## The Algebra of Coplanar Vectors and Trigonometry (Google eBook) |

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### Common terms and phrases

absolutely convergent asymptotes Binomial Theorem centre chapter circular measure coefficients coincides commutative law complete complex number convergent series corresponding cos2 cosec cosh cosine cosm coth curve deduced definite denote determined diagram distinct values divergent equal equation excircle expression factors formulae fraction functions geometric series given Hence hyperbola inclination increased without limit infinite number infinite series integer laws logarithm loge logometers mean point middle point multiple nth root number of terms obtained ordinary algebra perpendicular plane positive integer positive or negative positive sense prime vector project and traject Prove quantity radius of fluctuation represented respectively right angles roots of unity scalar series is convergent sin2 sine sinh sinh2 student tangent tanh tensor triangle trigonometrical functions ultimately unit circle unit vector vanish Vector Magnitude verify versor whence

### Popular passages

Page 4 - Symbolical Algebra" it is thus enunciated: "Whatever algebraical forms are equivalent, when the symbols are general in form but specific in value, will be equivalent likewise when the symbols are general in value as well as in form.

Page xix - On the geometrical representation of the powers of quantities, whose indices involve the square roots of negative quantities.

Page xxi - O'Brien (Rev. M.) Treatise on Plane Coordinate Geometry ; or the Application of the Method of Coordinates to the Solution of Problems in Plane Geometry. 8vo. Plates, 9s.

Page xx - Syllabus of a Course of Lectures upon Trigonometry and the Application of Algebra to Geometry. 8vo. 7*. 6d. MECHANICS AND HYDROSTATICS. Elementary Hydrostatics. By WH BESANT, MA, Late Fellow of St John's College. [Preparing. Elementary Hydrostatics for Junior Students. By R. POTTER, MA late Fellow of Queens...

Page 55 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the two pairs of opposite sides.

Page 160 - ... with the last, the second with the last but one, and so on.

Page xix - The Principles and Application of Imaginary Quantities, Book I. ; to which are added, some observations on Porisms ; being the first of a series of original tracts in various parts of the Mathematics ; by Benj.

Page xix - Consideration of the objections raised against the geometrical representation of the square roots of negative quantities.

Page 22 - The straight lines which join the vertices of a tetrahedron to the centroids* of the opposite faces meet in a point which is a point of quadrisection of each line.

Page 213 - But it is clear that there is a wide margin of cases in which more subtle tests will be needed. Examples LXVIII. 1. Apply Cauchy's and d'Alembert's tests (as specialised in 7 above) to the series Znkrn, where k is a positive integer.