# Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of Projection

Baldwin and Cradock, 1830 - Geometry - 272 pages

### Contents

 Definitions CONTENTS BOOK 1 Surfaces and contents of the right cylinder and right cone 2 Parallels 14 Parallelograms 17 Rectangles under the parts of divided lines 6 Relations of the sides of triangles 21 Problems 27 BOOK II 31 Proportion of commensurable magnitudes 46
 19 157 21 162 គ២៩ ៦៩ 7 183 BOOK VI 184 31 204 37 205 APPENDIX 208 48 216

 The general theory of proportion 48 Proportion of the sides of triangles 5 Proportion of the surfaces of rectilineal figures 6 Of lines in harmonical progression 67 Problems 71 BOOK III 78 Rectangles under the segments of chords 88 Regular polygons and approximation to the area of the circle 5 The circle a maximum of area and a minimum of perimeter 99 Simple and plane loci 106 Problems 116 vil 1 141 11 142 15 145
 57 230 62 234 71 246 78 261 208 272 84 275 91 275 106 xi 112 xii 234 xxii

### Popular passages

Page 196 - 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 64 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 20 - In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles ; and upon BC, one of the sides containing it, let fall the perpendicular...
Page 10 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 189 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Page 1 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 84 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference.
Page 78 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Page 79 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Page 264 - IF two straight lines cut one another, the vertical, or opposite, angles shall be equal.