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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...: Translated from the French for the Use of the ... - Σελίδα 166
των Adrien Marie Legendre, John Farrar - 1825 - 224 σελίδες
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - 1845 - 542 σελίδες
...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...

Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - 1845 - 506 σελίδες
...BAD =DAC, and the angle BDA=ADC. Hence the two last are right angles ; hence the arc drawn from Ike 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...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1847 - 204 σελίδες
...ADB^ADC, and, Isosceles Triangle. therefore, each is a right angle ; and also DAIi = 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. 455. Corollary. An equilateral spherical triangle is...

Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 326 σελίδες
...that the angle BAD = DAC, and the angle BDA = ADC. Hence the two last are right angles ; consequently the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to that bose, and bisects the opposite angle. X 2 PROPOSITION XXIX. THEOREM. In any...

Elements of Geometry and Conic Sections

Elias Loomis - 1849 - 252 σελίδες
...and the angle ADB to the angle ADC ; therefore each of the last two angles is a right angle. Hence 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 vertical angle. PROPOSITION XVII. THEOREM. In a spherical triangle, the greater...

Elements of Geometry: With, Practical Applications

George Roberts Perkins - 1850 - 332 σελίδες
...that the angle BAD=DAC, and the angle BDA - ADC. Hence the two last are right-angles ; consequently 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 XXIX. THEOREM. In any spherical...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1852 - 436 σελίδες
...parts (P. 10), the angle BAD=DAC, and BDA— ADC: consequently, ADB and ADC, 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 XII. THEOEEM. In any spherical,...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 436 σελίδες
...parts (P. 10), the angle BAD=DAC, and BDA — ADC: consequently, ADB and ADC, 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. BOOK IX. 237 PROPOSITION XII. THEOREM....

Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1856 - 460 σελίδες
...that the angle BAD = DAC, and the angle BDA = ADC. Hence the two last are right angles ; consequently, 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. THEOREM XIv. In any spherical triangle,...

Elements of Geometry and Conic Sections

Elias Loomis - 1858 - 256 σελίδες
...and the angle ADB to the angle ADC ; therefore each of the last two angles is a right angle. Hence 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 vertical angle. In a spherical triangle, the greater side is opposite the...




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