 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.  Plane and Solid Geometry - Page 383by George Albert Wentworth - 1899 - 473 pagesFull view - About this book
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...circle drawn from the vertex of an isosceles triangle to the middle of the base, bisects the rertical angle, is perpendicular to the base, and divides the triangle into two symmetrical triangles. PROPOSITION VIII. THEOREM. \" 274. The shortest distance on the surface of a sphere between any two... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...Hence, by Cor. 7, they are mutually equiangular, and the Sph. ^s at the base are equal, QED 273. COR. 9. The arc of a great circle drawn from the vertex of an isosceles triangle to the middle of the base, bisects the vertical angle, is perpendicular to the base, and divides... | |
 | William Chauvenet - 1893 - 340 pages
...an isosceles spherical triangle the angles opposite the equal sides are equal. 2. Theorem.—The arc drawn from the vertex of an isosceles spherical triangle to the middle point of the base is perpendicular to the base, and bisects the vertical angle. 3. Theorem.—If two... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...triangle are equal, the triangle is isosceles. Suggestion. Construct the polar of the given A. Ex. 394. The arc of a great circle drawn from the vertex of an isosceles spherical triangle to the middle point of the base is perpendicular to the base and bisects the vertical angle. SOLID GEOMETRY. PROPOSITION... | |
 | George Albert Wentworth - Geometry - 1895 - 468 pages
...sphere are mutually equiangular). .'.£B = ZC, (since they are homologous A of symmetrical A). QED 754. COR. The arc of a great circle drawn from the vertex...vertical angle, is perpendicular to the base, and divides tht triangle into two symmetrical triangles. Ex. 577. At a given point in a given arc of a great circle,... | |
 | John Macnie - Geometry - 1895 - 386 pages
...The arc of a great circle drawn from the vertex of an isosceles spherical triangle to the mid point of the base, bisects the vertical angle, is perpendicular...divides the triangle into two symmetrical triangles. PROPOSITION XVIII. THEOREM. 645. Two triangles on the same sphere are either equal or symmetrical,... | |
 | John Macnie - Geometry - 1895 - 390 pages
...isosceles. Hence, as ZB can be made to coincide with Z c, and Z c = Z C' = Z c, ZB = Z C. 644. COR. 2. The arc of a great circle drawn from the vertex of an isosceles spherical triangle to the mid point of the base, bisects the vertical angle, is perpendicular to the base, and divides the triangle... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...equivalent. 753. In an isosceles spherical triangle, the angles opposite the equal sides are equal. 754. Cor. The arc of a great circle drawn from the vertex...divides the triangle into two symmetrical triangles. 755. If two angles of a spherical triangle are equal, the sides opposite these angles are equal, and... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...(385) 508. In an isosceles spherical triangle, the angles opposite the equal sides are equal. 509. Tlie arc of a great circle 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. 510. If with the vertices of a spherical... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...sides compare ? Which is the greater ? Use method of exclusion. Write Prop. XXIII. EXKRCISES. 514. The arc of a great circle drawn from the vertex of an isosceles spherical A to the middle point of the base is 1 to the base and bisects the vertical angle. 515. Suppose one... | |
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