Elements of Quaternions |
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Page xxxvi
... manner , the reciprocal surface ( j ) is the envelope of this other plane , Έσω = 1 . ( E2 ' ) ( m ) . The equations ( W1 ) , ( W1 ' ) give ( comp . the Note to p . 684 ) , do = dR . Uv ; ( F2 ) combining which with ( C2 ) , we see that ...
... manner , the reciprocal surface ( j ) is the envelope of this other plane , Έσω = 1 . ( E2 ' ) ( m ) . The equations ( W1 ) , ( W1 ' ) give ( comp . the Note to p . 684 ) , do = dR . Uv ; ( F2 ) combining which with ( C2 ) , we see that ...
Page xliii
... manner it is found ( p . 702 ) , that the Condition * of In- tegrability of the equation ( Y2 ) is expressed by the very simple for- mala , Syv = 0 ; ( Y2 " ) in which y is a vector function of p , not generally linear , and deduced ...
... manner it is found ( p . 702 ) , that the Condition * of In- tegrability of the equation ( Y2 ) is expressed by the very simple for- mala , Syv = 0 ; ( Y2 " ) in which y is a vector function of p , not generally linear , and deduced ...
Page lvii
... manner the direction of the projection of the index - vector μ on the tangent plane to the index- surface so that the ray is thus perpendicular to the elastic force ARTICLE 423. - Mac Cullagh's Theorem of the Polar Plane , • lvii Pages ...
... manner the direction of the projection of the index - vector μ on the tangent plane to the index- surface so that the ray is thus perpendicular to the elastic force ARTICLE 423. - Mac Cullagh's Theorem of the Polar Plane , • lvii Pages ...
Page 5
... , which is obtained by adding the third to the sum of the first and second ; and in like manner the sum of any number of vectors is formed by adding the last to the sum of all that precede it : also , for any four vectors ,
... , which is obtained by adding the third to the sum of the first and second ; and in like manner the sum of any number of vectors is formed by adding the last to the sum of all that precede it : also , for any four vectors ,
Page 8
... manner , the double vector , a + a , is denoted by 2a , or 2. a , or ( + 2 ) a , & c . ; the rule being , that for any algebraical integer , m , regarded as a coefficient by which the vector a is multiplied , we have always , la + ma ...
... manner , the double vector , a + a , is denoted by 2a , or 2. a , or ( + 2 ) a , & c . ; the rule being , that for any algebraical integer , m , regarded as a coefficient by which the vector a is multiplied , we have always , la + ma ...
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Common terms and phrases
ABCD algebra angle anharmonic axis centre CHAP circle coefficients collinear comp Compare the Note complanar cone conic conjugate considered construction curvature curve cyclic deduced denote derived differential diplanar direction ellipsoid equal equation expression formula four fourth proportional function geometrical given plane given points harmonic conjugate imaginary interpreted intersection length line oa linear locus multiplication negative notation osculating osculating circle osculating plane P₁ parallelogram perpendicular positive quadratic quadrilateral quinary radius reciprocal relative direction represented right line right quaternions right quotient right versors roots rotation round scalar SECTION sides sphere spherical spherical angle sub-articles supposed surface symbol tangent tensor ternion theorem tion triangle ABC twisted cubic variable vector VIII whence whereof write