## Elements of Plane and Spherical Trigonometry: With Practical Applications |

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A B C ABCD adjacent altitude base called centre chord circle circumference common cone consequently contained corresponding Cosine Cotang described diagonal diameter difference distance divided draw drawn edge equal equal Prop equivalent EXAMPLES exterior angle extremities faces feet figure four frustum given gles greater half height hence homologous hypothenuse inches included inscribed intersect join length less logarithm magnitudes manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid radius ratio rectangle regular right angles right-angled triangle rods Scholium segment shown sides similar sine solidity sphere spherical triangle square straight line surface Tang tangent THEOREM third triangle ABC vertex whole

### Popular passages

Page 17 - 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 57 - 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 153 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.

Page 28 - 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 116 - The radius of a sphere is a straight line, drawn from the centre to any point of the...

Page 96 - 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 142 - The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude, AG (Prop.

Page 174 - Find the area of the sector having' the same arc with the segment, and also the area of the triangle formed by the chord of the segment and the radii of the sector. Then...

Page 14 - Straight lines which are parallel to the same line are parallel to each other. Let the straight lines AB, CD be each parallel to the line EF ; then are they parallel to each other.

Page 93 - STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.