 | Horatio Nelson Robinson - 1869 - 276 σελίδες
...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 σελίδες
...— 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 - 1870 - 392 σελίδες
...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 - 1870 - 304 σελίδες
...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 - 1871 - 380 σελίδες
...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 - 1871 - 370 σελίδες
...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 - 1872 - 562 σελίδες
...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 - 1872 - 96 σελίδες
...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 - 1872 - 102 σελίδες
...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 - 1872 - 382 σελίδες
...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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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. 
