| Euclides - 1821 - 294 pages
...side is the same.. For it is the O2 of the perpendicular. ,. • PROP. 48. TIIEOR. Jf the square of **one side of a triangle be equal to the sum of the squares** of the other troo sides, the angle opposite to that side is a right angle. From the vertex of this... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...to the turn of the squares of the sides which contain that angle : and conversely, if the square of **one side of a triangle be equal to the sum of the squares** of the other two sides, the angle contained by these two sides shall be a right angle. Let AB С be... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...was to be demonstrated. PROPOSITION XLVIII. THEOREM. — If the square described on one of the sides **of a triangle, be equal to the sum of the squares described on the other two sides** of it; the angle made by those two sides is a right angle. Let ABC be a triangle, which is such that... | |
| Mathematics - 1835 - 684 pages
...to the sum of the squares of the sides which contain that angle : and conversely, if the square of **one side of a triangle be equal to the sum of the squares** of the other two sides, the angle contained by those two sides shall be a right angle. Let ABC be a... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...(as in Simpson,) which only makes the figure unnecessarily complicated. PROPOSITION XLVIII. Theorem. **If the square described on one side of a triangle be equal to the** squares described upon the other two ; the angle contained by these two sides is a right angle. T>... | |
| Adrien Marie Legendre - Geometry - 1838 - 384 pages
...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... | |
| Charles Davies - Geometrical drawing - 1840 - 252 pages
...degrees, and 4=90 degrees. 10. 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 right angled triangle, right angled at C, then will the square D described on AB... | |
| Scotland free church, gen. assembly - 1847 - 552 pages
...straight lines, it makes the alternate angles equal. 2. If the square described on one of the sides **of a triangle be equal to the sum of the squares described on the other two sides,** these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...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... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...PROP. VII. THEOREM. The square described on the hypotenuse of a right-angled triangle is equivalent **to the sum of the squares described on the other two sides.** Let the triangle be Fig. 64. KDI, right angled at I. Describe squares on KD, KI, DI ; then we have... | |
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