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 181
... frustum of a pyramid . Leth = the altitude , s = the greater base and s ' the smaller base , and h ' = the altitude of the vertical pyramid taken from the top of the frustum , then we shall have ✓s ' : s :: h ' : h + h ' or the ...
... frustum of a pyramid . Leth = the altitude , s = the greater base and s ' the smaller base , and h ' = the altitude of the vertical pyramid taken from the top of the frustum , then we shall have ✓s ' : s :: h ' : h + h ' or the ...
Page 182
... frustum is equal to the sum of the greater base , the smaller base , and a mean proportional be- tween the two bases , multiplied by the altitude of the frustum ; which agrees with the proposition in geometry . And if the two bases are ...
... frustum is equal to the sum of the greater base , the smaller base , and a mean proportional be- tween the two bases , multiplied by the altitude of the frustum ; which agrees with the proposition in geometry . And if the two bases are ...
Page 183
... frustum in con- nection with the whole pyramid of which it is a part . Thus S ss √s :: h : hs ' √s the slant height of the whole pyramid , which make = k , and the vertical pyramid cut from the frustum will be k - h . Hence , we have ...
... frustum in con- nection with the whole pyramid of which it is a part . Thus S ss √s :: h : hs ' √s the slant height of the whole pyramid , which make = k , and the vertical pyramid cut from the frustum will be k - h . Hence , we have ...
Page 184
... frustum of the cone , then may the slant height of the frustum be h : k : h ' : h'k the slant height hsh required , which call k ' ; let the radius 184 APPLICATION OF.
... frustum of the cone , then may the slant height of the frustum be h : k : h ' : h'k the slant height hsh required , which call k ' ; let the radius 184 APPLICATION OF.
Page 185
... frustum ber ' , then will the lateral surface be = rk'a + r'k ' 2rx + 2r ' 2 -xk ' ( 11 ) = the greater base , and ... frustum , hence if one of those expressions is taken from that of the frustum , the remainder will express a ...
... frustum ber ' , then will the lateral surface be = rk'a + r'k ' 2rx + 2r ' 2 -xk ' ( 11 ) = the greater base , and ... frustum , hence if one of those expressions is taken from that of the frustum , the remainder will express a ...
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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.