An Elementary Treatise on Quaternions |
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Page xv
... ; a vector ; if quaternions are to deal with space indifferently in all directions . § 93 . EXAMPLES TO CHAPTER II . 46 , 47 CHAPTER III . - INTERPRETATIONS AND TRANSFORMATIONS OF QUATERNION EXPRESSIONS CONTENTS . XV.
... ; a vector ; if quaternions are to deal with space indifferently in all directions . § 93 . EXAMPLES TO CHAPTER II . 46 , 47 CHAPTER III . - INTERPRETATIONS AND TRANSFORMATIONS OF QUATERNION EXPRESSIONS CONTENTS . XV.
Page 3
... space the form a + b√1 for the plane , he is guided by analogy to write for a directed unit - line in space the form p cos a + q cos ẞ + r cos y , where a , ß , y are its inclinations to the three axes . He perceives easily that p , q ...
... space the form a + b√1 for the plane , he is guided by analogy to write for a directed unit - line in space the form p cos a + q cos ẞ + r cos y , where a , ß , y are its inclinations to the three axes . He perceives easily that p , q ...
Page 4
... space expressible by real numbers , the re- mainder being imaginaries of some kind , leading in general to equations which are heterogeneous ; Hamilton makes all directions in space equally imaginary , or rather equally real , thereby ...
... space expressible by real numbers , the re- mainder being imaginaries of some kind , leading in general to equations which are heterogeneous ; Hamilton makes all directions in space equally imaginary , or rather equally real , thereby ...
Page 5
... space ; it is only the relative coordinates that are contemplated . Hence any expression , as AB , denoting a line considered with reference to direction as well as length , contains implicitly three numbers , and all lines parallel and ...
... space ; it is only the relative coordinates that are contemplated . Hence any expression , as AB , denoting a line considered with reference to direction as well as length , contains implicitly three numbers , and all lines parallel and ...
Page 9
... space . As we have seen ( § 25 ) it is equivalent to three numerical equations ; but , as these involve the indefinite quantity a , they are virtually equivalent to but two , as in ordinary Geometry of Three Dimensions . ' 29. ] A good ...
... space . As we have seen ( § 25 ) it is equivalent to three numerical equations ; but , as these involve the indefinite quantity a , they are virtually equivalent to but two , as in ordinary Geometry of Three Dimensions . ' 29. ] A good ...
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Common terms and phrases
a₁ axes axis Cartesian centre of inertia Chapter circle cloth cone conjugate constant cöordinates coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression Extra fcap extremity fcap Find the equation Find the locus given equation given line given vectors gives Hamilton Hence hodograph integral intersection last section length linear and vector locus normal obviously once operator origin osculating osculating plane P₁ parabola parallel perpendicular properties quaternion radius rectangular represents result right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate shew solution sphere spherical straight line suppose surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vectors Vaß vector function versor w₁ write written Τρ φρ