 50 Plato’s Theaetetus, set in 399 BC, introduces us to two experts on the topic of incommensurables: Theodorus of Cyrene51 and his pupil Theaetetus, who died in 369 BC. We are told that Theodorus of Cyrene had studied with the sophist Protagoras, but had ‘very soon inclined away from abstract discussion to geometry’,52 and that he had explored some particular cases of squares with area 3, with area 5, and so on, observing that their sides were not commensurable with the unit.

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