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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. "
An Elementary Treatise on Plane and Solid Geometry - Page 79
by Benjamin Peirce - 1871 - 150 pages
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Elements of Arithmetic, Algebra, and Geometry

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....
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Elements of Geometry: With Practical Applications, for the Use of Schools

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...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

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,...
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Elements of Geometry: With Practical Applications, for the Use of Schools

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...
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Elements of Geometry: With Practical Applications, for the Use of Schools

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...
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The First Six Books of the Elements of Euclid: With Notes

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...
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Report of the Committee of Council on Education (England and Wales ..., Volume 2

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...
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An Elementary Treatise on Plane and Solid Geometry

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...
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The English Journal of Education, Volume 1

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...
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Minutes ...: Correspondence, Financial Statements, Etc., and ..., Volume 2

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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