Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page vi
... Equations for the Sines of the Angles .... 260 Natural Sines , Cosines , etc .... 265 Trigonometrical Lines for Arcs exceeding 90 ° .... 270 SECTION II . Plane Trigonometry , Practically Applied .... 272 vi CONTENTS .
... Equations for the Sines of the Angles .... 260 Natural Sines , Cosines , etc .... 265 Trigonometrical Lines for Arcs exceeding 90 ° .... 270 SECTION II . Plane Trigonometry , Practically Applied .... 272 vi CONTENTS .
Page 245
... Cosine of an arc is the per- pendicular distance from the center of the circle to the sine of the arc ; or , it is the same in magnitude as the sine of the complement of the arc . Thus , CF is the cosine of the arc AB ; but CF = KB ...
... Cosine of an arc is the per- pendicular distance from the center of the circle to the sine of the arc ; or , it is the same in magnitude as the sine of the complement of the arc . Thus , CF is the cosine of the arc AB ; but CF = KB ...
Page 246
... cosine are each equal to radius . 2d . The sine and versed sine of a quadrant are each equal to the radius ; its cosine is zero , and its secant and tangent are infinite . 3d . The chord of an arc is twice the sine of one half the arc ...
... cosine are each equal to radius . 2d . The sine and versed sine of a quadrant are each equal to the radius ; its cosine is zero , and its secant and tangent are infinite . 3d . The chord of an arc is twice the sine of one half the arc ...
Page 248
... cosines of all arcs from 0 ° to 360 ° . Now , since all other trigo- nometrical lines can be expressed in terms of the sine and cosine , it follows that the algebraic signs of all the circular functions result from those of the sine and ...
... cosines of all arcs from 0 ° to 360 ° . Now , since all other trigo- nometrical lines can be expressed in terms of the sine and cosine , it follows that the algebraic signs of all the circular functions result from those of the sine and ...
Page 249
... cosine of two arcs , to find the sine and the cosine of the sum and of the difference of the same arcs expressed by the sines and cosines of the separate arcs . Let G be the center of the circle , CD the greater arc , and DF the less ...
... cosine of two arcs , to find the sine and the cosine of the sum and of the difference of the same arcs expressed by the sines and cosines of the separate arcs . Let G be the center of the circle , CD the greater arc , and DF the less ...
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Common terms and phrases
ABē ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.b cos.c Cosine Cotang diagonal diameter dicular difference distance divided draw equal angles equation equiangular equivalent find the angle four magnitudes frustum given line greater half Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles less Let ABC logarithm measured multiplied N.sine number of sides opposite angles parallelogram parallelopipedon pendicular perpen perpendicular plane ST polyedron PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY straight line subtracting Tang tangent three angles three sides triangle ABC triangular prisms triedral angles TRIGONOMETRY vertex vertical angle volume
Popular passages
Page 320 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 65 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 121 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Page 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 34 - Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle it itosceles.
Page 126 - To inscribe a regular polygon of a certain number of sides in a given circle, we have only to divide the circumference into as many equal parts as the polygon has sides : for the arcs being equal, the chords AB, BC, CD, &c.
Page 22 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Page 277 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.