An elementary treatise on quaternions |
From inside the book
Results 1-5 of 100
Page v
... Quaternion analysis than I can now pretend to be . Had it been then completed I should have had means of testing its teaching capabilities , and of improving it , before publication , where found deficient in that respect . The duties ...
... Quaternion analysis than I can now pretend to be . Had it been then completed I should have had means of testing its teaching capabilities , and of improving it , before publication , where found deficient in that respect . The duties ...
Page vi
... Quaternions , will yet sufficiently show their admirable simplicity and naturalness to induce the reader to attack the Lectures and the Elements ; where he will find , in profusion , stores of valuable results , and of elegant yet ...
... Quaternions , will yet sufficiently show their admirable simplicity and naturalness to induce the reader to attack the Lectures and the Elements ; where he will find , in profusion , stores of valuable results , and of elegant yet ...
Page vii
... Quaternion logarithms and exponentials , I greatly regret not having given . But if I had printed all that seemed to me of use or interest to the student , I might easily have rivalled the bulk of one of Hamilton's volumes . The ...
... Quaternion logarithms and exponentials , I greatly regret not having given . But if I had printed all that seemed to me of use or interest to the student , I might easily have rivalled the bulk of one of Hamilton's volumes . The ...
Page viii
... Quaternions ; but what is true of operators and functions in other methods , that they are not generally com- mutative , is in Quaternions true in the multiplication of ( vector ) cöordinates . It will be observed by those who are ...
... Quaternions ; but what is true of operators and functions in other methods , that they are not generally com- mutative , is in Quaternions true in the multiplication of ( vector ) cöordinates . It will be observed by those who are ...
Page ix
... Quaternion solution becomes identical with the Cartesian one . Nothing therefore is ever lost , though much is generally gained , by employing Quaternions in preference to ordinary methods . In fact , even when Quaternions degrade to ...
... Quaternion solution becomes identical with the Cartesian one . Nothing therefore is ever lost , though much is generally gained , by employing Quaternions in preference to ordinary methods . In fact , even when Quaternions degrade to ...
Other editions - View all
Common terms and phrases
a₁ arcs axes axis B₁ Cartesian centre Chapter circle commutative law cone conjugate constant cöordinates coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression extremity Find the equation Find the locus formula geometry given equation given lines given point given vectors gives Hamilton Hence indeterminate intersection LAOB last section length linear and vector m₁ m₂ multiply normal obviously origin osculating plane P₁ parabola parallel properties prove quaternion radius rectangular represents right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate sides solution sphere spherical conic ẞ² straight line student surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vector Vaß vector function vector perpendicular versor written φρ
Popular passages
Page 153 - Find the locus of a point the ratio of whose distances from two given points is constant. Let the given points be 0 and A, the extremities of the vector a.
Page 149 - Find the equation of the locus of a point the sum of the squares of whose distances from a number of given planes is constant. 11. Substitute " lines" for "planes
Page 217 - Differentiation of the equations gives us 3p + q+l equations, linear and homogeneous in the 3m + n differentials of the scalar parameters, so that by the elimination of these we have one final scalar equation in the first case, two in the second ; and thus in each case we have just equations enough to eliminate all the arbitrary parameters.
Page 14 - The bisectors of the sides of a triangle meet in a point, which trisects each of them.
Page 195 - Find the equation of the locus of a point the square of whose distance from a given line is proportional to its distance from a given plane.
Page 50 - It is curious to compare the properties of these quaternion symbols with those of the Elective Symbols of Logic, as given in BOOLE'S wonderful treatise on the Laws of Thought ; and to think that the same grand science of mathematical analysis, by processes remarkably similar to each other, reveals to us truths in the science of position far beyond the powers of the geometer, and truths of deductive reasoning to which unaided thought could never have led the logician.