# Elements of Geometry: With Practical Applications to Mensuration

R.S. Davis & Company, 1868 - Geometry - 320 pages
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### Contents

 PLANE GEOMETRY 23 LEMENTARY PRINCIPLES 7 43 BOOK III 55 PROPORTIONS AREAS AND SIMILARITY OF FIGURES 76 BOOK V 118 BOOK VI 142 BOOK VII 165
 POLYEDRONS 184 THE SPHERE AND ITS PROPERTIES 214 BOOK X 238 MENSURATION 253 BOOK XII 281 MISCELLANEOUS GEOMETRICAL EXERCISES 301 APPLICATION OF ALGEBRA TO GEOMETRY 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 101 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 37 - 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 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal. Let ABC be an isosceles triangle, in which the side AB is equal to the side AC ; then will the angle B be equal to the angle C.
Page 36 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
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 166 - ... the same, or a like inclination to one another, which two other planes have, when the said angles of inclination are equal to one another.
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 272 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...