## The Elements of Geometry |

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adjacent angle altitude apothem Axiom axis bisected bisector called central angle chord circumference circumscribed cone construct a triangle cuboid cylinder denote diagonals diameter dihedrals distance divided Draw drawn equal circles equal respectively equally distant equilateral triangle equivalent EXERCISES face-angles faces figure Find the area frustum given circle given line given point given polygon given triangle greater homologous hypotenuse inches indefinitely increased inscribed isosceles triangle lateral edges length line joining lune magnitudes mean proportional median middle point number of equal number of sides parallelepiped parallelogram perimeter perpendicular Plane Geometry polyhedral polyhedron prism prismatic surface PROBLEM Prop PROPOSITION Prove pyramid quadrilateral radii radius rectangle regular polygon right angles right bisector right triangle secant segments similar polygons SIMON NEWCOMB sphere spherical triangle straight line tangent tetrahedron THEO THEOREM trapezoid triangle ABC triangular trihedral variable vertex vertical angle volume

### Popular passages

Page 29 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 148 - 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 9 - 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 193 - 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 150 - 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 80 - 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 10 - 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 143 - 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 90 - ... 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 181 - 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.