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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 Geometry and Trigonometry from the Works of A.M. Legendre ... - Page 97
by Charles Davies - 1854 - 432 pages
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The Modern Preceptor ; Or, a General Course of Education, Volume 1

John Dougall - 1810
...the 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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...— 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, let...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 272 pages
...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....
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...- ; and multiplying both sides by a, we have a2 = 62 -f- c8, that is — The 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...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...PROPOSITION XLVIII. THEOREM. — If the square described on one of the sides of a triangle, be equal to the sum of the squares described on the other two sides of it; the angle made by those two sides is a right angle. Let ABC be a triangle, which is such that...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 386 pages
...LCBI 78 GEOMETRY, PROPOSITION XI. THEOREM. 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 the triangle ABC be right angled at A. Having described squares on the three sides, let fall from A,...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 252 pages
...4=90 degrees. 10. In every right angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a right angled triangle, right angled at C, then will the square D described on AB...
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Proceedings

Scotland free church, gen. assembly - 1847 - 552 pages
...makes the alternate angles equal. 2. If the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...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...the squares described on the other two sides. Let the triangle be Fig. 64. KDI, right angled at I. Describe squares on KD, KI, DI ; then we have to prove...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...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 triangle is equivalent...
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