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ABCD altitude axis bisector bisects called centre chord circumference circumscribed coincide construct curve cylinder denote diagonals diameter dihedral angles directrix distance divided Draw ellipse equiangular equidistant equilateral triangle equivalent feet Find the area Find the locus frustum given circle given line given point given straight line greater Hence homologous hyperbola hypotenuse inches inscribed intersection isosceles triangle lateral area lateral edges latus rectum limit middle point number of sides opposite parabola parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedron prism prismatoid Proof proportional prove Q. E. D. PROPOSITION radii radius ratio rectangle regular polygon respectively rhombus right angle right circular right triangle secant segments similar slant height sphere spherical triangle square surface tangent tetrahedron THEOREM trapezoid triangle ABC triangle is equal trihedral vertex vertices
Page 66 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 372 - Each side of a spherical triangle is less than the sum of the other two sides. Let ABC be a spherical triangle, AB the longest side.
Page 385 - If two angles of a spherical triangle are unequal, the sides opposite are unequal,, and the greater side is opposite the greater angle...
Page 191 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 360 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 383 - 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.
Page 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 150 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C