Elements of Geometry and Trigonometry |
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Page 275
... sine , at the top of the page , should correspond with cosine , at the bottom ; cosine with sine , tang with cotang , and cotang with tang , as in the tables ( Art . 12 ) . If the angle is greater than 90 ° , we have only to sub tract ...
... sine , at the top of the page , should correspond with cosine , at the bottom ; cosine with sine , tang with cotang , and cotang with tang , as in the tables ( Art . 12 ) . If the angle is greater than 90 ° , we have only to sub tract ...
Page 276
... sine and cotangent , it must be remembered , that they in- crease while the arcs decrease , and decrease as the arcs are increased ; consequently , the proportional numbers found for the seconds , must be subtracted , not added ...
... sine and cotangent , it must be remembered , that they in- crease while the arcs decrease , and decrease as the arcs are increased ; consequently , the proportional numbers found for the seconds , must be subtracted , not added ...
Page 277
... sine and tangent , and subtracted for the cosine and cotangent . EXAMPLES . 1. Find the arc answering to the sine 9.880054 Sine 49 ° 20 ′ , next less in the table Tabular difference , 9.879963 1.81 ) 91.00 ( 50 " . Hence , the arc 49 ...
... sine and tangent , and subtracted for the cosine and cotangent . EXAMPLES . 1. Find the arc answering to the sine 9.880054 Sine 49 ° 20 ′ , next less in the table Tabular difference , 9.879963 1.81 ) 91.00 ( 50 " . Hence , the arc 49 ...
Page 278
Adrien Marie Legendre. dicular to AB : now DE is the sine of the angle A , and CF is the sine of B , to the same radius AD or BC . But by similar triangles , AD : DE :: AC : : OF But AD being equal to BC , we have BC : sin A :: AC : sin ...
Adrien Marie Legendre. dicular to AB : now DE is the sine of the angle A , and CF is the sine of B , to the same radius AD or BC . But by similar triangles , AD : DE :: AC : : OF But AD being equal to BC , we have BC : sin A :: AC : sin ...
Page 283
... sine ( Art . 13 ) . As long as the two triangles exist , the ambiguity will con- tinue . But if the side CB , opposite the given angle , is greater than AC , the arc BB will cut the line ABB ' , on the same side of the point A , in but ...
... sine ( Art . 13 ) . As long as the two triangles exist , the ambiguity will con- tinue . But if the side CB , opposite the given angle , is greater than AC , the arc BB will cut the line ABB ' , on the same side of the point A , in but ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
adjacent angles altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² Cosine Cosine D Cotang cylinder diagonal diameter distance divided draw drawn equations equivalent feet figure find the area frustum given angle given line gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices ΙΟ
Popular passages
Page 24 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Page 38 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 43 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the sum of the exterior angles.
Page 215 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 107 - 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 93 - The area of a parallelogram is equal to the product of its base and altitude.
Page 231 - The angles of spherical triangles may be compared together, by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle.
Page 232 - F, be respectively poles of the sides BC, AC, AB. For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...