Plane Geometry: A Complete Course in the Elements of the Science

Christopher Sower Company, 1901 - Geometry, Modern - 266 pages

Contents

 INTRODUCTION 13 Geometrical Language 20 Plane Angles 26 Parallel Lines 43 Quadrilaterals 63 Polygons 72 Theorems for Demonstration 78 Theorems 85
 Incommensurable Quantities 91 Practical Examples 98 Regular Polygons 211 Axioms and Postulates 233 SUPPLEMENT 237 SECTION II 244 Copyright

Popular passages

Page 112 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 244 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 60 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 57 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 28 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Page 48 - If two parallel lines are cut by a transversal, the sum of the two interior angles on the same side of the transversal is two right angles.
Page 53 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 183 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 156 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.
Page 179 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.