...Demonstrative geometry will show the truth in all cases of the following principle : PRINCIPLE 54. — The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. 57. Measure off 6 inches on one side of a square surface and 8...

...symbolism which they had had since the third or fourth century. THE PYTHAGOREAN THEOREM. The square upon the hypotenuse of a rightangled triangle is equal to the sum of the squares upon the other two sides. A very neat method of showing the truth of this proposition is...

...of the squares on the parts is equal to a given square. 120 The proof of the theorem "the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other sides," which we have given in the text of the 47th proposition, is attributed...

...Demonstrative geometry will show the truth in all cases of the following principle : PRINCIPLE 54. — The square of the hypotenuse of a right-angled triangle is equal to the sujn of the squares of the other two sides. 57. Measure off 6 inches on one side of a square surface...

...circles cut one another at right angles. 4. Prove that the area of any rectilineal figure described on the hypotenuse of a right-angled triangle is equal to the sum of the similar figures described on the sides. 5. Through a point 0 in a parallelogram straight lines...

...diameter ; divide the circumference by the diameter; the quotient will be 3.1416 approximately. II. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. For proof, the pupil is referred to geometry. We may illustrate...

...school. He did the world great service in the discovery of the so-called Pythagorean theorem in geometry, that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. CHAPTER XI ROME Literature. — Bryce, The Holy Roman Empire; Bury,...

...polygons are in a ratio which is the duplicate of the ratio of two corresponding sides. A polygon on the hypotenuse of a right-angled triangle is equal to the sum of the polygons similarly described on the other sides. 5. Shew that the radian is a constant angle, and...

...join CG, FH; show that the angles GCB and HFE are equal. (35.) 42. Show that a polygon described on the hypotenuse of a rightangled triangle is equal to the sum of the similar polygons, similarly described on the other sides. Given two similar triangles, show how...

...it, described on the other two sides. Solution by the PROPOSER. Lemma I. — A rhombus described on the hypotenuse of a right-angled triangle is equal to the sum of the rhombi equiangular to it described on the other two sides. Let ABC be a triangle, right-angled...