### Contents

 ELEMENTARY PRINCIPLES 7 RATIO AND PROPORTION 43 BOOK III 55 BOOK IV 76 POLYEDRONS 118 SOLID GEOMETRY 165 THE SPHERE AND ITS PROPERTIES 214 THE THREE ROUND BODIES 239
 BOOK XIII 301 BOOK XIV 311 TRIGONOMETRY 1 BOOK II 13 BOOK IV 61 BOOK V 72 165 77 BOOK VI 105

### Popular passages

Page 28 - 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 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 79 - Two rectangles having equal altitudes are to each other as their bases.
Page 251 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 35 - If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles.
Page 168 - 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 303 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.
Page 4 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X ��12.
Page 102 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing.