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 8
... Circle, and Some Other Curve Nathan Scholfield. 5. The pole of a circle of a sphere is ... segment is the portion of the solid sphere included between two parallel ... circular sector , as DCF or FCH , describes a solid , which is named a ...
... Circle, and Some Other Curve Nathan Scholfield. 5. The pole of a circle of a sphere is ... segment is the portion of the solid sphere included between two parallel ... circular sector , as DCF or FCH , describes a solid , which is named a ...
Page 186
... segment BDA ; in order to express these portions , it will be necessary to find the area of the cir- cular section ... circular section BPD , hence the area of the circle will be 2 * rh— « h3 , And the solidity of the cone will be ( 2xrh - ...
... segment BDA ; in order to express these portions , it will be necessary to find the area of the cir- cular section ... circular section BPD , hence the area of the circle will be 2 * rh— « h3 , And the solidity of the cone will be ( 2xrh - ...
Page 187
... segment , and whose vertice is the centre of the polyedroid or sphere , formula ( 6 , Art . 9 , ) may be expressed ... circular segment as BD , about the axis DC , passing through the centre of curvature , and per- pendicular to the arc ...
... segment , and whose vertice is the centre of the polyedroid or sphere , formula ( 6 , Art . 9 , ) may be expressed ... circular segment as BD , about the axis DC , passing through the centre of curvature , and per- pendicular to the arc ...
Page 35
... Circle, and Some Other Curve Nathan Scholfield. 6. A portion cut from a segment of a sphere by a plane perpendicular to the base of the segment is called a second segment . H The portion CceA is a second segment of a sphere . 7. Conical ...
... Circle, and Some Other Curve Nathan Scholfield. 6. A portion cut from a segment of a sphere by a plane perpendicular to the base of the segment is called a second segment . H The portion CceA is a second segment of a sphere . 7. Conical ...
Page 40
... Circle, and Some Other Curve Nathan Scholfield. the conical section KSHO is a ... circular sec- tion of the cylinder , and in the plane KSH of the base of the ... segment , whose base is the base of the ungula , and whose vertice is the ...
... Circle, and Some Other Curve Nathan Scholfield. the conical section KSHO is a ... circular sec- tion of the cylinder , and in the plane KSH of the base of the ... segment , whose base is the base of the ungula , and whose vertice is the ...
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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 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.