| Horatio Nelson Robinson - 1869 - 276 pages
...and (a + b) x (a — b) = a * — b\ THEOREM XXXIX. TJte square described on the hypotenuse of any **right-angled triangle is equivalent to the sum of the squares described on the other two sides. Let** ABC represent any right-angled triangle, the right angle at B; we are to prove that the square on AC... | |
| Benjamin Greenleaf - 1869 - 516 pages
...— b\ PROPOSITION XI. — THEOREM. 237. The square described on the hypothenuse of a fight-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 H on the hypothenuse... | |
| Charles Davies - Geometry - 1870 - 398 pages
...the language of algebra, thus, THEOREM XII. 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.** 1 • " / Of Bight Angled Triangles. Let BAC be a right angled triangle, right angled at A: then will... | |
| Richard Wormell - Geometry, Plane - 1870 - 304 pages
...quadrilateral AFDE, and then a rectangle equivalent to the triangle. The square on the hypothenuse **of a right-angled triangle is equivalent to the sum of the squares** on the other sides. 148. Describe the squares on the sides (fig. 126), and through D, the right-angle,... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...of the 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.** IZ LS Let the triangle ABC be right angled at C; then, the square AH, described upon the hypotenuse,... | |
| James De Mille - Adventure stories - 1871 - 370 pages
...added in the same tone, " 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** of the same." " And I," said Arthur, " find Arnold's Latin Exercises the worst. The most solemn thing... | |
| Edward Olney - Geometry - 1872 - 566 pages
...lines. OJ Fio. 370. oS Fio. 871. Fio. 873. VARIOUS DEMONSTRATIONS OF THE PYTHAGOREAN PROPOSITION. 668. **The square described on the hypotenuse of a right-angled...sum of the squares described on the other two sides.** 1st METHOD.— Let ABC be the given triangle, and ACEO the square described on the hypotenuse. Complete... | |
| Edward Olney - Geometry - 1872 - 96 pages
...ft EXEKCISES IN GEOMETRICAL INVENTION. YARIOUS DEMONSTRATIONS OP THE PYTHAGOREAN PROPOSITION. 668. **The square described on the hypotenuse of a right-angled...sum of the squares described on the other two sides.** 1st METHOD. — Let ABC be the given triangle, and AGED the square described on the hypotenuse. Complete... | |
| Edward Olney - Geometry - 1872 - 102 pages
...squares described on the lines. FIG. 370. VARIOUS DEMONSTRATIONS OF THE PYTHAGOREAN PROPOSITION. 668. **The square described on the hypotenuse of a right-angled...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.... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...of the 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 equal in area to... | |
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