| American Academy of Arts and Sciences - Humanities - 1913 - 1034 pages
...and the other diagonal is a singular line of the other class. XIX. Pythagorean Theorem. The area of **the square on the hypotenuse of a right triangle is equal to the** difference of the areas of the squares on the other two sides. For by XVIII the diagonals of the squares... | |
| American Academy of Arts and Sciences - Humanities - 1913 - 1092 pages
...and the other diagonal is a singular line of the other class. XIX. Pythagorean Theorem. The area of **the square on the hypotenuse of a right triangle is equal to the** difference of the areas of the squares on the other two sides. For by XVIII the diagonals of the squares... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...the diameter and the segment adjacent to that chord. PBOPOSITION XIV.— THEOREM. 48. The square of **the hypotenuse of a right triangle is equal to the sum of** the squares of the other two sides. Let ABC be right angled at C; then, AB' = A For, by the preceding... | |
| Philosophy - 1871 - 396 pages
...bodies or in the infinite world of conceivable atoms ; and so, also, the theorem that the square upon **the hypotenuse of a right triangle is equal to the sum of** the squares upon its other two sides, is necessary in its truth, and universal in its application,... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...the diameter and the segment adjacent to that chord. PROPOSITION XIV.— THEOREM. 48. The square of **the hypotenuse of a right triangle is equal to the sum of** the squares of the other two sides. Let ABC be right angled at C; then, IB* = AC-' + BC\ For, by the... | |
| Samuel Mecutchen, George Mornton Sayre - Arithmetic - 1877 - 200 pages
...corners; what is the area of the field? Note. — It is established by Geometry that "The square of **the hypotenuse of a right triangle is equal to the sum of** the squares of the other two sides." Hence the following : — To find the hypotenuse of a right triangle.... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...squares of two lines is 81, and one of the lines is 12; required the other. THEOREM XL The square of **the hypotenuse of a right triangle is equal to the sum of** the squares of the other two sides. Let ABC be a right triangle, whose hypotenuse is AB; then will... | |
| James Wallace MacDonald - Geometry - 1889 - 80 pages
...SCHOLIUM. Compare (a + b) (a — b) = a* — P. Proposition XI. A Theorem. 246. The square described **on the hypotenuse of a right triangle is equal to the sum of** the squares of the other two sides. COROLLARY. The square described on either side forming the right... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...SCHOLIUM. Compare (a + b) (a — b) = a1 — 63. Proposition XI. A Theorem. 246. The square described **on the hypotenuse of a right triangle is equal to the sum of** the squares of the other two - sides. COROLLARY. The square described on either side forming the right... | |
| Charles Austin Hobbs - Arithmetic - 1889 - 370 pages
...triangle, when the sides are respectively 12cm, 15cm, and 20cm. RIGHT TRIANGLES. ito. The square of **the hypotenuse of a right triangle is equal to the sum of** the squares of the other two sides. This principle is illustrated in the annexed diagram. To find the... | |
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