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 20
... proportionality among the sides . Nor is it difficult to account for the difference observable , in this respect , between spheri- cal and rectilineal triangles . In the proposition now before us , as well as in Propositions XII , XIII ...
... proportionality among the sides . Nor is it difficult to account for the difference observable , in this respect , between spheri- cal and rectilineal triangles . In the proposition now before us , as well as in Propositions XII , XIII ...
Página 27
... proportional to their mutual inclination , and hence ( Prop . XVIII . Cor . B. III . El . Geom . ) the arc of the circumference of a circle intercepted by two lines drawn from its centre , may be regarded as the mea- sure of the angle ...
... proportional to their mutual inclination , and hence ( Prop . XVIII . Cor . B. III . El . Geom . ) the arc of the circumference of a circle intercepted by two lines drawn from its centre , may be regarded as the mea- sure of the angle ...
Página 74
... above mentioned has been repeated so many times , the sine of the arc is halved at the same time that the arc itself is bisected : that is , The sines of very small arcs are nearly proportional to 74 ANALYTICAL PLANE TRIGONOMETRY .
... above mentioned has been repeated so many times , the sine of the arc is halved at the same time that the arc itself is bisected : that is , The sines of very small arcs are nearly proportional to 74 ANALYTICAL PLANE TRIGONOMETRY .
Página 75
... proportional to the arcs themselves . Hence we shall have Sin . 52 " 44 " 3iv 45v : sin . 1 ' :: 52 " 44 " 3v 45 ° : 1 ' 60 :: 212 :: 3600 60 : 60 × 60 : 4096 .. sin . 1 ' : sin . 52 " 44 " 3iv 45 ′ X 4096 3600 .0002556634 X 4096 3600 ...
... proportional to the arcs themselves . Hence we shall have Sin . 52 " 44 " 3iv 45v : sin . 1 ' :: 52 " 44 " 3v 45 ° : 1 ' 60 :: 212 :: 3600 60 : 60 × 60 : 4096 .. sin . 1 ' : sin . 52 " 44 " 3iv 45 ′ X 4096 3600 .0002556634 X 4096 3600 ...
Página 77
... proportional logarithms , whether intregers or decimals . It also appears from the construction of these series , that if any two indices be added together , their sum will be the in- dex of that number which is equal to the product of ...
... proportional logarithms , whether intregers or decimals . It also appears from the construction of these series , that if any two indices be added together , their sum will be the in- dex of that number which is equal to the product 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.