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

Collins, Brother, 1845 - 232 sider

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 SPHERICAL GEOMETRY 7 Definitions and Illustration of Principles 27 General Formulae 45 Formula for the Solution of Triangles 66 Construction of Trigonometrical Tables? 73 Logarithms 93 On the use of Subsidiary Angles 107 CHAP XProblems in Trigonometrical Surveying c 113
 SPHERICAL TRIGONOMETRY 131 Solution of Oblique Angled Spherical Triangles 150 PAGE 158 Geometrical Questions the modes of forming Equations therefrom 165 Determination of Algebraic Expressions for Surfaces and Solids 180 CONIC SECTIONS 189 The Ellipse and its Properties 197 The Hyperbola and its Properties 215

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Side 122 - E to A, from A to B, from B to C, and from C to...
Side 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Side 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.
Side 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".
Side 27 - The circumference of every circle is supposed to be divided into 360 equal parts...
Side 7 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Side 8 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Side 14 - ... point of intersection, as a pole, and limited by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then...
Side 18 - For, if the arc AD be drawn from the vertex A to the middle point D of the base, the two triangles ABD, ACD will have all the sides of the one respectively equal to the corresponding sides of the other, namely, AD common, BD=DC, and AB= AC : hence by the last Proposition, their angles will be equal ; therefore B=C.
Side 11 - The sum of all the sides of any spherical polygon is less than the circumference of a great circle.