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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.
Elements of Plane Geometry: For the Use of Schools - Page 63
by Nicholas Tillinghast - 1844 - 96 pages

Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1869 - 276 pages
...and (a + b) x (a — b) = a * — b\ THEOREM XXXIX. TJte square described on the hypotenuse of any right-angled triangle is equivalent to the sum of the squares described on the other two sides. Let ABC represent any right-angled triangle, the right angle at B; we are to prove that the square on AC...

Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...— b\ PROPOSITION XI. — THEOREM. 237. The square described on the hypothenuse of a fight-angled triangle is equivalent to the sum of the squares described on the other two sides. Let ABC be a right-angled triangle, having the right angle at A ; then the square described H on the hypothenuse...

Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 398 pages
...the language of algebra, thus, THEOREM XII. 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. 1 • " / Of Bight Angled Triangles. Let BAC be a right angled triangle, right angled at A: then will...

An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...quadrilateral AFDE, and then a rectangle equivalent to the triangle. The square on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares on the other sides. 148. Describe the squares on the sides (fig. 126), and through D, the right-angle,...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...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 upon the hypotenuse,...

The Boys of Grand Pré School

James De Mille - Adventure stories - 1871 - 370 pages
...added in the same tone, " 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 of the same." " And I," said Arthur, " find Arnold's Latin Exercises the worst. The most solemn thing...

A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 566 pages
...lines. OJ Fio. 370. oS Fio. 871. Fio. 873. VARIOUS DEMONSTRATIONS OF THE PYTHAGOREAN PROPOSITION. 668. The square described on the hypotenuse of a right-angled...sum of the squares described on the other two sides. 1st METHOD.— Let ABC be the given triangle, and ACEO the square described on the hypotenuse. Complete...

A Treatise on Special Or Elementary Geometry: In Four Parts ..., Part 3

Edward Olney - Geometry - 1872 - 96 pages
...ft EXEKCISES IN GEOMETRICAL INVENTION. YARIOUS DEMONSTRATIONS OP THE PYTHAGOREAN PROPOSITION. 668. The square described on the hypotenuse of a right-angled...sum of the squares described on the other two sides. 1st METHOD. — Let ABC be the given triangle, and AGED the square described on the hypotenuse. Complete...