By Heiberg J.L. (ed.)

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**Extra resources for A treatise of Archimedes: Geometrical solutions derived from mechanics**

**Example text**

Math, What is the Pythagorean theorem? C. The Babylonians came up with this idea a thousand years earlier, but Pythagoras might have been the first to prove it, so it was named for him. The Pythagorean theorem has to do with the lengths of the sides of a right triangle. A right triangle is any triangle that has one right angle (an angle of 90 degrees)—like this: If the sides next to the right angle are of lengths a and b, and the third side is of length c, then the Pythagorean theorem says that a2 + b2 = c2.

The ancient Babylonians (not the Greeks) decided that a circle should contain 360 degrees. In 1 degree there are 60 minutes (that’s the same word as the unit of time, but this means one-sixtieth of a degree). Furthermore, in 1 minute there are 60 seconds (again, although they are the same word, this is a unit of measure for angles, not time). Introduction to Two-Dimensional (2-D) Geometric Figures 29 The French in the early days of the metric system, and the British separately around 1900, chose a different way to divide the circle, specifically into 400 gradients.

40 Dr. Math Introduces Geometry 3. Let ABC be a triangle. Let A′ be the midpoint of BC, B′ the midpoint of AC, and C′ the midpoint of AB: In this way we form four congruent triangles A′B′C′, AB′C′, A′BC′, and A′B′C, of which the sum of the angles is equal to the sum of the angles of ABC. If we leave out the angles of triangle ABC, three straight angles are left for the sum of three of the triangles. So each triangle must have a sum equal to one straight angle: 180 degrees. 4. Let ABC be a triangle, and consider the following figure: Note that the three angles marked with ✽ add up to one complete turn—that is, 360 degrees.

### A treatise of Archimedes: Geometrical solutions derived from mechanics by Heiberg J.L. (ed.)

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