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In any triangle, the difference of the squares of the two sides w equal to the difference of the squares of the segments of the base, or of the two lines or distances included between the extremes of the base and the perpendicular.
A Course of Mathematics: For the Use of Academies as Well as Private Tuition - Page 301
by Charles Hutton - 1812
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## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 318 pages
...isosceles; BC2=2AB'=2AC2 ; therefore, BC^AB/ 2. COR. 3. Hence, also, if two right angled triangles have two sides of the one, equal to two corresponding sides...third sides will also be equal, and the triangles will be identical. PROP. XLVIII. THEOR. If the square described upon one of the sides of a triangle,...
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## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 390 pages
...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 sum and difference of the...
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## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...perpendicular be drawn to the opposite side, the difference of the squares of the sides containing that angle is equal to the difference of the squares of the segments of the side on which the perpendicular falls. It is manifest that the difference of the squares of AC and...
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## Elements of geometry

Adrien Marie Legendre - Mathematics - 1841 - 235 pages
...drawn from the vertex A perpendicular to the base, the difference of the squares of the sides AB and AC is equal to the difference of the squares of the segments of the base, BD andZ>C. (186.) Fig. 340. Q. LII. If an equilateral triangle ABC, be inscribed in a circle, the square...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...isosceles; BC2=2AB2=2AC2 ; therefore, BC^AB/ 2. COR. 3. Hence, also, if two right angled triangles have two sides of the one, equal to two corresponding sides...third sides will also be equal, and the triangles will be identical. PROP. XLVIII. THEOR. If the square described upon one of the sides of a triangle,...
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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...triangle, a perpendicular fall upon the base or the base produced, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. 74. If from the middle point of one of the sides of a right-angled triangle a perpendicular be drawn...
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## The first six and the eleventh and twelfth books of Euclid's Elements; with ...

James Thomson - Geometry - 1845 - 358 pages
...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 sum and difference of the...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1846 - 317 pages
...isosceles; BC2=2AB2=2AC2 ; therefore, BC—AB-/ 2. COR. 3. Hence, also, if two right angled triangles have two sides of the one, equal to two corresponding sides...third sides will also be equal, and the triangles will be identical. PROP. XLVIII. THEOR. If the square described upon one of the sides of a triangle,...
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## Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 103 pages
...other side; for (Alg. 13) a2-F = (a+l) (ab). Corol. 2. Hence, also, if two right-angled triangles have two sides of the one equal to two corresponding sides...also be equal, and the triangles identical. THEOREM XXVII.* In any triangle, the difference of the squares of the two sides is equal to the difference...
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## Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...hypothenuse and other side (B. II, Prop. vn). Cor. 2. Hence, also, if two right-angled triangles have two sides of the one equal to two corresponding sides of the other, their third sides will be equal, and the triangles themselves equal. Cor. 3. The square on the diagonal of a square is double...
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