# Elements of Geometry: With Practical Applications to Mensuration

R.S. Davis & Company, 1866 - Geometry - 320 pages
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### Contents

 PLANE GEOMETRY 7 BOOK II 43 BOOK III 55 PROPORTIONS AREAS AND SIMILARITY OF FIGURES 76 BOOK V 118 PLANES 165
 BOOK VIII 184 BOOK IX 214 BOOK X 238 MENSURATION 253 SOLIDS 281 BOOK XIV 311

### Popular passages

Page 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 168 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 159 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Page 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 254 - RULE. — Multiply the base by the altitude, and the product will be the area.
Page 35 - If a side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles.
Page 32 - If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line...