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 Mensuration
Collins, Brother, 1845 - 232 sider
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...
Uten tilgangsbegrensning - 1845
abscissa altitude arithmetical progression asymptotes 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 OREM parabola parallel parallelogram passing perpendicular plane portion prism Prop proportional PROPOSITION pyramid quadrant quadrature quantity radii radius ratio rectangle represent revoloidal curve revoloidal surface right angles Scholium sector segment sides similar similar triangles sine solidity sphere spherical triangle spheroid spindle square straight line tangent THEOREM tion trian trigonometrical ungula versed sine vertex vertical virtual centre whence
Side 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".
Side 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.
Side 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.
Side 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.
Side 8 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Side 27 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Side 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.