...fixed. The accuracy of the angles laid out in this manner may be checked by the rule (The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides). The survey of the property gives the lines and levels and locates...

...equal to one of the angles of the given triangle. 8. Prove that the equilateral triangle described on the hypotenuse of a right-angled triangle is equal to the sum of the equilateral triangles described on the sides containing the right angle. [Let ABC be the triangle...

...3. Parallelograms on equal bases and between the same parallels are equal. 4. Prove that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. 5. If a straight line be divided into two parts, the square on...

...The compliments of the parallelograms about the diagonal of any parallelogram are equal. The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides. If a straight line be divided into any two parts, the sum of the square?...

...two thousand years ago by a Greek philosopher and mathematician that the area of the square described on the hypotenuse of a rightangled triangle is equal to the sum of the areas of the squares described on the other two sides. From this principle we have the following:...

...person's belief, or to influence his behavior, is argumentation. The proof that the square described on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides, or that each molecule of water contains two atoms of hydrogen and...

...To illustrate this point with a representative example, Euclid holds with Pythagoras that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides: s 2 = a 2 + b 2 . Schopenhauer holds this too. But in addition...

...God's creation: that he move forward down the hall, calm and rational in his actions. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. The theorem gave him a hold. He was sane. He was himself. He was...

...whose entries form a magic square. I 7. Pythagoras' theorem states that the area of the square drawn on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the squares drawn on the other two sides of the triangle. Investigate other similar shapes...

...corps sonore that the Egyptian priests first discovered the Pythagorean theorem, to wit, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of its two sides.10 How could this be? Rameau thought that in perceiving the arithmetic...