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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Common terms and phrases
a+b+c A₁ angle b₁ Binomial Binomial Theorem bisects C₁ centre changes of sign chord circle column conjugate constant constituents continued fraction convergent d₁ determinant diameter differential divided divisible divisors eliminant ellipse equal equate coefficients expansion factors formula function given Hence hyperbola imaginary roots infinite integer integral intersect last term limits logarithm method Multiply negative nine-point circle obtained P₁ parabola parallel partial fractions perpendicular plane positive powers prime PROOF PROOF.-By PROOF.-Let quadratic quantities quotient radical axis radius ratio respectively result rows RULE sides Similarly sin² sine singular solution solution square Substitute successive tangent theorem unity vanish variables zero
Popular passages
Page 193 - ... 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 186 - 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 187 - 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 187 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 176 - 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.