# Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra Exercises, Both Theorems and Problems, for Advance Work

D.C. Health, 1891 - Geometry, Plane - 179 pages

### Contents

 DEFINITIONS 1 PARTICULAR AXIOMS 7 ANGLE MEASUREMENT 15 TRIANGLES 24 ADVANCE THEOREMS 32 35 52 80 94 117 32 CIRCLES 38 RATIO AND PROPORTION 54 PROPORTIONAL LINES 68
 AREAS 84 REGULAR POLYGONS AND CIRCLES 98 MAXIMA AND MINIMA 124 PROBLEMS OF CONSTRUCTION 133 OPTIONAL PROBLEMS FOR ADVANCE WORK 143 APPENDIX 168 SYMMETRY 175 Copyright

### Popular passages

Page 38 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 78 - 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, minus twice the product of one of these sides and the projection of the other side upon it.
Page 81 - 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 3 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 71 - 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, &c.
Page 25 - In a right triangle, the side opposite the right angle is called the hypotenuse and is the longest side.
Page 80 - In any quadrilateral, the sum of the squares of the four sides is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 79 - 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 70 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 72 - The sum of the interior angles of a polygon is equal to two right angles, taken as many times less two as the figure has sides.