## The Essentials of Geometry |

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ABCD altitude approach the limit axis base bisector bisects Book called centre chord circle circumference circumscribed coincide common cone construct cylinder describe diagonals diameter diedral distance divided Draw line drawn equal equally distant equilateral equivalent EXERCISES extremities faces fall figure Find follows frustum Given Given line given point greater Hence homologous hypotenuse included inscribed intersecting isosceles lateral area length manner measured meet middle point multiplied Note opposite parallel parallelogram passing perimeter perpendicular plane polygon prism produced Proof PROP proportional Prove pyramid quadrilateral radii radius rectangle regular Required respectively right angles segment sides similar solid sphere spherical square straight line surface tangent THEOREM triangle triangle ABC unit vertex vertices volume Whence

### Popular passages

Page 371 - A zone is a portion of the surface of a sphere included between two parallel planes.

Page 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...

Page 261 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.

Page 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...

Page 73 - A chord is a straight line joining the extremities of an arc ; as AB.

Page 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 205 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.

Page 170 - 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 224 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.

Page 325 - A right circular cone may be generated by the revolution of a right triangle about one of its legs as an axis.