 ADC ; the last two are therefore right angles ; 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.  The Elements of Geometry - Page 334by Webster Wells - 1886 - 371 pagesFull view - About this book
 | Edward Albert Bowser - Geometry - 1891 - 424 pages
...A s ABD and ACD are mutually equilateral, and . •. mutually equiangular. (706) 713. COR. 2. TJie 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. POLAR TRIANGLES. 714. One... | |
 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...editions of Euclid contain this Eider : — " The straight line drawn from the vertex of an isosceles triangle to the middle point of the base is perpendicular to the base." Boys who have learnt Euclid for years will refuse to attempt the Eider in this form. But the same Eider... | |
 | Euclid - Geometry - 1892 - 460 pages
...KXERCISES ON PROPOSITIONS 1 TO \'l. 1. Shew that the straight line which joins the vertex of an isosceles triangle to the middle point of the base is perpendicular to the base. 2. Shew that the straight lines which join the extremities of the base of an isosceles triangle to... | |
 | 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...perpendicular to the base, and bisects the vertical angle. 3. Theorem.—If two angles of a spherical triangle are equal, the triangle is isosceles. PROPOSITION... | |
 | 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... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...Any side of a spherical triangle is less than the sum of the other two. SuG. See Art. 388. Ex. 345. The arc of a great circle drawn from the vertex of...perpendicular to the base and bisects the vertical angle. Ex. 346. The angles opposite the equal sides of an isosceles spherical triangle are equal. Ex. 847.... | |
 | John Macnie - Geometry - 1895 - 386 pages
...isosceles. Hence, as ZB can be made to coincide with Z c, and Z c = Z C' = ZC, 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 of an isosceles spherical triangle to the middle of the base bisects the vertical angle, is perpendicular to the base, and divides the triangle into... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...ACD and SCD, we have ZADC=ZBDC; then CD LAB by §24.) 32. The line joining the vertex of an isosceles triangle to the middle point of the base, is perpendicular to the base, and bisects the vertical angle. (Fig. of Prop. XXX. Prove CD J- AB as in Ex. 31.) 33. If one angle of a parallelogram is a right angle,... | |
 | 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... | |
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