Elements of Geometry and Trigonometry |
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Page 214
... tang ( an arc ) = - tang ( its supplement ) cot ( an arc ) -cot ( its supplement ) . It is no less evident , that if one or several circumfe- rences were added to any arc AM , it would still termi- nate exactly at the point M , and the ...
... tang ( an arc ) = - tang ( its supplement ) cot ( an arc ) -cot ( its supplement ) . It is no less evident , that if one or several circumfe- rences were added to any arc AM , it would still termi- nate exactly at the point M , and the ...
Page 216
... tang A = CP : CM : CA : CT ; or cos A : R :: R : sec A : PM : CP :: CD : DS ; or sin A : cos A :: R : cot A = PM : CM : CD : CS ; or sin A : R :: R : cosec A = R sin A cos A R2 cos A R cos A sin A R2 sin A which are the four formulas ...
... tang A = CP : CM : CA : CT ; or cos A : R :: R : sec A : PM : CP :: CD : DS ; or sin A : cos A :: R : cot A = PM : CM : CD : CS ; or sin A : R :: R : cosec A = R sin A cos A R2 cos A R cos A sin A R2 sin A which are the four formulas ...
Page 217
... tang 90 ° = R2 0 ' an expression which designates an infinite quantity ; for , the quotient of radius divided by a very small quantity , is very great , and increases as the divisor diminishes ... tang B : tang T 28 PLANE TRIGONOMETRY . 217.
... tang 90 ° = R2 0 ' an expression which designates an infinite quantity ; for , the quotient of radius divided by a very small quantity , is very great , and increases as the divisor diminishes ... tang B : tang T 28 PLANE TRIGONOMETRY . 217.
Page 218
Adrien Marie Legendre Charles Davies. Hence cot A cot B : tang B : tang A ; that is , the colan- gents of two arcs are reciprocally proportional to their tangents . The formula cot Ax tang A = R2 might be deduced imme- diately , by ...
Adrien Marie Legendre Charles Davies. Hence cot A cot B : tang B : tang A ; that is , the colan- gents of two arcs are reciprocally proportional to their tangents . The formula cot Ax tang A = R2 might be deduced imme- diately , by ...
Page 221
... tang p R + cos P R sin P cot P = R cot p otp R R - cos p R = tangp : formulas which are often employed in ... tang a cos a Ꭱ . R cot a sin p + sin q sin ( p + q ) cos } ( p — q ) tang ( p + q ) sin p - sin q cos ( p + q ) sin ( p - q ) ...
... tang p R + cos P R sin P cot P = R cot p otp R R - cos p R = tangp : formulas which are often employed in ... tang a cos a Ꭱ . R cot a sin p + sin q sin ( p + q ) cos } ( p — q ) tang ( p + q ) sin p - sin q cos ( p + q ) sin ( p - q ) ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex