| George Lees - 1826 - 272 pages
...right-angled triangle, SeC. QED Cor. If the square described upon one of the sides of a triangle, be **equivalent to the sum of the squares described upon the other two sides,** the angle contained by these twq sides is a right angle. ELEMENTS OF GEOMETRY. BOOK II. DEFINITIONS.... | |
| Timothy Walker - Geometry - 1829 - 158 pages
...method just explained ; and the area of this triangle will be the area of the polygon. 108. THEOKEM. — **The square described upon the hypothenuse of a right...of the squares described upon the other two sides.** This is the celebrated proposition, with the discovery of which Pythagoras is said to have been so... | |
| James Hayward - Geometry - 1829 - 172 pages
...we have « 2 =: b 2 + c 2 , that is — 7Vtc square described upon the hypothenuse of a right-angled **triangle, is equivalent to the sum of the squares described upon the other two sides.** 173. We may demonstrate this truth from the areas immediately, without referring the lines to numbers,... | |
| Timothy Walker - Geometry - 1829 - 129 pages
...of the triangle, we have the area of the polygon. 108. — The square described upon the hypothemise **of a • right triangle is equivalent to the sum of the squares described upon** tht other twn sides — . This is the celebrated proposition, with the discovery of which Pythagoras... | |
| Timothy Walker - Geometry - 1831 - 166 pages
...by the method just explained ; and the area of this triangle will be the area of the polygon. 108. **THEOREM. — The square described upon the hypothenuse...of the squares described upon the other two sides.** This is the celebrated proposition, with the discovery of which Pythagoras is said to have been so... | |
| Euclid - Euclid's Elements - 1833 - 183 pages
...PROP. XLVIII. THEOR. Fig. 72. If the square described upon one side (AC] of a triangle (ABC) be equal **to the sum of the squares described upon the other two sides** (AB andBC), the angle (ABC) opposite to that side is a right angle. 1 i ) SchoL From the point B draw... | |
| Great Britain. Council on Education - 1845
...shall contain a greater angle. 60.*If the square described upon one of the sides of a trinngle be equal **to the sum of the squares described upon the other two sides** of it, the angle contained by these two sides is a right angle. 61. If a straight line be divided into... | |
| Benjamin Peirce - Geometry - 1847 - 150 pages
...Corollary. The area of a trapezoid is the product of its altitude by the line joining the middle points **of the sides which are not parallel. ' 256. Theorem....fall upon AC the perpendicular BDE, and the square** ACSR is divided into the two rectangles ADER and DCES. Now the area of ADER is, by § 242, AD X AR... | |
| Education - 1847 - 508 pages
...parts, are between the same parallels. 3. If the square described upon one side of a triangle be equal **to the sum of the squares described upon the other two sides** of it, the angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight... | |
| Great Britain. Committee on Education - 1850 - 914 pages
...right angles as the figure has sides. 2. If the square described upon one side of a triangle be equal **to the sum of the squares described upon the other two sides** of it, the angle contained by these two sides is a right angle. 3. In every triangle the square of... | |
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