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" In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side. "
Elements of Geometry - Page 168
by Adrien Marie Legendre - 1841 - 235 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...then cannot be supposed unequal to AC; therefore the sides AB, AC, opposite to the equal angles It. C, are equal. 484. Scholium. It is evident, from the...triangle to the middle of the base, is perpendicular lo this base, and divides the angle opposite into two equal parts. THEOREM. Fig. 332. 485. In any spherical...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...demonstration proves the angle BAD=DAC, and the angle BDA=ADC. Hence the two 172 last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to that base, and bisects the opposite angle. PROPOSITION XVI. THEOREM. In a spherical...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...BC, are equal to the two AC, BC ; and the angle OBC contained by the first is equal to the angle ACB contained by the second. Consequently the two triangles...and divides the angle opposite into two equal parts. I s~ THEOREM. I ' 485. In any spherical triangle ABC (fig. 232), if the angle A is greater than the...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...cannot be supposed unequal to AC; therefore the sides AB, AC, opposite to the equal angles B, C, arc equal. 484. Scholium. It is evident, from the same...from the vertex of an isosceles spherical triangle to ihe middle of the base, is perpendicular to this base, and divides the angle opposite into two equal...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pages
...DAC, and the angle BDA = ADC. Consequently the two last arc right angles ; therefore, the arc draxn from the vertex of an isosceles spherical triangle to the middle of iht base, is perpendicular to this base, and divides the angle opposite into two equal parts. THEOREM....
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - Plane trigonometry - 1828 - 317 pages
...sides, they will be symmetrically equal, and the proposition has been already proved. (152.) Cor. Hence the arc drawn from the vertex of an isosceles spherical triangle to the point of bisection of the base, bisects the vertical angle, and is perpendicular to the base. * In...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...demonstration proves the angle BAD = DAC, and the angle BDA— ADC. Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to that base, and bisects the vertical angle. PROPOSITION XIV. THEOREM. In any spherical...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 159 pages
...Corollary. Also the angle ADB = ADC, and, therefore, each is a right angle ; and also DAB = DAC, that . is> The arc, drawn from the vertex of an isosceles spherical...triangle to the middle of the base, is perpendicular to the base, and bisects the angle at the vertex. 454. Corollary. An equilateral spherical triangle is...
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A Series on Elementary and Higher Geometry, Trigonometry, and ..., Parts 3-4

Nathan Scholfield - Conic sections - 1845
...demonstration proves the angle BAD =DAC, and the angle BDA— ADC. Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle. PROPOSITION XVI. THEOREM. In any spherical...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 232 pages
...demonstration proves the angle BAD =DAC, and the angle BDA=ADC. Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle. PROPOSITION XVI. THEOREM. In any spherical...
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