James Baquet

    Westerners who studied mathematics a few generations ago would have used a book written over 2,000 years earlier: Euclid’s “Elements,” called the most successful textbook ever written.

    As well-known as the book is, Euclid of Alexandria remains somewhat mysterious. Known to have flourished around 300 BCE, he may have lived from 325 to 270. He was born in Alexandria, Egypt, during the rule of the Ptolemies, so he spoke and wrote in Greek. Details are so sparse that some have suggested he was not an individual, but a “school” of mathematicians that wrote under the name of a famous mathematician.

    The “Elements” is the best-known of at least six remaining works of Euclid. The Greek word for “elements” in the title is the same word once used to designate the letters of the Greek alphabet, so the book is a sort of “ABC” of geometry.

    Modern thinkers from Copernicus and Kepler to Bertrand Russell and Einstein (who called it the “holy little geometry book”) held the “Elements” in high esteem, and based much of their work on the foundations Euclid laid. Abraham Lincoln felt an understanding of Euclid was essential to his understanding of law. And the poet Edna St. Vincent Millay wrote that his apprehension of mathematical truth was the purest form of esthetics: “Euclid alone has looked on Beauty bare.” The book has been translated into European languages over 75 times in the last half-millennium, and several English translations are currently in print.

    Gathering theorems devised by previous mathematicians, Euclid set them out in six parts: the “enunciation” sets forth the problem (e.g., “construct an equilateral triangle on a finite given right line”); the “setting out” shows a figure and designates each part with letters (“line AB” etc.); the “definition” applies the enunciation to the figure; the “construction” carries out the necessary steps of the solution; the steps establish the “proof”; and the “conclusion” ties the proof back to the original enunciation.

    The clean logic of this “axiomatic method” is the basis of Western science.

    Vocabulary:

    Which word above means:

    1. grasp, understanding

    2. having equal sides

    3. pure, without covering

    4. stated in a way that proves itself

    5. mathematical study of shapes

    6. period of 500 years

    7. propositions to be proved

    8. was most active

    9. clear statement of something

    10. scanty, limited in number