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### Contents

 Definitions 1 Perpendicular 15 The Secant Tangent and Normal 21 Problems 29 SECTION II 37 Problems 48 Polygons 54 Proportional Lines 60
 Equivalent Figures 97 Problems 104 Relative Position of Lines and Planes 110 Lines Parallel to a Plane 117 Relative Position of Planes 118 Planes which Intersect 122 PART IV 129 Surface of a Sphere 136

 Properties of Triangles from Proportional Lines 68 Problems 77 Exercises 83 Area of a Rectangle 91
 Pyramid and Cone 147 The Sphere 155 Similar Pyramids and Cones 162

### Popular passages

Page 64 - 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 14 - Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.
Page 64 - ... 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, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...
Page 108 - The area of a triangle is equal to half the product of its base by its altitude.
Page 92 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 73 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 105 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 72 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 60 - The square described on a straight line drawn from one of the angles at the base of a triangle to the middle point of the opposite side, is equal to the sum or difference of the square...
Page 108 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.