| Peter Fleming - Surveying - 1815 - 164 pages
...half of a parallelogram, when they stand upon the same base, and are between the same parallels, 10. **The square described upon the hypothenuse of a right angled triangle, is equivalent to the** square of the other two sides, 11. If a right line be divided iuto any two parts, then will the square... | |
| George Lees - 1826
...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. I.... | |
| Timothy Walker - Geometry - 1829 - 129 pages
...be the area of the polygon. 108. THEOKEM. — The square described upon the hypothenuse of a right **triangle is equivalent to the sum 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 - 1829
...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,... | |
| 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... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...(a—b)= a*— 62. CB I X . IP C VI £ J D a » I j B PROPOSITION XI. THEOREM. The square described on **the hypothenuse of a right angled triangle is equivalent to the sum of the squares described** on tlte other two sides, Ixet the triangle ABC be right nngled at A. Having described squares on the... | |
| Benjamin Peirce - Geometry - 1837 - 159 pages
...the sides which are not parallel. 256. Theorem. The square described upon the hypothenuse of a right **triangle is equivalent to the sum of the squares described upon the other two sides.** Demonstration. Let squares be constructed upon the three sides of the right triangle ABC (fig. 130),... | |
| Francis Henney Smith - Mathematics - 1841 - 35 pages
...philosopher we are indebted for the important proposition which forms the 47th of Euclid, that the square on **the hypothenuse of a right angled triangle, is equivalent to the sum of the squares** on the other two sides ; and also that of all plane bodies, the circle has the greatest area under... | |
| Nathan Scholfield - 1845
...are in that ratio, (Prop. XVII. Cor. 6.) BOOK IT. PROPOSITION XXIV. THEOREM. %'he square described on **the hypothenuse of a right angled triangle is equivalent to the sum of the** squ-ires described on the other two sides. Let the triangle ABC be right angled at A. Having described... | |
| 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... | |
| |