When George Shoobridge Carr (1837–1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887–1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 1, presented here in its 1886 printing, contains sections on mathematical tables, algebra, the theory of equations, plane trigonometry, spherical trigonometry, elementary geometry and geometrical conics.
Author(s): George Shoobridge Carr
Edition: 1
Publisher: Cambridge University Press
Year: 2013
Language: English
Pages: 298
Front Cover
PART
Circle of similitude
-MATHEMATICAL TABLES
ELIMINATION-
FACTORS
100
MULTIPLICATION AND DIVISION
ANHARMONIC RATIO AND PENCIL
LOWEST COMMON MULTIPLE
ARITHMETICAL PROGRESSION
SIMULTANEOUS EQUATIONS AND EXAMPLES
CONTINUED FRACTIONS AND CONVERGENTS
TO REDUCE A QUADRATIC SURD TO A CONTINUED FRACTION
IMAGINARY EXPRESSIONS
EXPANSION OF A FRACTION
POLYGONAL NUMBERS
INEQUALITIES
Common and Hyperbolic Logarithms
FACTORS OF AN EQUATION
LIMITS OF THE ROOTS
-THEORY OF EQUATIONS
COMMENSURABle Roots
SYMMETRICAL FUNCTIONS OF THE ROOTS OF AN EQUATION-
Definitions
JOINT PROPERTIES OF THE ELLIPSE AND HYPERBOLA—
Symmetrical Determinants
CS: CA CX
Orthogonal Transformation
-PLANE TRIGONOMETRY
Squares of distances of P from equidistant points on
RATIOS OF 45°, 60°, 15°, 18°,
multiples
ADDITIONAL FORMULE
Explanation of the Table
RIGHT-ANGLED TRIANGLES-
POLYHEDRONS
RADICAL AXIS-
Of two Circles
POLE AND POLAR
Page
1151
1174
ASYMPTOTIC PROPERTIES OF THE HYPERBOLA—
DIAMETERS
CIRCLE OF CURVATURE
THE GENERAL EQUATION
—DIFFERENTIAL CALCULUS
PARTIAL DIFFERENTIATION
IMPLICIT FUNCTIONS-
Abel's series
JACOBIANS
Expansion of cos no, &c in powers of sin and cos 0
One independent variable
FUNCTIONS OF TWO INDEPENDENT VARIABLES
CHANGE OF THE INDEPENDENT VARIABLE
MAXIMA AND MINIMA-
—INTEGRAL CALCULUS
STANDARD INTEGRALS
Taylor's and Maclaurin's theorems
SUCCESSIVE INTEGRATION
DEFINITE INTEGRALS-
APPROXIMATE INTEGRATION BY BERNOULLI'S SERIES
INTEGRATION OF LOGARITHMIC AND EXPONENTIAL FORMS
INTEGRATION OF CIRCULAR FORMS
INTEGRATION OF CIRCULAR LOGARITHMIC AND EXPONENTIAL FORMS
MISCELLANEOUS THEOREMS-
Fourier's formula
Summation of series by the function
MULTIPLE INTEGRALS-
Method by Maclaurin's theorem
EXPANSION OF FUNCTIONS IN TRIGONOMETRICAL SERIES
FUNCTIONS OF ONE INDEPENDENT VARIABLE
FUNCTIONS OF TWO DEPENDENT VARIABLES
—CALCULUS OF VARIATIONS
APPENDIX-
SINGULAR SOLUTIONS
Riccati's Equation
HIGHER ORDER LINEAR EQUATIONS
EXACT DIFFERENTIAL EQUATIONS
EQUATIONS WITH MORE THAN TWO VARIABLES
PARTIAL DIFFERENTIAL EQUATIONS
SECOND ORDER P D EQUATIONS
LAW OF RECIPROCITY
SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS BY SERIES
FORMULE FOR FIRST AND nth DIFFERENCES
MECHANICAL QUADRATURE
THE CIRCLE
LENGTHS AND AREAS
Co-axal circles
THE ELLIPSE AND HYPERBOLA
THE HYPERBOLA REFERRED TO ITS ASYMPTOTES
ANALYTICAL CONICS IN TRILINEAR COORDINATES
NINE-POINT CIRCLE
ANHARMONIC RATIO
PARTICULAR CONICS
CONIC AND SELF-CONJUGATE TRIANGLE
CARNOT'S, PASCAL'S, AND BRIANCHON'S THEOREMS
THE METHOD OF RECIPROCAL POLARS
ON THE INTERSECTION OF TWO CONICS-
INVARIANTS AND COVARIANTS
TANGENT AND NORMAL
SINGULARITIES OF CURVES---
INVERSE CURves
Instantaneous centre
LINKAGES AND LINKWORK
A linkage for drawing an Ellipse
-SOLID COORDINATE GEOMETRY
TRANSFORMATION OF COORDINATES
CENTRAL QUADRIC SURFACE-
THE GENERAL EQUATION OF A QUADRIC
RECIPROCAL POLARS
GENERAL THEORY OF SURFACES-
GEODESICS
Momental ellipsoids
PERIMETERS, AREAS, VOLUMES, CENTRES OF MASS, AND MOMENTS
ELLIPSOID, HYPERBOLOID, AND PARABOLOID
Arbogast's method of expanding ø
COLLINEAR AND CONCURRENT SYSTEMS
5626
3150
3380
5590
4001-28
