## The Elements of Geometry |

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### Common terms and phrases

altitude axis base bisected bisector Book called chord circle circular circumference circumscribed common cone construct contains cylinder denote diagonals diameter difference dihedrals distance divided Draw drawn edges equal equilateral equivalent EXERCISES extremities faces figure Find fixed four Geometry given circle given line given point greater half homologous inches included increased inscribed intersect isosceles triangle lateral length less limit locus lune magnitudes mean measure median normal NOTE opposite parallel parallelogram passes perimeter perpendicular plane polyhedral polyhedron prism PROBLEM Prop proportional PROPOSITION Prove pyramid radii radius ratio rectangle regular polygon respectively right angles right triangle sector segments Show sides similar solid sphere spherical spherical triangle square straight line surface tangent tetrahedron THEOREM third trapezoid triangle triangle ABC trihedral unit variable vertex vertices volume zone

### Popular passages

Page 33 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 152 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 13 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.

Page 197 - A sphere is a solid bounded by a surface, all the points of which are equally distant from a point within called the center.

Page 154 - Prove that, if from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and the part without the circle.

Page 84 - If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. Let...

Page 14 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.

Page 147 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.

Page 94 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.

Page 185 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.