A Text-book of Geometry |
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Common terms and phrases
ABCD altitude axis base bisector bisects called centre chord circumference circumscribed coincide common cone construct curve cylinder denote diagonal diameter dihedral angles directrix distance divide draw ellipse equal respectively equidistant equilateral triangle equivalent face angles feet Find the area frustum given circle given line given point given straight line greater Hence homologous homologous sides hypotenuse inches inscribed intersection isosceles lateral area lateral edges latus rectum locus middle point number of sides opposite parabola parallelogram parallelopiped perimeter perpendicular plane MN plane passed polyhedral angle polyhedron prism prove Proof pyramid Q. E. D. PROPOSITION radii radius ratio rectangle regular polygon right angle right circular right triangle SCHOLIUM secant segment similar polygons slant height sphere spherical polygon spherical triangle square surface tangent tetrahedron THEOREM triangle ABC trihedral vertex vertices
Popular passages
Page 94 - Any two sides of a triangle are together greater than the third side.
Page 246 - ... of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 146 - 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' are similar. In this case we prove the A similar by proving them mutually equiangular. Proof. Place the A A'B'C...
Page 346 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB, AC "be arcs of great circles Intersecting at A; AB...
Page 67 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.
Page 329 - The volume of a frustum of a cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the bases of the frustum.
Page 183 - Two triangles having 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 132 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 348 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 198 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.