| William Chauvenet - Geometry - 1871 - 368 pages
...proportional between 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, = A~U' + BC*. For, by the preceding... | |
| Philosophy - 1871
...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 - Geometry - 1872 - 368 pages
...proportional between 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
...length, joining opposite 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 - 267 pages
...difference of the 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... | |
| Charles Austin Hobbs - Arithmetic - 1889 - 343 pages
...opposite sides of a 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... | |
| James Wallace MacDonald - Geometry - 1889 - 63 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 - 65 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... | |
| Edward Albert Bowser - Geometry - 1890 - 393 pages
...projection of AB upon the line XY Proposition 25. Theorem. 327. The square of the number which measures **the hypotenuse of a right triangle is equal to the sum of** the squares of the numbers which measure the other two sides. Hyp. Let ABC be a rt. A , with rt. Z... | |
| George Clinton Shutts - Geometry - 1894 - 389 pages
...find X? § 317. 4. Construct the rectangle. PROPOSITION X. 341. Theorem. The square described upon **the hypotenuse of a right triangle is equal to the sum of** the squares described upon the other two sides. Let ABC represent a right triangle, whose hypotenuse... | |
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