# An Elementary Course of Mathematics: Designed Principally for Students of the University of Cambridge

J. & J.J. Deighton, 1846 - Mathematics - 468 pages

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### Contents

 ALGEBRA 1 Subtraction 7 Negative and Fractional Indices 13 Least Common Multiple 19 Involution and Evolution 25 Equations 36 Problems producing Equations 49 Proportion 57
 Motion on a Curve 245 NEWTON 259 Digression concerning the Curvature of Curve Lines containing 275 On the motion of a Body in a Conic Section about a Centre of Force 296 APPENDIx To SECTION II 304 HYDROSTATICS 313 Floating Bodies 323 Barometer 329

 Geometrical Progression 64 Binomial Theorem 71 Logarithms 78 Mode of measuring angles 84 Formulae involving more than one angle 95 Solution of Triangles 103 Finding Heights and Distances 114 Circular measure of angles 125 Introduction 129 Ellipse 142 Hyperbola 155 and CY CY are in the same straight line Therefore SCP HCP are similar 156 MECHANICS 173 Any number of Forces acting in one Plane at the same point 185 Action and Reaction of Smooth Bodies 191 Friction 203 Introduction Velocity uniform and variable measure of Velocity 227 Rectilinear Motion of a Particle 237
 Airpump 335 The Diving Bell 342 OPTICS 349 Combined Reflexions 363 mbined Refractions 373 Images formed by Reflexion or Refraction 384 On the Bye 390 Refracting Telescopes 396 On the Sphere 411 The Seasons 417 Mode of determining the place of a heavenly Body 423 Methods of finding the Latitude of a place 433 Aberration 441 Proper Motion of the Fixed Stars 448 Tides 454 On the Satellites of the Planets 460 On Comets 467

### Popular passages

Page ii - The elementary parts of Astronomy, so far as they are necessary for the explanation of the more simple phenomena, without the use of spherical trigonometry ; astronomical instruments.
Page 49 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page ii - Arithmetic ; and the elementary parts of Algebra : namely, the rules for the fundamental operations upon algebraical symbols with their proofs, the solution of simple and quadratic equations, ratio and proportion, arithmetical, geometrical and liarmouical progression, permutations and combinations, the binomial theorem, and logarithms. The elementary parts of Plane Trigonometry, so far as to include the solution and properties of triangles. T cxcl...
Page 65 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 459 - The mean solar day is divided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds.
Page iii - Honours in the preceding January to have deserved to pass (according to the present standard) for an Ordinary Degree, so far as the Mathematical part of the Examination for such Degree is concerned, shall have afterwards passed in the other subjects of that Examination. (3) Those whose names shall have been placed (according to the present standard) in the first class in the Examination for an Ordinary Degree in the preceding January. (4) Those persons, entitled to Noblemen's Degrees, who shall...
Page i - That those who are declared to have so acquitted themselves, and no others, be admitted to the Examination in the higher parts of Mathematics ; and that after that Examination, the Moderators and Examiners, taking into account the Examination of all the eight days, shall arrange all the Candidates who have been declared to deserve Mathematical...
Page 20 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page ii - Trigonometry, namely, the composition and resolution of forces acting in one plane at a point, the mechanical powers, and the properties of the centre of gravity.