...PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on the other two sides. • Let the triangle ABC be right angled at A. Having described squares on the three sides, let fall...

...degrees, and 4=90 degrees. 10. In every right angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a right angled triangle, right angled at C, then will the square D described on AB...

...it makes the alternate angles equal. 2. If the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained...

...Proposition of the First Book of Euclid, it is demonstrated, that in any right angled triangle the square of the side subtending the right angle, is equal to the sum of the squares of the sides containing the right angle. In a right angled triangle, the side subtending the...

...PROP. VII. THEOREM. The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides. Let the triangle be Fig. 64. KDI, right angled at I. Describe squares on KD, KI, DI ; then we have...

...BC^AB'-f-AC". Therefore, The square described on the hypolhcnuse of a right-angled triangle, is equivalent to the sum of the squares described on the other two sides. Cor. 1. Hence, by transposition, the square of one of the sides of a right-angled triangle is equivalent...

...principle in geometry, that the square described on the hypothenuse of a right-angled triangle, is equal to the sum of the squares described on the other two sides. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle ABC is 4 feet, and the perpendicular 3...

...right-angled triangle equal to ? In every right-angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a rightangled triangle, right-angled at C, then will the square D, described on AB,...

...THEOR. 47.1 Eu. In any rig'fit-angled triangle, the square which is described upon the hypothenuse, or side subtending the right angle, is equal to the sum of the squares described upon the sides which contain the right angle. Let ABC be a rt. angled ./^, having...

...10342656. 30. 34967ft-. 371 578. The square described on the hypothenuse of a rightangled triangle, is equal to the sum of the squares described on the other two sides. (Thomson's Legendre, B. IV. 11, Euc. I. 47.) The truth of this principle may be seen from the following...