The Pythagorean Proposition by Elisha Scott Loomis

If you're looking to find a copy of The Pythagorean Proposition, see the bottom of this page.

Elisha Scott Loomis. Photograph taken 1935.

The book The Pythagorean Proposition by E. S. Loomis, the second edition of which was published in 1940, is a collection of 370 different proofs of the Pythagorean theorem. The proofs include those given by Euclid, by Bhaskara (the Indian mathematician) by the Chinese, by modern mathematicians such as Legendre, Leibniz, and Huygens, by a former president of the United States (James Garfield), and several proofs discovered by high school students. While not a particularly novel or groundbreaking book, it has made the Guinness Book of World Records (now Guinness World Records) under the heading "Most-proved theorem". (the image below is from the 1991 book, page 186).

In The Pythagorean Proposition, Loomis classifies all proofs into one of four categories; most proofs fall into either the algebraic or geometrical categories. Algebraic proofs show (usually algebraically) that the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse. Geometric proofs show (usually geometrically) that the area of the squares produced on the two legs equals the area of the square produced on the hypotenuse. The book gives 109 algebraic proofs and 255 geometric proofs (there are also 4 "quaternionic" proofs and 2 "dynamic" proofs, making 370 in all).

Because The Pythagorean Proposition has entered the public domain in Canada, I have chosen to reproduce portions of it on Math Lair. The pages reproduce the feel of the original work (the work appears to have been self-typeset as well as self-published; it was probably a labour of love for Loomis, who published the second edition when he was 87 years of age). The available selections are:

• Foreword
• Algebraic proof #1
• Algebraic proof #36
• Algebraic proof #53
• Algebraic proof #89
• Geometric proof #15
• Geometric proof #31
• Geometric proof #32
• Noted Proofs

Finding a copy of the book

The first edition of The Pythagorean Proposition was published in 1928 and the second edition in 1940; both are very rare. The second edition was reprinted in its entirety in 1968 and 1972 by The National Council of Teachers of Mathematics; this reprint is not easy to find either, but it can be found on Amazon.com (there are separate listings for the 1968 edition and the 1972 edition) and on Amazon.ca.

If you're looking for the original 1928 edition, you might be able to find a copy at this link but it will likely be quite expensive.