| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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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