| Eli Todd Tappan - Geometry - 1873 - 288 pages
...equivalent to 2 2 AB + AC + 2ACXAD. 413. Corollary — If the square described on one side of a triangle is equivalent to the sum of the squares described on the other two sides, then the opposite angle is a right angle. For the last two theorems show that it can be neither acute... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...polygons. PROPOSITION X.—THEOREM. 25. The square described upon the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides. Let the triangle ABC be right angled at C', then, the square AH, described upon the hypotenuse, is... | |
| Edward Olney - Geometry - 1872 - 102 pages
...THE PYTHAGOREAN PROPOSITION. 668. 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. Fio. 372. 1st METHOD.—Let ABC be the given triangle, and ACED the square described on the hypotenuse.... | |
| Charles Davies - Geometry - 1872 - 464 pages
...PROPOSITION XI. THEOREM. CBK 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. Let ABC be a triangle, right-angled at A : then will = Al? + AC\ Construct the square BG on the side... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...B. BOOK IV. EQ THEOREM IX. 195. 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 ABC be a right-angled M triangle, having the right angle at A . then the square described on the... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...G BOOK IV. F E THEOREM IX. 195. 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 ABC be a right-angled triangle, having the right angle at A ; then the square described on the... | |
| Bombay city, univ - 1874 - 648 pages
...point without it. 2. Show that if the square described on one of the sides 8 of a triangle be equal to the sum of the squares described on the other two sides of it, the anglo contained by these two sides is a right angle. 3. In every triangle the square on... | |
| United States Naval Academy - 1874 - 888 pages
...sides. 1. Prove that the square described on the hypothenu.se of a right triangle is ci ; ni valent to the sum of the squares described on the other two sides. .">. Prove that a triangular pyramid is one-third of a triangular prism of the samo base and altitnde,... | |
| Adrien Marie Legendre - Geometry - 1874 - 500 pages
...PROPOSITION XI. THEOREM. 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. , Let ABC be a triangle, right-angled at A : then will SO* = AS2 + AC2. Construct the square BG on... | |
| Education - 1875 - 398 pages
...is regular. • 3. PROPOSITION. 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. 4. PROPOSITION. If the diagonals of a quadrilateral bisect each other the figure is a parallelogram.... | |
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