## A Text-book of Geometry |

### Other editions - View all

### Common terms and phrases

ABCD altitude angles are equal axis bisector bisects called centre chord circumference circumscribed coincide construct convex curve denote diagonal diameter dihedral angles directrix distance divide draw ellipse equal respectively equidistant equilateral triangle equivalent face angles feet Find the area frustum given line given point given straight line greater Hence homologous homologous sides hypotenuse inches inscribed intersection isosceles lateral area lateral edges lateral faces latus rectum middle point number of sides opposite parabola parallel planes parallelogram parallelopiped perimeter perpendicular plane MN plane passed polyhedral angle polyhedron prove Proof Q. E. D. PROPOSITION radii radius ratio rectangle rectangular parallelopipeds regular polygon right angles right section SCHOLIUM segment slant height sphere spherical polygon spherical triangle square surface symmetrical tangent tetrahedron THEOREM triangle ABC triangular triangular prism trihedral vertex vertices

### Popular passages

Page 96 - Any two sides of a triangle are together greater than the third side.

Page 270 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.

Page 187 - 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 64 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 141 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 134 - 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 296 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids 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 two bases of the frustum.

Page 344 - 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 395 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.

Page 132 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.