# Plane and Solid Geometry

Century, 1906 - Geometry - 418 pages

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 RECTILINEAR FIGURES 15 TRIANGLES 30 QUADRILATERALS 53 POLYGONS IN GENERAL 62 ANALYSIS OF THEOREMS 69 THE CIRCLE 78 MEASUREMENT 91 CONSTRUCTIONS 110
 SYMMETRY 262 SOLID GEOMETRY 268 DIEDRAL ANGLES 284 POLYEDRAL ANGLES 296 POLYEDRONS CYLINDERS AND CONES 303 SIMILAR POLYEDRONS 338 CYLINDERS 344 PAGE 365

 ANALYSIS OF PROBLEMS 125 Review QUESTIONS 132 SIMILAR POLYGONS 154 AREAS OF POLYGONS 192 COMPARISON OF POLYGONS 199 BOOK V 225 MAXIMA AND MINIMA 254
 SPHERICAL ANGLES 374 SYMMETRICAL SPHERICAL POLYGONS 382 SPHERICAL SURFACES 392 SPHERICAL VOLUMES 400 FORMULAS OF MENSURATION 411 Copyright

### Popular passages

Page 168 - 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 diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 41 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 38 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 35 - Any side of a triangle is less than the sum of the other two sides...
Page 242 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Page 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 192 - The areas of two rectangles having equal altitudes are to each other as their bases.
Page 65 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...