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" If the square described on one side of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by these two sides is a right angle. "
Gibson's London matriculation guide, by J. Gibson [and others]. - Page 33
1882
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...PROPOSITION XI. THEOREM. CBK The square described on the hypothenuse of a right-angled triangle, is equal to the sum of the squares described on the other two sides. Let ABC be a triangle, right-angled at A : then will = Al? + AC\ Construct the square BG on the side...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...compared? 346. COR. 3. — 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. DEM.— From Oar. 1, AC* = AB x AD and also CB* = AB x DB. Therefore, adding, AC* + CB* =AB (AD + DB)...
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A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - Geometry - 1872 - 102 pages
...PYTHAGOREAN PROPOSITION. 668. 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. Fio. 372. 1st METHOD.—Let ABC be the given triangle, and ACED the square described on the hypotenuse....
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...346. COR.. 3. — .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. DEM.— From Cor. 1, AC" = AB x AD and also CBa = AB x DB. Therefore, adding, AC4 + CB =AB (AD + DB)...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...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 upon the hypotenuse,...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - Geometry - 1873 - 288 pages
...AB + AC + 2ACXAD. 413. Corollary — If the square described on one side of a triangle is equivalent to the sum of the squares described on the other two sides, then the opposite angle is a right angle. For the last two theorems show that it can be neither acute...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...EQ THEOREM IX. 195. 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 ABC be a right-angled M triangle, having the right angle at A . then the square described on the...
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The Bombay university calendar, Volume 1

Bombay city, univ - 1874 - 648 pages
...unlimited length, from a given point without it. 2. Show that if the square described on one of the sides 8 of a triangle be equal to the sum of the squares described on the other two sides of it, the anglo contained by these two sides is a right angle. 3. In every triangle the square on...
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Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 25-32

United States Naval Academy - 1874 - 888 pages
...sides. 1. Prove that the square described on the hypothenu.se of a right triangle is ci ; ni valent to the sum of the squares described on the other two sides. .">. Prove that a triangular pyramid is one-third of a triangular prism of the samo base and altitnde, and that the...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...proved. c PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right-angled triangle, is equal to the sum of the squares described on the other two sides. , Let ABC be a triangle, right-angled at A : then will SO* = AS2 + AC2. Construct the square BG on...
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