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 7
... diameter , or axis , is a line passing through this centre , and terminated on both sides by the surface . All the radii of a sphere are equal ; all the diameters are equal , and each double of the radius . 3. It will be shown ( Prop ...
... diameter , or axis , is a line passing through this centre , and terminated on both sides by the surface . All the radii of a sphere are equal ; all the diameters are equal , and each double of the radius . 3. It will be shown ( Prop ...
Page 8
... diameter . 10. A spherical wedge , or ungula , is that portion of the solid sphere which is included between the same great semi - circles , and has the lune for its base . 11. A spherical pyramid is a portion of the solid sphere in ...
... diameter . 10. A spherical wedge , or ungula , is that portion of the solid sphere which is included between the same great semi - circles , and has the lune for its base . 11. A spherical pyramid is a portion of the solid sphere in ...
Page 9
... diameter . Cor . 3. Every great circle divides the sphere and its sur- face into two equal parts ; for , if the two hemispheres were separated , and afterwards placed on the common base , with their convexities turned the same way , the ...
... diameter . Cor . 3. Every great circle divides the sphere and its sur- face into two equal parts ; for , if the two hemispheres were separated , and afterwards placed on the common base , with their convexities turned the same way , the ...
Page 12
... diameter of the sphere which is perpendicular to this cir- cle ; and these extremities are also the poles of all small circles parallel to it . Let ED be perpendi- cular to the great circle AMB ; then will E and D be its poles ; as also ...
... diameter of the sphere which is perpendicular to this cir- cle ; and these extremities are also the poles of all small circles parallel to it . Let ED be perpendi- cular to the great circle AMB ; then will E and D be its poles ; as also ...
Page 162
... diameter , describe a semicircle , cutting in D , the perpendicular CD , raised upon AB at the point C ; then CD will be the value of Vab ; that is , the value of vab is obtained by finding a mean proportional between the two quantities ...
... diameter , describe a semicircle , cutting in D , the perpendicular CD , raised upon AB at the point C ; then CD will be the value of Vab ; that is , the value of vab is obtained by finding a mean proportional between the two quantities ...
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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.