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" The difference of the squares of two sides of a triangle is equal to the difference of the squares of the segments made by the altitude upon the third side. "
ELEMENTARY SYNTHETIC GEOMETRY OF THE POINT, LINE AND CIRCLE IN THE PLANE - Page 124
by N. F. DUPUIS, M.A., F.R.S.C. - 1894
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 390 pages
...maximum when the line is bisected. Cor. 4. Since (I. 47. cor. 4.) the difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base, it follows, from the first corollary above, that the rectangle under the...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...maximum when the line is bisected. Cor. 4. Since (I. 47, cor. 4) the difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base, it follows, from the first corollary above, that the rectangle under the...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...and also one equal to the difference of two given squares. 49. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular from the opposite angle. 50. The three straight...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...which it is divided is equal to the square on the other side. 63. The difference of the squares on the sides of a triangle is equal to the difference of the squares on the segments of the base made by a perpendicular from the opposite angle. 64. The square on the side subtending...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...BC will be the difference of the given squares. Cor. 3. — a. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular. For the square of AB is equal to the squares of...
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The Elementary Geometry of the Right Line and Circle ... With Exercises

William Alexander Willock - 1875 - 172 pages
...of CP remains equal to the rectangle AP-BP, as stated. Con. 3. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by the perpendicular from the vertical angle upon the base. Let ACB...
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Exercises on Euclid and in modern geometry, New ed., revised

James McDowell - 1878
...rectangle under the hypotenuse and its adjacent segment 28 40. The difference of the squares on the sides of a triangle is equal to the difference of the squares on the segments of the base, made by the perpendicular from the vertex on the base or the base produced, and...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 399 pages
...c), the required expression. THEOREMS FOR EXERCISE. THEOREM 1. The difference of the squares upon any two sides of a triangle is equal to the difference of the squares of the projections of these sides upon the third side. THEOREM 2. The sum of the squares upon the diagonals...
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Geometrical Exercises for Beginners

Samuel Constable - Geometry - 1882 - 203 pages
...each side add AD * , and BD.DC+ OD* + AD* = OA* + AD*; PROP. 11. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by the perpendicular from the vertex on the base. B Let ABC be any...
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The elements of plane geometry, Volume 1

Mathematical association - Geometry, Plane - 1884
...at E : shew that the triangle BEC is double the triangle ABE. *39- The difference of the squares on two sides of a triangle is equal to the difference of the squares on the segments of the base made by a perpendicular from the opposite vertex. *4o. If O be a point in the...
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