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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. "
Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ... - Pągina 141
per Eli Todd Tappan - 1868 - 420 pągines
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1822 - 394 pągines
...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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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 168 pągines
...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 - 1838 - 382 pągines
...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...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - 1840 - 262 pągines
...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 - 554 pągines
...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 Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - 1844 - 268 pągines
...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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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - 1844 - 108 pągines
...Appendix, Problem IV.) PROP. VII. THEOREM. 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. Let the triangle be KDI, right angled at I. Describe squares onKD, KI, DI ; then we have to prove that...
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Elements of Drawing and Mensuration Applied to the Mechanic Arts: A Book for ...

Charles Davies - 1846 - 254 pągines
...triangle equal to ? 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 rightangled triangle, right-angled at C, then will the square D, described on AB,...
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Practical Arithmetic, Uniting the Inductive with the Synthetic Mode of ...

James Bates Thomson - 1846 - 354 pągines
...principle in geometry, that 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. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle ABC is 4 feet, and the perpendicular 3...
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Higher Arithmetic: Or, The Science and Application of Numbers; Combining the ...

James Bates Thomson - 1847 - 432 pągines
...contains 25 sq. ft. Hence, the square described on the hi/pothenuse of any right-angled triangle, is equal to the sum of the squares described on the other two sides. DBS. Since the square of the hypothenuse BC, is 25, it follows that the , or 5, must be the hypothenuse...
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