 | Mathematics - 1835 - 684 pages
...that is, to a right angle.* Therefore, &c. Cor. 1. In a right-angled triangle, the square of either of the two sides is equal to the difference of the squares of the hypotenuse and the other side. Cor. 2. It appears, from the demonstration, that if a perpendicular... | |
 | John Playfair - Euclid's Elements - 1837 - 332 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, James Thomson - Geometry - 1837 - 410 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 - 192 pages
...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 - Geometry - 1841 - 288 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 - 332 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,... | |
 | Euclides - 1845 - 546 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 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 - 248 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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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. 
