...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...

...cone and a sphere, is not of j the sect of Archimedes ; and he who \ perceived that the squares of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, is in consequence a Pythagorean. W hen we вау that the blood...

...practical examples, before the science was established by abstract reasoning. Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice...

...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...

...between the definition of a straight line and the celebrated Pythagorean demonstration that the square of the hypothenuse of a rightangled triangle is equal to the sum of the squares of the two sides, so we may be able to trace but little resemblance between the great law...

...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...

...right-angled at B, and the side AC is the hypothenuse. 356. It is an established 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 too sides. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle...

...right-angled at B, and the side AC is the hypothenuse. 356. It is an established 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...

...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,...

...right-angled at B, and the side AC is the hypotheimse. 356. It is an established principle in geometry, that the square described on the hypothenuse of a right-angled triangle, is equal to the sumo? the squares described on the other two sides. (Leg. IV. 11., Euc. I. 47.) Thus, if the base...