# Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration : Accompanied with All the Necessary Logarithmic and Trigonometric Tables

D. Appleton, 1860 - Geometry - 443 pages

### Contents

 Introduction 3 FIRST BOOK 9 Axioms 13 Additional Theorems of triangles 37 Of the measure of angles 47 Of secant and tangent circles 57 THIRD BOOK 73 Similar polygons 80
 Construction of similar polygons under certain conditions 132 Theorems 138 SIXTH BOOK 152 SEVENTH BOOK 174 EIGHTH BOOK 191 Regular polyedrons 208 CHAPTER II 17 Arithmetical calculations by logarithms 24 24

### Popular passages

Page 113 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 31 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 112 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 33 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 80 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 139 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 15 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Page 174 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 107 - ... similar figures are to each other as the squares of their homologous sides.
Page 180 - Every section of a sphere, made by a plane, is a circle.