 | Benjamin Peirce - Geometry - 1865 - 184 pages
...product of its altitude by the line joining the middle points of the sides which are not parallel. >v 256. Theorem. The square described upon the hypothenuse...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... | |
 | Leland A. Webster - Sociology - 1866 - 372 pages
...could the square described upon the hypothenuse of a right-angled triangle be otherwise than precisely equivalent to the sum of the squares described upon the other two sides. The integral and differential calculus of this mathematics, however, as manifested in the complex activities... | |
 | Benjamin Peirce - Geometry - 1869 - 194 pages
...we have DO = TB ; whence and also HI=AT = AB me sum of which is 2H1 = AB + CD, or • HI= i (AB -f CD). 255. Corollary. The area of a trapezoid is the...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 JR... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...homologous lines of the polygons. PROPOSITION X.— THEOREM. 25. The square described upon the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides. IZ LS Let the triangle ABC be right angled at C; then, the square AH, described... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...the segments of the base. THEOREM XII. 27. The square described on the hypothenuse of a right angle is equivalent to the sum of the squares described upon the other two sides. Let ABC be a triangle rightangled at B ; then TO* = TJ? + WC* On the three sides construct squares,... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...the segments of the base. THEOREM XII. 271 The square described on the hypothenuse of a right angle is equivalent to the sum of the squares described upon the other two sides. Let AB C be a triangle rightangled at B ; then AC* = AJ/ -j- B C" On the three sides construct squares,... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...homologous lines of the polygons. PROPOSITION X.— THEOREM. 25. The square described upon the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides. ia a Let the triangle ABC be right angled at C; then, the square AH, described... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...square ABED. PBOPOSITION XLVIII. If the square described upon one of the sides of a triangle bo equal to the sum of the squares described upon the other two sides, the angle contained by these two sides is a right angle. For the construction employed in this proposition... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...mean proportional between the segment* of the hi/pothenuse. ^ THEOREM XII. 27. The square described on the hypothenuse of a right triangle is equivalent...of the squares described upon the other two sides. Let ABG be a triangle rightangled at B; then On the three sides construct squares, draw BD perpendicular... | |
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The square described upon the hypothenuse of a right triangle is equivalent to the sum of the squares described upon the other two sides. 
