The Elements
Comments by Two Popular Authors


Journey through Genius  
By William Dunham
   What Euclid did that established him as one of the greatest names in mathematics history was to write the Elements. This work had a profound impact on Western thought as it was studied, analyzed, and edited for century upon century, down to modern times.   . . .
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   Euclid's great genius was not so much in creating a new mathematics as in presenting the old mathematics in a thoroughly clear, organized, and logical fashion. This is no small accomplishment. It is important to recognize the Elements as more than just mathematical theorems and their proofs; after all, mathematicians as far back as Thales had been furnishing proofs of propositions. Euclid gave us a splendid axiomatic development of his subject, and this is a critical distinction. He began the Elements with a few basics: 23 definitions, 5 postulates, and 5 common notions or general axioms. These were the foundations, the "givens," of his system. He could use them at any time he chose. From these basics, he proved his first proposition. With this behind him, he could then blend his definitions, postulates, common notions, and this first proposition into a proof of his second. And on it went.

Calculus Gems
By George F. Simmons
   The Elements purports to begin at the very beginning of geometry, with nothing required of the reader in the way of previous knowledge or experience. Yet it offers no preliminary explanations, and nowhere does it provide illuminating remarks of any kind. It has no direct scientific content and doesn't even hint at a single application. It makes no attempt to place its subject in any mathematical or historical context, and nowhere is the name of any person mentioned. Its stony impersonality stuns the mind.  . . .  The Elements begins with a definition -- "A point is that which has no part" -- and marches with inhuman, undeviating monotony through 13 Books and 465 Propositions, none of which are discussed or motivated in any way. It conveys the impression of simply existing, like a rock, indifferent to human concerns.  . . .
   In view of its tone and style, the most surprising thing about the Elements is that it seems to have had an author.  . . .

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