Plane and Solid Geometry

American Book Company, 1908 - Geometry - 340 pages

Contents

 BOOK IITHE CIRCLE 81 Historical Note 99 PROPORTION AND SIMILAR FIGURES 117 AREAS OF POLYGONS 147 81 199
 81 232 BOOK VIIPOLYHEDRONS CYLINDERS AND CONES 249 2002 333 Copyright

Popular passages

Page 63 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 128 - 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.
Page 217 - If two triangles have two sides of 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. 132. If two triangles have two sides of...
Page 134 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The two triangles thus formed are similar to each other and to the whole triangle. II. The perpendicular is a mean proportional between the segments of the hypotenuse.
Page 120 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 221 - If the product of two numbers -is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion.
Page 223 - Prove that in any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares on the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 131 - If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar.
Page 255 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'.
Page 221 - In any proportion, the product of the means is equal to the product of the extremes.