An Elementary Treatise on Quaternions |
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Page vii
... easily have rivalled the bulk of one of Hamilton's volumes . The beginner is recommended merely to read the first five Chapters , then to work at Chapters VI , VII , VIII ( to which numerous easy Examples are appended ) . After this he ...
... easily have rivalled the bulk of one of Hamilton's volumes . The beginner is recommended merely to read the first five Chapters , then to work at Chapters VI , VII , VIII ( to which numerous easy Examples are appended ) . After this he ...
Page ix
... easily introduced into Quaternions as into Cartesian methods ) are quite beyond the amount of mathematics which even the best students can master in three years ' reading . One grand step to the supply of this want is , of course , the ...
... easily introduced into Quaternions as into Cartesian methods ) are quite beyond the amount of mathematics which even the best students can master in three years ' reading . One grand step to the supply of this want is , of course , the ...
Page 3
... easily that p , q , r must be non - reals : but , he asks , " seraient - elles imaginaires réductibles à la forme générale A + B√ − 1 ? " This he could not answer . In fact they are the i , j , k of the Quaternion Calculus . ( See ...
... easily that p , q , r must be non - reals : but , he asks , " seraient - elles imaginaires réductibles à la forme générale A + B√ − 1 ? " This he could not answer . In fact they are the i , j , k of the Quaternion Calculus . ( See ...
Page 7
... easily extended to incommensurables by the usual reductio ad absurdum . 23. ] An important , but almost obvious , proposition is that any vector may be resolved , and in one way only , into three components parallel respectively to any ...
... easily extended to incommensurables by the usual reductio ad absurdum . 23. ] An important , but almost obvious , proposition is that any vector may be resolved , and in one way only , into three components parallel respectively to any ...
Page 11
... easily verified by producing Aa to twice its length and joining the extremity with B. ( b ′ . ) The bisectors of the sides of a triangle meet in a point , which trisects each of them . Taking A as origin , and putting a , ß , y for ...
... easily verified by producing Aa to twice its length and joining the extremity with B. ( b ′ . ) The bisectors of the sides of a triangle meet in a point , which trisects each of them . Taking A as origin , and putting a , ß , y for ...
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Common terms and phrases
a₁ axes axis Cartesian centre Chapter circle condition cone conjugate cöordinates coplanar curvature curve cylinder developable surface direction drawn easily Eliminating ellipsoid equal equation becomes evidently expression extremity Find the equation Find the locus formula given equation given lines given point gives Hamilton Hence integral intersection LAOB last section length linear and vector normal obviously once operating origin osculating plane parallel perpendicular properties prove quaternion radius rectangular system represents result right angles rotation S.aßp S.aßy Sapa Saß scalar scalar equations second order shew sin sin sin solution sphere spherical conic Spopp ẞ² suppose surface of revolution tangent plane tensor tetrahedron theorem three vectors triangle unit-vector Vaß vector function vector perpendicular versor write written Τρ φρ