## The Elements of Geometry |

### From inside the book

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**angle of the other are to each other as the products of the**sides including the equal angles . Describe an isosceles triangle equal in area to a given triangle and having its vertical angle equal to one angle of the given triangle . 11 ... Page 152

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**angle of the other are to each other as the products of the**sides including the equal angles , prove that the bisector of an angle of a triangle . divides the opposite side into parts which are proportional to the sides adjacent to them ...### Other editions - View all

### Common terms and phrases

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 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.