Higher Geometry and Trigonometry: Being the Third Part of a Series on Elementary and Higher Geometry, Trigonomentary and Mensuration : Containing Many Valuable Discoveries and Improvements in Mathematical Science, Especially in Relation to the Quadrature of the Circle, and Some Other Curves, as Well as the Cubature of Certain Curvilinear Solids : Designed as a Text-book for Collegiate and Academic Instruction, and as a Practical Compendium of MensurationCollins, Brother, 1845 - 232 páginas |
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Página 7
... through the centre ; a small circle , one which does not pass through the centre . 4. A plane is tangent to a sphere , when their surfaces have but one point in common . 5. The pole of a circle of a sphere is SPHERICAL GEOMETRY.
... through the centre ; a small circle , one which does not pass through the centre . 4. A plane is tangent to a sphere , when their surfaces have but one point in common . 5. The pole of a circle of a sphere is SPHERICAL GEOMETRY.
Página 8
... tangent to the sphere ; in which case , the zone has only a single base . 13. A spherical segment is the portion of the solid sphere included between two parallel planes which form its bases . One of these planes may be tangent to the ...
... tangent to the sphere ; in which case , the zone has only a single base . 13. A spherical segment is the portion of the solid sphere included between two parallel planes which form its bases . One of these planes may be tangent to the ...
Página 14
... tangents AF , AG , and be measured by the arc DE , described about A as a pole . For the tangent AF , drawn in the plane of the arc AB , is perpendicular to the ra- 0 dius AO ; and the tangent AG , drawn in the plane of the arc AC , is ...
... tangents AF , AG , and be measured by the arc DE , described about A as a pole . For the tangent AF , drawn in the plane of the arc AB , is perpendicular to the ra- 0 dius AO ; and the tangent AG , drawn in the plane of the arc AC , is ...
Página 30
... tangent to the circumference at A. Produce CP to meet AT in T. S B E 4. Then the ratio of PS to the radius CA of the circle , is called the sine of the angle PCA . Or , PS = sin . 0 . CA 5. The ratio of AT to the radius CA of the circle ...
... tangent to the circumference at A. Produce CP to meet AT in T. S B E 4. Then the ratio of PS to the radius CA of the circle , is called the sine of the angle PCA . Or , PS = sin . 0 . CA 5. The ratio of AT to the radius CA of the circle ...
Página 31
... tangent of the complement of any given angle , is called the cotangent of that angle . Thus , tan . ( 90 ° -4 ) = cot . 4 , hence cot . ( 90 ° -4 ) = tan . 10. The secant of the complement of any given angle , is called the cosecant of ...
... tangent of the complement of any given angle , is called the cotangent of that angle . Thus , tan . ( 90 ° -4 ) = cot . 4 , hence cot . ( 90 ° -4 ) = tan . 10. The secant of the complement of any given angle , is called the cosecant of ...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ... Nathan Scholfield Visualização integral - 1845 |
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... Nathan Scholfield Pré-visualização indisponível - 2015 |
Palavras e frases frequentes
abscissa altitude arithmetical progression axes base bisected chord circle circular circular segment circumference cone conjugate construction convex surface corresponding cosec cosine cylinder described diameter distance divided draw drawn ellipse equal to half equation expression feet formed formula frustum Geom geometrical given height hence hyperbola inches infinite series latus rectum length logarithm major axis multiplied opposite ordinates parabola parallel parallelogram perpendicular plane portion prism Prop PROPOSITION pyramid quadrant quadrature quantity radii radius ratio rectangle represent revoloidal surface right angles Scholium sector segment sides similar similar triangles sine solidity specific gravity sphere spherical triangle spheroid spindle square straight line tangent THEOREM tion trian triangle ABC trigonometrical ungula versed sine vertex vertical virtual centre whence
Passagens conhecidas
Página 122 - E to A, from A to B, from B to C, and from C to...
Página 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 81 - N .-. by definition, x — x" is the logarithm of ^ ; that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the nth power. N"=a".
Página 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.
Página 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.
Página 138 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Página 8 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 27 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 78 - In a system of logarithms all numbers are considered as the powers of some one number, arbitrarily chosen, which is called the base of the system, and the exponent of that power of the base which is equal to any given number, is called the logarithm of that number. Thus, if a be the base of a system of logarithms, N any number, and x such that N = a* then x is called the logarithm of N in the system whose base is a.