Key to Bradbury's Elementary Geometry and Trigonometry

Thompson, Bigelow and Brown, 1872 - Geometry - 79 pages

Contents

 Section 1 3 Section 2 5 Section 3 6 Section 4 12
 Section 5 24 Section 6 32 Section 7 1

Popular passages

Page 11 - 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 11 - ... straight line. By the above theorem, these sums are always equal, and (7) the halves of equal quantities are equal. 91. Corollary — The sum of all the successive angles formed in a plane and upon one side of a straight line, is equal to two right angles. 92. Corollary — The sum of all the successive angles formed in a plane about a point, is equal to four right angles. 93. Corollary — When two lines cut each other, if one of the angles thus formed is a right angle, the other three must...
Page 10 - XXVIII.) ; therefore the sum of the angles of all these triangles is equal to twice as many right angles as there are triangles, or sides, to the polygon. But the sum of all the angles about the point P is equal to four right angles (Prop.
Page 10 - The sum of the angles of the polygon is equal to the sum of the angles of the A, diminished by the sum of the angles about O ; that is, by 4 RA's.
Page 56 - Every point in the bisector of an angle is equally distant from the sides of the angle; and every point not in the bisector, but...
Page 25 - If the sum of the two arcs is greater than" a circumference, the greater arc is subtended by the less chord, and the less arc by the greater chord.
Page 37 - The intersection of the surfaces of two spheres is the circumference of a circle whose plane is perpendicular to the Hue which joins their centres.
Page 10 - ... polygon has sides, less two. For the polygon may be divided into as many triangles as it has sides, less two (417); and the angles of these triangles coincide altogether with those of the polygon. The sum of the angles of each triangle is two right angles. Therefore, the sum of the angles of the polygon is equal to twice as many right angles as it has sides, less two. The remark in Article 346 applies as well to this theorem.
Page 58 - S' as a center and a radius equal to the difference of the radii of the two given circles, construct a circle concentric with the greater of the two given circles.
Page 46 - ... common perpendicular, these triangles would be equal. Secondly. If the given angle be acute, and the side opposite to it greater than the adjacent side, the same mode of construction will apply : for, making BCA equal to the given angle, and AC equal to the adjacent side ; then, from A as centre, with a radius equal to the other given side, describe an arc, cutting CB in B; draw AB, and CAB will be the triangle required. But if the given angle is acute, and the side opposite to it less than the...