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

J.B. Lippincott, 1872 - 368 σελίδες

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### Περιεχόμενα

 INTRODUCTION 9 BOOK II 52 BOOK III 91 BOOK IV 126
 BOOK V 142 GEOMETRY OF SPACE 171 The THREE ROUND BODIES THE CYLINDER THE CONE 238 EXERCISES IN ELEMENTARY GEOMETRY 293

### Δημοφιλή αποσπάσματα

Σελίδα 245 - It will be shown that every section of a sphere made by a plane is a circle...
Σελίδα 128 - The area of a rectangle is equal to the product of its base and altitude.
Σελίδα 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.
Σελίδα 129 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 107 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Σελίδα 127 - Any two rectangles are to each other as the products of their bases by their altitudes.