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The Pythagorean Proposition Elisha S. Loomis
Publisher: Natl Council of Teachers of

In trigonometric terms, the Pythagorean theorem asserts that in a triangle ABC, the equality sin²A + sin²B = 1 is equivalent to the angle at C being right. A more symmetric assertion is that ΔABC is right iff sin²A + sin²B + sin²C = 2. The Pythagorean Theorem is Proposition 47 of Euclid's Elements. By any measure, the Pythagorean theorem is the most famous statement in all of mathematics, one remembered from high school geometry class by even the most math-phobic students. The great problem at this date was the duplication of the square, a problem which gave rise to the theorem of the square on the hypotenuse, commonly known still as the Pythagorean proposition (Euclid, I. THE PYTHAGOREAN THEOREM AND SPECIAL RELATIVITY. The underlying configuration became known under a variety of names, the Bride's Chairlikely being the most popular. Euclid's 47th Proposition of course presents what we commonly call the Pythagorean Theorem. Cesar proclaimed “Veni, vidi, vici” in 47 B.C.. This is probably the most famous of all proofs of the Pythagorean proposition. The 47th Proposition of Euclid is known as "that amazing Proposition which is the foundation of all Masonry." It is also known as the Pythagorean Theorem. SLE T.2.G.4 – Apply the Pythagorean Theorem and its converse in solving practical problems. Once you understand a proof of, say, the Pythagorean theorem, you can be sure this knowledge won't be contradicted by any future discovery nor changed by any new insight. The tropics of Cancer and Capricorn are located 47 degrees apart. You can deduce Pythagorean theorem out of “nowhere” and it is valid. It's the first of Euclid's two proofs (I.47).