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" 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. "
Solid Geometry - Page 383
by George Albert Wentworth - 1902 - 218 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...ZXBCare mutually equilateral. Hence they are mutually equiangular. § 603 Therefore ZA = /. BQED 608. COR. — The arc of a great circle drawn from the vertex of an isosceles triangle to the middle of the base bisects the vertical angle and is perpendicular to the base. EXERCISES....
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...BAD = DAC, and the angle BDA = ADC. Consequently the two last are right angles ; therefore, the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular lo this base, and divides the angle opposite into two equal parts. THEOREM. Fig. 332....
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...BAD — DAC, and the angle BDA = ADC. Consequently the two last are right angles ; therefore, the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to this base, and divides the angle opposite into two equal parts. I s~ THEOREM. I...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 570 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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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...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 - 216 pages
...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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...BAD = DAC, and the angle BDA — ADC. Consequently the two last are right angles ; therefore, the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to this base, and divides the angle opposite into two equal parts. THEOREM. . 232....
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...proves the angle BAD =DAC, and the angle BDA=ADC. Hence the two last are ri^rht 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...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 244 pages
...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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