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 9
... greater CO is , the less is the chord AB , the diameter of the small circle AMB . Cor . 6. An arc of a great circle may always be made to pass through any two given points of the surface of the sphere ; for the two given points , and ...
... greater CO is , the less is the chord AB , the diameter of the small circle AMB . Cor . 6. An arc of a great circle may always be made to pass through any two given points of the surface of the sphere ; for the two given points , and ...
Página 11
... greater than AD . Hence no point of the shortest line from A to B can lie out of the arc ADB ; hence this arc is itself the shortest distance be- tween its two extremities . PROPOSITION IV . THEOREM . The sum of the three sides of a ...
... greater than AD . Hence no point of the shortest line from A to B can lie out of the arc ADB ; hence this arc is itself the shortest distance be- tween its two extremities . PROPOSITION IV . THEOREM . The sum of the three sides of a ...
Página 14
... greater than OA . Hence the point M lies without the sphere ; and as the same can be shown for every other point of the plane FAG , this plane can have no point but A common to it and the sur- face of the sphere ; hence ( Def . 4. ) it ...
... greater than OA . Hence the point M lies without the sphere ; and as the same can be shown for every other point of the plane FAG , this plane can have no point but A common to it and the sur- face of the sphere ; hence ( Def . 4. ) it ...
Página 19
... greater of the two ; take BO = AC , and join OC . The two sides BO , BC are equal to the two AC , BC ; the angle OBC ... greater side is opposite the great- er angle ; and conversely , the greater angle is opposite the greater side . Let ...
... greater of the two ; take BO = AC , and join OC . The two sides BO , BC are equal to the two AC , BC ; the angle OBC ... greater side is opposite the great- er angle ; and conversely , the greater angle is opposite the greater side . Let ...
Página 20
... greater than two . For , in the first place , every angle of a spherical triangle . is less than two right angles ( see the following Scholium ) : hence the sum of all the three is less than six right angles . Secondly , the measure of ...
... greater than two . For , in the first place , every angle of a spherical triangle . is less than two right angles ( see the following Scholium ) : hence the sum of all the three is less than six right angles . Secondly , the measure 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.