NEW PLANE GEOMETRY

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Contents

 INTRODUCTION 1 BOOK II 90 BOOK III 114 METHODS 152 Book IV 159 THE THEORY OF LIMITS 169 A PENCIL CUT BY ANTIPARALLELS OR BY A CIRCUMFERENCE 177
 SIMILAR FIGURES 185 PROBLEMS 194 THE MENSURATION OF PLANE FIGURES 201 THE MENSURATION OF THE CIRCLE 216 APPENDIX TO PLANE GEOMETRY 226 MAXIMA AND MINIMA 237 TABLES 245

Popular passages

Page 104 - Definition. The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Page 161 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Page 147 - To draw a tangent to a given circle from a given point.
Page 121 - XLI. 2. The perpendicular bisector of a chord passes through the center of the circle and bisects the subtended ares.
Page 38 - If two triangles have two sides of the one respectively equal to two sides of the other, and the...
Page 131 - An angle in a segment is greater than, equal to, or less than, a right angle, according as the segment is less than, equal to, or greater than, a semicircle.
Page 65 - The lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Page 46 - P' two parallels, and T, a transversal. To prove that any Z c equals its alternate Z a'. Proof. 1. Suppose Z c > Z. a!, and that Q is drawn as in the figure, making an Z equal to Z a'.
Page 132 - COROLLARY. Tangents to a circle from the same external point are equal. For, connect the points of tangency, and two angles of the triangle are equal by this theorem. 198. The theorem is often stated thus: An angle formed by a tangent and a chord of a circle is measured by half its intercepted arc.
Page 202 - That is, the number which represents its square units of area is the product of the two numbers which represent its base and altitude. For in prop. II, if R' = 1, the square unit of area, then a' and 6' must each equal 1, the unit of length.