## The Elements of Geometry |

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### Common terms and phrases

ABCD adjacent altitude angles are equal approaches arc AC base bisector bisects called centre chord circle circumference circumscribed coincide common cone construct COROLLARY DEFINITIONS denote describe diagonals diameter diedral angles divided Draw drawn edges equally distant equilateral equivalent EXERCISES exterior angle extremities faces fall figure formed four frustum given given point greater Hence homologous hypothesis included inscribed intersect isosceles triangle lateral length less limit measured meet middle point one-half opposite sides parallel parallelogram passing perimeter perpendicular plane polygon prism PROBLEM produced proportional PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle regular respectively right angles right triangle SCHOLIUM segment side BC sides similar sphere spherical square straight line surface symmetrical tangent THEOREM third triangle ABC triangles are equal unit vertex vertices volume Whence

### Popular passages

Page 60 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.

Page 277 - The volume of a triangular prism is equal to the product of its base and altitude. Let AE be the altitude of the triangular prism ABC-C'. To prove that volume ABC-C' = ABC x AE. Construct the parallelopiped ABCD-D' having its edges equal and parallel to AB, BC, and BB'.

Page 112 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.

Page 31 - 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 313 - A Sphere is a solid bounded by a curved surface all points of which are equally distant from a point within called the centre.

Page 50 - 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 44 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.

Page 161 - 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 46 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.

Page 167 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.