# Mensuration for Beginners: With Numerous Examples

Macmillan and Company, 1869 - Measurement - 296 pages

### Contents

 INTRODUCTION 1 Problems 15 SECOND SECTION LENGTHS 23 Similar Figures 31 Chords of a Circle 37 VIII 45 THIRD SECTION AREAS 55 Parallelogram 70
 Irregular Solids 178 Similar Solids 180 FIFTH SECTION AREAS OF THE SURFACES OF SOLIDS XXXIII Plane Surfaces 185 Right Circular Cylinder 192 Segments of a Right Circular Cylinder Ring 198 Right Circular Cone 201 Frustum of a Right Circular Cone 207 Sphere 212

 Quadrilaterals 80 Rectilineal Figure 88 Sector of a Circle and Segment of a Circle 100 Simpsons Rule 108 FOURTH SECTION VOLUMES 121 Solid Measure 128 Parallelepiped Prism Cylinder 138 Segments of a Right Circular Cylinder Ring 146 Pyramid Cone 149 Frustum of a Pyramid or Cone 155 Wedge 159 Prismoid 164 XXIX Sphere 169 Zone and Segment of a Sphere 174
 Zone of a Sphere Segment of a Sphere 215 SIXTH SECTION PRACTICAL APPLICATIONS XL Introduction 221 Artificers Work 224 Timber Measure 228 Gauging 232 SEVENTH SECTION LAND SURVEYING XLIV Use of the Chain 237 Perpendiculars 240 The Fieldbook 244 Problems 255 Duodecimals 257 Metrical System 264 Miscellaneous Examples 267 ANSWERS 285

### Popular passages

Page 4 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 124 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 17 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw a straight line through the point A parallel to the straight line BC. In BC take any point g D, and join AD ; at the point A in the straight line AD, make the angle DAE equal to the angle
Page 74 - RULE. — From half the sum of the three sides, subtract each side separately; multiply the half -sum and the three remainders together; the square root of the product is the area.
Page 18 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. Let AB be the given straight line, which may be produced to any length both ways, and let c be a point without it.
Page 7 - 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 4 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Page 272 - The content of a cistern is the sum of two cubes whose edges are 10 inches and 2 inches, and the area of its base is the difference of two squares whose sides are 1¿ and If feet.
Page 155 - To the areas of the two ends of the frustum add the square root of their product ; multiply the sum by the height of the frustum ; and one-third of the product will be the volume.
Page 230 - Add into one sum 39 times the square of the bung diameter, 25 times the square of the head diameter, and 26 times the product of the...