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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, After Legendre, with a Selection of Geometrical ... - Page 107
by Charles Scott Venable - 1881
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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 - Euclid's Elements - 1833 - 168 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 - 1836 - 394 pages
...CB I X . IP C VI £ J D a » I j B PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on tlte other two sides, Ixet the triangle ABC be right nngled at A. Having described squares on the three...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 376 pages
...the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on tha other two sides. Let the triangle ABC be right angled at A. Having described squares on the three sides, let fall from A, on the hypothenuse, the perpendicular AD, which...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 382 pages
...b)—a9 — b3. D K LCBI 78 GEOMETRY, PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum...Let the triangle ABC be right angled at A. Having described squares on the three sides, let fall from A, on the hypothenuse,. the perpendicular AD, which...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 262 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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Lecture on the History of Mathematics

Francis Henney Smith - Mathematics - 1841 - 46 pages
...indebted for the important proposition which forms the 47th of Euclid, that the square on the hypothenuse of a right angled triangle, is equivalent to the sum of the squares on the other two sides ; and also that of all plane bodies, the circle has the greatest area under...
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Proceedings

Scotland free church, gen. assembly - 1847 - 554 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 - 108 pages
...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 the square KDCA...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...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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