Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 9
... greater than a right angle ; as the angle EFG . F G Acute and obtuse angles have their sides oblique to each other , and are sometimes called oblique angles . 17. PARALLEL LINES are such as , being in the same plane , cannot meet ...
... greater than a right angle ; as the angle EFG . F G Acute and obtuse angles have their sides oblique to each other , and are sometimes called oblique angles . 17. PARALLEL LINES are such as , being in the same plane , cannot meet ...
Page 13
... greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. A straight line is the shortest line that can be drawn from one point to another . 11. From one point to another only one straight line can be drawn ...
... greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. A straight line is the shortest line that can be drawn from one point to another . 11. From one point to another only one straight line can be drawn ...
Page 20
... greater than the other . Let A B be the greater ; then take DB equal to AC the less , and draw CD . Now , in the two triangles DBC , ABC , we have DB equal to A C by construction , the side B C common , and the angle B equal to the ...
... greater than the other . Let A B be the greater ; then take DB equal to AC the less , and draw CD . Now , in the two triangles DBC , ABC , we have DB equal to A C by construction , the side B C common , and the angle B equal to the ...
Page 21
... greater side of any triangle is opposite the greater angle . In the triangle CAB , let the angle A C be greater than B ; then will the side . A B , opposite to C , be greater than A C , opposite to B. Draw the straight line CD , making ...
... greater side of any triangle is opposite the greater angle . In the triangle CAB , let the angle A C be greater than B ; then will the side . A B , opposite to C , be greater than A C , opposite to B. Draw the straight line CD , making ...
Page 22
... greater angle of any triangle is opposite the greater side . In the triangle CA B , suppose the A Be A B to be greater than AC ; then will the angle C , opposite to A B , be greater than the angle B , opposite to A C. с B For , if the ...
... greater angle of any triangle is opposite the greater side . In the triangle CA B , suppose the A Be A B to be greater than AC ; then will the angle C , opposite to A B , be greater than the angle B , opposite to A C. с B For , if the ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angles ACD angles equal base bisect centre chord circle circumference cone convex surface cosec cosine Cotang diagonal diameter distance divided drawn equal angles equal Prop equiangular equilateral equivalent exterior angle feet four right angles frustum gles greater half the sum homologous homologous sides hypothenuse inches included angle inscribed less Let ABC line A B logarithm mean proportional multiplied parallelogram parallelopipedon perimeter perpendicular polyedron prism PROPOSITION pyramid quadrilateral radii radius ratio rectangle regular polygon right angles Prop right-angled triangle Scholium secant secant line segment side A B side BC similar slant height solidity solve the triangle sphere spherical triangle Tang tangent THEOREM triangle ABC trigonometric functions vertex
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 155 - 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 118 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 98 - 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 144 - The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude, AG (Prop.
Page 176 - 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 95 - STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.