## A Synopsis of Elementary Results in Pure Mathematics: Containing Propositions, Formulæ, and Methods of Analysis, with Abridged Demonstrations. Supplemented by an Index to the Papers on Pure Mathematics which are to be Found in the Principal Journals and Transactions of Learned Societies, Both English and Foreign, of the Present Century |

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please publish this book and send to india many people are waiting for this book

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I was so glad to find this book online. It conciseness and logical flow is legendary and is a wonderful example of a great and humble teacher creating a work that enables attentive students to witness the beautiful consistency and interconnectiveness of mathematics.

Thanks for keeping this book alive.

Charley

### Contents

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### Common terms and phrases

angle Binomial Theorem centre changes of sign CM CM CO CO column complete quotient conic conjugate constant continued fraction convergent CT Ft cubic cubic equation curve determinant diameter differentiating divided divisible divisors ellipse equal Equate coefficients expansion factors FN FN formula Ft Ft function hyperbola imaginary roots integer integral intersect last term logarithm maxima and minima method Multiply negative Nine-point circle number of changes o o o o o r obtained Ol Ol parallel partial fractions perpendicular plane powers prime Proof Proof.—By proper fraction quadratic quantity quotient radical axis radius ratio real root remainder result rt rt sides Similarly square Substitute tangent triangle unity vanish zero

### Popular passages

Page 203 - ... lines drawn from the angles of a triangle to the middle points...

Page xiv - These criteria were derived by a new transformation, namely the one which yields an equation whose roots are the squares of the differences of the roots of the given...

Page xxiv - If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to that plane. Let AB, A'B', be parallel lines, and let n s' AB be perpendicular to the plane MN; then, A'B

Page xxii - To divide a given straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part*.

Page 196 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.

Page xxi - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.

Page 197 - The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the mid-points of the diagonals.

Page 197 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.

Page 186 - If two angles of a triangle are equal, the opposite sides are also equal, and the triangle is isosceles.

Page xxii - Angle formed by a Tangent to a Circle, and a Chord drawn from the Point of Contact, is Equal to the Angle in the Alternate Segment.