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 |
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Page 6
... Expressions for Surfaces and Solids , 180 CONIC SECTIONS . The Parabola and its Properties , The Ellipse and its Properties , The Hyperbola and its Properties , 189 - - 197 215 SPHERICAL GEOMETRY . SPHERICAL GEOMETRY . DEFINITIONS . 1 ...
... Expressions for Surfaces and Solids , 180 CONIC SECTIONS . The Parabola and its Properties , The Ellipse and its Properties , The Hyperbola and its Properties , 189 - - 197 215 SPHERICAL GEOMETRY . SPHERICAL GEOMETRY . DEFINITIONS . 1 ...
Page 23
... expression , A represents such a part of unity , as the angle of the lune is of one right angle . Scholium . The spherical ungula , bounded by the planes AMB , ANB , is to the whole solid sphere , as the angle A is to four right angles ...
... expression , A represents such a part of unity , as the angle of the lune is of one right angle . Scholium . The spherical ungula , bounded by the planes AMB , ANB , is to the whole solid sphere , as the angle A is to four right angles ...
Page 27
... expression 30 ° 20 ′ 12 ′′ 22 ' ' , repre- sents an arc or an angle of 30 degrees 20 minutes 12 seconds 22 thirds . The circumference of any circle may in this manner be ap- plied as the measure of angles , without regard to its magni ...
... expression 30 ° 20 ′ 12 ′′ 22 ' ' , repre- sents an arc or an angle of 30 degrees 20 minutes 12 seconds 22 thirds . The circumference of any circle may in this manner be ap- plied as the measure of angles , without regard to its magni ...
Page 46
... expression , from its great importance , is called the fundamental formula of Plane Trigonometry , and nearly the whole science may be derived from it . Given the sines and cosines of two angles , to find the sine of By formula ( a ) ...
... expression , from its great importance , is called the fundamental formula of Plane Trigonometry , and nearly the whole science may be derived from it . Given the sines and cosines of two angles , to find the sine of By formula ( a ) ...
Page 47
... expression , = cos . A cos . β + sin . 4 sin . β - - ( d ) That is , the cosine of the difference of two arcs or angles , is equal to the cosine of the first multiplied by the cosine of the second , plus sine of the first into the sine ...
... expression , = cos . A cos . β + sin . 4 sin . β - - ( d ) That is , the cosine of the difference of two arcs or angles , is equal to the cosine of the first multiplied by the cosine of the second , plus sine of the first into the sine ...
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Common terms and phrases
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 passing 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 triangle ABC Trigonometry ungula versed sine vertex vertical virtual centre whence
Popular passages
Page 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 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".
Page 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.
Page 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.
Page 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.
Page 8 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 27 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 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.