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### Contents

 63 16 65 37 To multiply or divide Surds 60 Geometrical Ratio 67 Proportion Theorems 75 Axioms and Explanation of Symbols 131 Solid Geometry 139
 Geometrical Exercises 152 General Exercises in Algebra 164 Quadratic Equations 170 139 vii 152 152 164 159 167 36

### Popular passages

Page 124 - 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 115 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth : or...
Page 79 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 80 - 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 84 - ... is supposed . to be divided into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are designated respectively, by the characters � ' ". For example, ten degrees, eighteen minutes, and fourteen seconds, would be written 10� 18
Page 80 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 136 - To draw a straight line perpendicular to a plane, from a given point above it. Let A be the given point above the plane BH ; it is required to draw from the point A a straight line perpendicular to the plane BH.
Page 118 - ... of the base, have the same ratio which the other sides of the triangle have to one...
Page 71 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Page 125 - Weigh the denser body and the compound mass, separately, both in water and out of it ; then find how much each loses in water, by subtracting its weight in water from its weight in air ; and subtract the less of these remainders from the greater. Then...