A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration, Containing Many Valuable Discoveries and Impovements in Mathematical Science ...: Designed as a Text Book for Collegiate and Academic Instruction, and as a Practical Compendium on MensurationCollins brothers & Company, 1845 - Conic sections |
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Page 31
... cosine of that angle . Thus , sin . ( 90 ° -4 ) = cos . 4 , hence cos . ( 90 ° -4 ) = sin . 4 . 9. The tangent of the complement of any given angle , is called the cotangent of that angle . Thus , tan . ( 90 ° -4 ) = cot . & , hence cot ...
... cosine of that angle . Thus , sin . ( 90 ° -4 ) = cos . 4 , hence cos . ( 90 ° -4 ) = sin . 4 . 9. The tangent of the complement of any given angle , is called the cotangent of that angle . Thus , tan . ( 90 ° -4 ) = cot . & , hence cot ...
Page 36
... cosines of angles in the different quadrants . PS In the first quadrant , sin . = СА CS . cos . = CA Here PS Cc is ... cosine negative . In the third quadrant , sin . 6 = PS3 СА Cos . CS , СА Here P , S , = Cc , is reckoned from C ...
... cosines of angles in the different quadrants . PS In the first quadrant , sin . = СА CS . cos . = CA Here PS Cc is ... cosine negative . In the third quadrant , sin . 6 = PS3 СА Cos . CS , СА Here P , S , = Cc , is reckoned from C ...
Page 37
... cosine are both negative . In the fourth quadrant , sin . 8 = P.S CA 4 Cos . 8- CS 4 CA Sa B 4 Here P1S1 = Cc , is ... cosine positive . Hence we conclude , that the sine is positive in the first and second quadrants , and negative in ...
... cosine are both negative . In the fourth quadrant , sin . 8 = P.S CA 4 Cos . 8- CS 4 CA Sa B 4 Here P1S1 = Cc , is ... cosine positive . Hence we conclude , that the sine is positive in the first and second quadrants , and negative in ...
Page 38
... cosine for angles of different magnitudes . In the first quadrant : 39 Let CP , CP2 , CP . ..... be different positions of the revolving radius in the first quadrant ; and from P , P ,, P3 , draw PS , P , S ,, P , S ,, perpendiculars on ...
... cosine for angles of different magnitudes . In the first quadrant : 39 Let CP , CP2 , CP . ..... be different positions of the revolving radius in the first quadrant ; and from P , P ,, P3 , draw PS , P , S ,, P , S ,, perpendiculars on ...
Page 39
... cosine increases ; for CS СА CS and < CA CS , CS , СА < CA and when the revolving radius coincides with CD and the an- gle becomes 180 ° , CP coincides with CD and is equal to it . CS Hence since , generally , cos . = and since , when ...
... cosine increases ; for CS СА CS and < CA CS , CS , СА < CA and when the revolving radius coincides with CD and the an- gle becomes 180 ° , CP coincides with CD and is equal to it . CS Hence since , generally , cos . = and since , when ...
Other editions - View all
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield No preview available - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield No preview available - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield No preview available - 2018 |
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abscissa altitude arithmetical progression axes base bisected chord circle circular circular segment circumference cone conjugate axis construction convex surface corresponding cosec cosine cylinder described diameter distance divided draw drawn ellipse equal to half equation expression feet find the solidity formed formula Geom geometrical given height hence hyperbola inches infinite series latus rectum length logarithm major axis middle frustum minor axis multiplied ordinate parabola paraboloid parallel parallelogram perpendicular plane portion prism PROBLEM Prop PROPOSITION pyramid quadrant quantity radii radius ratio rectangle revoloidal surface right angles Scholium sector segment sides similar similar triangles sine specific gravity sphere spherical triangle spheroid spindle square straight line tangent THEOREM tion transverse axis Trigonometry ungula versed sine vertex vertical virtual centre zone
Popular passages
Page 44 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 197 - ... is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Page 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 219 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...
Page 68 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Page 14 - ... this point of intersection, as a pole, and limited by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described about A as a pole.
Page 27 - The circumference of every circle is supposed to be divided into 360 equal parts...
Page 36 - The solidity of a cylinder is equal to the area of its base multiplied by its altitude.
Page 7 - The radius of a sphere is a straight line, drawn from the centre to any point of the surface ; the diameter, or axis, is a line passing through this centre, and terminated on both sides by the surface.