# Elementary Geometry, Plane and Solid: For Use in High Schools and Academies (Google eBook)

Macmillan, 1901 - Geometry - 440 pages

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### Contents

 PART 1 Classified Summary 19 Parallel Lines 61 Closed Rectilinear Figures Parallelograms 71 Miscellaneous Theorems 78 Additional Problems of Construction 84 Miscellaneous Exercises 90 CHAPTER II 98
 Miscellaneous Exercises 258 Dihedral Angles 284 Polyhedral Angles 2 296 Prisms and Pyramids 310 Pyramids 328 Similar Polyhedrons 339 Polyhedrons in General 345 CHAPTER VIII 353

 Angles inscribed in Arcs 111 Circles in Contact 130 Classified Summary 136 Miscellaneous Exercises 189 Areas of Similar Polygons 207 Problems of Construction 220 Maxima and Minima 226 CHAPTER V 233 Measurement of the Circle 244 Problems of Construction 251
 The Cone 361 Classified Summary 368 Spherical Angles Triangles and Polygons 380 Polar Triangles 387 Areas of Spherical Triangles 394 Volume of the Sphere 405 Miscellaneous Exercises 3 409 APPENDIX 416 Mensuration Formulas 435 Copyright

### Popular passages

Page 187 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 207 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Page 78 - 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 45 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.
Page 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.
Page 95 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 200 - The area of a triangle is equal to half the product of its base by its altitude.
Page 161 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 201 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.
Page 29 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.