## A Text-book of Geometry |

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ABCD altitude axis base bisects called centre chord circle circular circumference circumscribed coincide common cone construct contained convex curve cylinder denote describe diagonal diameter difference dihedral angles distance divide draw drawn ellipse equal equidistant equilateral equivalent faces feet figure Find formed four frustum given line given point greater height Hence homologous inches included inscribed intersection isosceles joining lateral edges length less limit measured meet middle point opposite parallel parallel planes parallelogram parallelopiped pass perimeter perpendicular plane plane MN polygon polyhedron prism PROBLEM Proof proportional PROPOSITION prove prove Proof pyramid radii radius ratio rectangle regular respectively right angles segment sides similar solid sphere spherical triangle square straight line surface symmetrical tangent tetrahedron THEOREM third touches triangle trihedral vertex vertices volume

### 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.