...triangles ABD, ADC, AB = AC, by hypothesis; AU = AD ; BD = DC, by construction ; B = C. QED Cor.—The arc 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...

...with A DEF, .-. A ABC = A DEF. I. Ax. 9 1. The straight line which joins the vertex of an isosceles triangle to the middle point of the base, is perpendicular to the base, and bisects the vertical angle. 2. The opposite angles of a rhombus are equal. 3. Either diagonal of a rhombus bisects the angles through...

...the base, and is perpendicular to the base. 6. In an isosceles triangle the line joining the vertex to the middle point of the base is perpendicular to the base, and bisects the angle at the vertex. 6. If the angle ABC of the triangle ABC be double of the angle C, and BD bisect...

...uniformly bright isosceles triangle is placed with its plane vertical and its such that the line joining 0 to the middle point of the base is perpendicular to the base and equal to half of it, varies as • where 2o is the length of the base and b that of either side. xi....

...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...

...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...

...triangles are equal, by Proposition VI. EXERCISE. Theorem. — A line drawn from the vertex of an isosceles triangle to the middle point of the base is perpendicular to the base, and bisects the vertical angle. cf PROPOSITION X.— THEOREM. 26. Two right triangles are equal when they have the hypotenuse and a...

...horizontal table. Prove that the illumination at a point 0 of the table such that the line joining 0 to the middle point of the base is perpendicular to the base and equal to half of it, varies as ,aa .a ~*~- z tcos — r' where 2a is the length of the base, and 6...

...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 angles...

...the A s ABD and ACD are mutually equilateral, and . • . mutually equiangular. (706) 713. COR. 2. The 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...