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 10
... measured by AB , AC , BC , the sides of the spherical triangle . But each of the three plane angles forming a solid A B angle is less than the sum of the other two ( Prop . XXI . , B. I. El . S. Geom . ) : hence any side of the triangle ...
... measured by AB , AC , BC , the sides of the spherical triangle . But each of the three plane angles forming a solid A B angle is less than the sum of the other two ( Prop . XXI . , B. I. El . S. Geom . ) : hence any side of the triangle ...
Página 14
... measured by the arc described from 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 ...
... measured by the arc described from 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 ...
Página 15
... measured by the semicircumference minus the side lying opposite to it in the other triangle . Produce the sides ( see the preceding diagram ) AB , AC , if necessary , till they meet EF , in G and SPHERICAL GEOMETRY . 15.
... measured by the semicircumference minus the side lying opposite to it in the other triangle . Produce the sides ( see the preceding diagram ) AB , AC , if necessary , till they meet EF , in G and SPHERICAL GEOMETRY . 15.
Página 16
... measured by that arc . But the arc EH is a quadrant , and likewise GF , E be- ing the pole of AH , and F of AG ; hence EH + GF is equal to the semicircumference . Now , EH + GF is the same as EF + GH ; hence the arc GH , which measures ...
... measured by that arc . But the arc EH is a quadrant , and likewise GF , E be- ing the pole of AH , and F of AG ; hence EH + GF is equal to the semicircumference . Now , EH + GF is the same as EF + GH ; hence the arc GH , which measures ...
Página 20
... ; hence the sum of all the three , is measured by three semicircumferences minus the sum of all the sides of the polar triangle . Now ( Prop . IV . ) , this latter sum is less than a circumference ; therefore , 20 SPHERICAL GEOMETRY .
... ; hence the sum of all the three , is measured by three semicircumferences minus the sum of all the sides of the polar triangle . Now ( Prop . IV . ) , this latter sum is less than a circumference ; therefore , 20 SPHERICAL GEOMETRY .
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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.