## A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry |

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A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2016 |

A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2015 |

### Common terms and phrases

ABCD adjacent angles altitude apothem base bisects centre of similitude chord circumference circumscribed coincide common cone convex Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw equally distant equilateral equivalent exterior angle faces figure find the locus fixed point frustum given circles given plane given point given straight line hence homologous indefinitely inscribed angle isosceles Let ABC measure medial lines middle point number of sides one-half opposite sides parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume

### Popular passages

Page 245 - It will be shown that every section of a sphere made by a plane is a circle...

Page 128 - The area of a rectangle is equal to the product of its base and altitude.

Page 216 - 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.

Page 129 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.

Page 219 - THEOREM. 611. -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.

Page 44 - Every point in the bisector of an angle is equally distant from the. sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.

Page 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.

Page 263 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 107 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 127 - Any two rectangles are to each other as the products of their bases by their altitudes.