## The Elements of Geometry |

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ABC and DEF ABCD adjacent angles altitude angles are equal approach the limit arc BC area ABC bisector bisects centre chord circle circumference circumscribed cone of revolution construct the triangle Converse of Prop cylinder denote diagonals diameter diedral Draw AC equal respectively equally distant equilateral triangle equivalent exterior angle Find the area frustum given point given straight line Hence homologous hypotenuse intersection isosceles triangle lateral area lateral edges Let ABC measured by arc middle point number of sides parallelogram parallelopiped perimeter perpendicular to MN plane MN polyedral polyedrons prism produced PROPOSITION prove pyramid quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron THEOREM trapezoid triangle ABC triangles are equal triangular prism triedral vertex vertices volume Whence

### Popular passages

Page 38 - If two triangles have two sides of 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.

Page 65 - 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.

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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.

Page 120 - The first and fourth terms of a proportion are called the extremes, and the second and third terms the means.

Page 24 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...

Page 123 - In any proportion the terms are in proportion by composition and division ; that is, the sum of the first two terms is to their difference as the sum of the last two terms to their difference.

Page 322 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...

Page 248 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane.