 | John Dougall - 1810 - 734 Seiten
...square of the whole line AB, or 6 X6 = 36. PROP. XVTII. for. t, Plate 2. The square constructed on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares constructed or the two sides containing the right angle. Let ABC be a trianale, having a right angle... | |
 | Adrien Marie Legendre - 1822 - 394 Seiten
...— BC) = AB2 — BC*. LFGI E JJ 57 PROPOSITION XI. THEOREM. The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of the squares described on the two sides. Let the triangle ABC be rightangled at A. Having formed squares on the three sides,... | |
 | George Lees - 1826 - 276 Seiten
...polygons are to one another as the squares of their corresponding sides. Cor- 2. The rectilineal figure described upon the hypothenuse of a right-angled triangle, is equivalent to the sum of the similar rectilineal figures described upon the sides containing the right angle. i •;.•_,, PROP.... | |
 | Timothy Walker - 1829 - 156 Seiten
...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... | |
 | Euclid - 1833 - 216 Seiten
...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... | |
 | Benjamin Peirce - 1837 - 216 Seiten
...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),... | |
 | James Bates Thomson - 1844 - 268 Seiten
...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... | |
 | Nicholas Tillinghast - 1844 - 110 Seiten
...equal to > — ; (See Appendix, Problem IV.) 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,... | |
 | Great Britain. Council on Education - 1845 - 696 Seiten
...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 - 1847 - 204 Seiten
...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. Proof. Let squares be constructed upon the three sides of the right triangle ABC (fig. 130), right-angled... | |
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The square described upon the hypothenuse of a rightangled triangle is equivalent to the sum of the squares described upon the other two sides. 
