An Elementary Treatise on Quaternions |
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Page xi
... prove of interest to even the advanced student . Since the appearance of the first edition I have managed ( at least partially ) to effect the application of Quaternions to line , surface , and volume integrals , such as occur in ...
... prove of interest to even the advanced student . Since the appearance of the first edition I have managed ( at least partially ) to effect the application of Quaternions to line , surface , and volume integrals , such as occur in ...
Page 3
... proves . 11. ] A very curious speculation , due to Servois and published in 1813 in Gergonne's Annales , is the only one , so far as has been discovered , in which the slightest trace of an anticipation of Quaternions is contained ...
... proves . 11. ] A very curious speculation , due to Servois and published in 1813 in Gergonne's Annales , is the only one , so far as has been discovered , in which the slightest trace of an anticipation of Quaternions is contained ...
Page 4
... prove , it can be established , ab initio , in various ways , without even an allusion to Cartesian Geometry . As this work is written for students acquainted with at least the elements of the Cartesian method , we keep to the first ...
... prove , it can be established , ab initio , in various ways , without even an allusion to Cartesian Geometry . As this work is written for students acquainted with at least the elements of the Cartesian method , we keep to the first ...
Page 8
... prove this for the sign + , it will be equally proved for - , because before a vector ( § 20 ) merely indicates that it is to be reversed before being considered positive . Let A , B , C , D be , in order , the corners of a ...
... prove this for the sign + , it will be equally proved for - , because before a vector ( § 20 ) merely indicates that it is to be reversed before being considered positive . Let A , B , C , D be , in order , the corners of a ...
Page 10
... proving , in a very simple manner , numerous classes of propositions in plane and solid geo- metry . A very few examples , however , must suffice at this stage ; since we have hardly , as yet , crossed the threshold of the subject , and ...
... proving , in a very simple manner , numerous classes of propositions in plane and solid geo- metry . A very few examples , however , must suffice at this stage ; since we have hardly , as yet , crossed the threshold of the subject , and ...
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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