 | Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...BC; hence any two sides of a spherical triangle are together greater than the remaining side. 1 1. The sum of the three sides of a spherical triangle is less than the circumference of a great circle. For the solid angle at 0 is contained by plane angles, the sum of which is always less than four right... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...distance between B and A can lie out of the arc of the great circle BDA. PROPOSITION III. THEOREM. The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD,... | |
 | Education - 1849 - 682 pages
...The solidity of a cone is equal to the area of its base multiplied by a third of its altitude. 10. The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Plane and Spherical Trigonometry. 1. What is meant by the secant and cosecant of an arc t 2. What is... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...itself the shortest distance between its two extremities. PROPOSITION XVII. THEOREM. The sum of all the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle: produce the sides AB, AC till they meet again in D. The arcs ABD,... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...hence, any side of the triangle ABC is less than the sum of the other two. THEOREM II. The sum of all the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle ; produce the sides AB, AC till they meet again in D. The arcs ABD,... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...hence, any side of the triangle ABC is less than the sum of the other two. THEOREM II. The sum of all the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle ; produce the sides AB, AC till they meet again in D. The arcs ABD,... | |
 | Charles Hutton - Mathematics - 1860 - 1020 pages
...the arcs AB, AC, BCt which measures these angles, is less than the sum of the two others. PROP. Till. The sum of the three sides of a spherical triangle is less than the етят/тж» of a great circle. Let ABC be any spherical triangle. Produce the sides AB, AC, to... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...angles, and bound the spherical polygon, is less than the circumference of a great circle. 526. Cor. The sum of the three sides of a spherical triangle is less than the circumference of a great circle, since a triangle is a polygon of three sides. PROPOSITION V. — THEOREM. 527. The extremities of a... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...angles, and bound the spherical polygon, is less than tho circumference of a great circle. 526. Cor. The sum of the three sides of a spherical triangle is less than the circumference of a great circle, since a triangle is a polygon of three sides. PROPOSITION V. — THEOREM. 527. Tlie extremities of... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...angles, and bound the spherical polygon, is less than the circumference of a great circle. 526. Cor. The sum of the three sides of a spherical triangle is less than the circumference of a great circle, since a triangle is a polygon of three sides. PROPOSITION V. — THEOREM. 527. The extremities of a... | |
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ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be... 
