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 3
... taken mostly from Brewster's translation of Legendre's work . Ana- lytical plane and spherical trigonometry , based on the subject , as found in Rutherford's edition of Hutton's Mathematics , being originally abridged from the larger ...
... taken mostly from Brewster's translation of Legendre's work . Ana- lytical plane and spherical trigonometry , based on the subject , as found in Rutherford's edition of Hutton's Mathematics , being originally abridged from the larger ...
Page 15
... taken toge- ther , are equal to two right angles . PROPOSITION IX . THEOREM . If from the vertices of the three angles of a spherical triangle , as poles , three arcs be described forming a second triangle , the vertices of the angles ...
... taken toge- ther , are equal to two right angles . PROPOSITION IX . THEOREM . If from the vertices of the three angles of a spherical triangle , as poles , three arcs be described forming a second triangle , the vertices of the angles ...
Page 21
... taken together , are equal to two right angles ; hence the angle ABC itself , is less than two right angles . We may observe , however , that some spherical triangles do exist , in which certain of the sides are greater than a semi ...
... taken together , are equal to two right angles ; hence the angle ABC itself , is less than two right angles . We may observe , however , that some spherical triangles do exist , in which certain of the sides are greater than a semi ...
Page 22
... taken for unity , the surface of the sphere will be represented by 8. This granted , the surface of the lune , whose angle is A , will be ex- pressed by 2A ( the angle A being always estimated from the right angle assumed as unity ...
... taken for unity , the surface of the sphere will be represented by 8. This granted , the surface of the lune , whose angle is A , will be ex- pressed by 2A ( the angle A being always estimated from the right angle assumed as unity ...
Page 23
... taken away from them , there will remain the angle QFE , equal to PCB . Also the sides QF , FE are equal to the sides PC , CB ; hence the two triangles FQE , CPB are equal in all their parts ; hence the side QE = PB SPHERICAL GEOMETRY . 23.
... taken away from them , there will remain the angle QFE , equal to PCB . Also the sides QF , FE are equal to the sides PC , CB ; hence the two triangles FQE , CPB are equal in all their parts ; hence the side QE = PB SPHERICAL GEOMETRY . 23.
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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
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.