| Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...EF(AB-HDC) area ot the trapezoid, is equal to > 1 ; (See Appendix, Problem IV.) PROP. VII. THEOREM. The square described on the hypotenuse of a right-angled...sum of the squares described on the other two sides. Let the triangle- be KDI, right angled at I. Describe squares onKD, KI, DI ; then we have to prove... | |
| James Bates Thomson - Geometry - 1844 - 268 pages
...the other two sides; in other words, BC^AB'-f-AC". Therefore, The square described on the hypolhcnuse of a right-angled triangle, is equivalent to the sum of the squares described on the other two sides. Cor. 1. Hence, by transposition, the square of one of the sides of a right-angled triangle is equivalent... | |
| Charles Davies - Geometrical drawing - 1846 - 254 pages
...triangle equal to ? In every right-angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a rightangled triangle, right-angled at C, then will the square D, described on AB,... | |
| James Bates Thomson - Arithmetic - 1846 - 354 pages
...principle in geometry, that 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. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle ABC is 4 feet, and the perpendicular 3... | |
| James Bates Thomson - Arithmetic - 1847 - 432 pages
...contains 25 sq. ft. Hence, the square described on the hi/pothenuse of any right-angled triangle, is equal to the sum of the squares described on the other two sides. DBS. Since the square of the hypothenuse BC, is 25, it follows that the , or 5, must be the hypothenuse... | |
| James Bates Thomson - Arithmetic - 1847 - 426 pages
...30. 34967ft-. 371 578. The square described on the hypothenuse of a rightangled triangle, is equal to the sum of the squares described on the other two sides. (Thomson's Legendre, B. IV. 11, Euc. I. 47.) The truth of this principle may be seen from the following... | |
| James Bates Thomson - Arithmetic - 1848 - 434 pages
...575-580.] SQUARE ROOT. 371 578. The square described on the hypothenuse of a rightangled triangle, is equal to the sum of the squares described on the other two sides. (Thomson's Legendre, B. IV. 11, Euc. I. 47.) The truth of this principle may be seen from the following... | |
| Almon Ticknor - Measurement - 1849 - 156 pages
...D, respectively equal to 0 C, 0 B, and therefore AC, BD, are bisected at the point 0. Fig. 25. 26. The square described on the hypotenuse of a right-angled...sum of the squares described on the other two sides. (Pig. B) Fig. A. Let the triangle ABC be right-angled at A. Having described squares on the three,... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
.... X E D ? GI D K PROPOSITION XI. THEOREM. 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 the triangle ABC be right angled at A. Having described squares on the three sides, let fall from... | |
| Charles Davies - Logic - 1850 - 398 pages
...class will be common to every individual of the class. For example : " the square on the hypothenuse of a right-angled triangle is equivalent to the sum...of the squares described on the other two sides," is a proposition equally true of every right-angled triangle: and "every straight line perpendicular... | |
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