SHAWORDS

Eudoxes... not only based the method [of exhaustion] on rigorous demon — Democritus

HomeDemocritusQuote
"Eudoxes... not only based the method [of exhaustion] on rigorous demonstration... but he actually applied the method to find the volumes (1) of any pyramid, (2) of the cone, proving (1) that any pyramid is one third part of the prism which has the same base and equal height, and (2) that any cone is one third part of the cylinder which has the same base and equal height. Archimedes, however, tells us the remarkable fact that these two theorems were first discovered by Democritus, though he was not able to prove them (which no doubt means, not that he gave no sort of proof, but that he was not able to establish the propositions by the rigorous methods of Eudoxes. Archimedes adds that we must give no small share of the credit for these theorems to Democritus... another testimony to the marvellous powers, in mathematics as well as in other subjects, of the great man who, in the words of Aristotle, "seems to have thought of everything". ...Democritus wrote on irrationals; he is also said to have discussed the question of two parallel sections of a cone (which were evidently supposed to be indefinitely close together), asking whether we are to regard them as equal or unequal... Democritus was already close on the track of infinitesimals."
D
Democritus
Democritus
author78 quotes

Democritus was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. Democritus wrote extensively on a wide variety of topics.

More on Friendship

View all →
Quote
"I guess you could say that I was somewhat withdrawn from my classmates. I spent a good deal of time being a loner. I suppose that had something to do with the way we lived — always on the move, never living in one town very long. Its very hard to make lasting friendships that way. And my father was rather strict with me and my two younger sisters. He insisted on proper behaviour and very often vetoed our choices of boyfriends. There was always a curfew whenever my sisters or I would go out on a date — we had to be home on time or else. But I never resented his authority. In fact, Im thankful for my strict upbringing; I feel it has helped me learn discipline — and thats very important in this business."
S
Sharon Tate