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 5
... Spherical Triangles , - CHAP . III . - Solution of Oblique Angled Spherical Triangles , 144 150 CHAP . IV . On the use of Subsidiary Angles , 154 APPLICATION OF ALGEBRA TO GEOMETRY . Construction of Algebraical Quantities.
... Spherical Triangles , - CHAP . III . - Solution of Oblique Angled Spherical Triangles , 144 150 CHAP . IV . On the use of Subsidiary Angles , 154 APPLICATION OF ALGEBRA TO GEOMETRY . Construction of Algebraical Quantities.
Page 6
... Quantities , Geometrical Questions , the modes of forming Equations therefrom , and their Solutions , Determination of Algebraic Expressions for Surfaces and Solids , CONIC SECTIONS . The Parabola and its Properties , The Ellipse and ...
... Quantities , Geometrical Questions , the modes of forming Equations therefrom , and their Solutions , Determination of Algebraic Expressions for Surfaces and Solids , CONIC SECTIONS . The Parabola and its Properties , The Ellipse and ...
Page 21
... quantity CBD . The triangles whose sides and angles are so large , have been excluded from our Definition ; but the only reason was , that the solution of them , or the determination of their 3 SPHERICAL GEOMETRY . 21.
... quantity CBD . The triangles whose sides and angles are so large , have been excluded from our Definition ; but the only reason was , that the solution of them , or the determination of their 3 SPHERICAL GEOMETRY . 21.
Page 33
... quantities which are immediately deducible from the above definitions , and from the principles of Geometry . Resuming the figure of Def . ( 3 ) : Since CSP is a right - angled triangle , and CP the hypothenuse , PS + CS2 = CP2 Dividing ...
... quantities which are immediately deducible from the above definitions , and from the principles of Geometry . Resuming the figure of Def . ( 3 ) : Since CSP is a right - angled triangle , and CP the hypothenuse , PS + CS2 = CP2 Dividing ...
Page 35
... CA = 2CA or , chord 2 sin . PCA 8 2 sin . 2 We shall now proceed to explain the principle by which the signs of the trigonometrical quantities are regulated- All lines measured from the point C along CA , ANALYTICAL PLANE TRIGONOMETRY . 35.
... CA = 2CA or , chord 2 sin . PCA 8 2 sin . 2 We shall now proceed to explain the principle by which the signs of the trigonometrical quantities are regulated- All lines measured from the point C along CA , ANALYTICAL PLANE TRIGONOMETRY . 35.
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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.