An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina xvi
... differential , dr = dFq = ↓ „ n { F ( q + d ) - Pq } , £ where dq is any quaternion whatever . We may write dFq = f ( q , dq ) , 68-70 71-76 where f is linear and homogeneous in dq ; but we cannot generally write dFq = f ( q ) dq ...
... differential , dr = dFq = ↓ „ n { F ( q + d ) - Pq } , £ where dq is any quaternion whatever . We may write dFq = f ( q , dq ) , 68-70 71-76 where f is linear and homogeneous in dq ; but we cannot generally write dFq = f ( q ) dq ...
Pagina xvii
... differential may be written where v is a vector normal to the surface . § 137 . EXAMPLES TO CHAPTER IV . . 76 CHAPTER V. - THE SOLUTION OF EQUATIONS OF THE FIRST DEGREE . 77-100 The most general equation of the first degree in an ...
... differential may be written where v is a vector normal to the surface . § 137 . EXAMPLES TO CHAPTER IV . . 76 CHAPTER V. - THE SOLUTION OF EQUATIONS OF THE FIRST DEGREE . 77-100 The most general equation of the first degree in an ...
Pagina 17
... differential , which is , simply , what Newton called a fluxion . As with the Laws of Motion , the basis of Dynamics , so with the foundations of the Differential Calculus ; we are gradually coming to the conclusion that Newton's system ...
... differential , which is , simply , what Newton called a fluxion . As with the Laws of Motion , the basis of Dynamics , so with the foundations of the Differential Calculus ; we are gradually coming to the conclusion that Newton's system ...
Pagina 21
... differential calculus . The equations of any two of the enveloping lines are p = at + x - ( 2 — at ) , B - — atı ) , p = at1 + x1 t and t1 being given , while x and x1 are indeterminate . At the point of intersection of these lines we ...
... differential calculus . The equations of any two of the enveloping lines are p = at + x - ( 2 — at ) , B - — atı ) , p = at1 + x1 t and t1 being given , while x and x1 are indeterminate . At the point of intersection of these lines we ...
Pagina 71
... differential , or differential coefficient , thus found , is in general another function of the same scalar variable ; and can therefore be differentiated anew by a second , third , & c . application of the same process . And precisely ...
... differential , or differential coefficient , thus found , is in general another function of the same scalar variable ; and can therefore be differentiated anew by a second , third , & c . application of the same process . And precisely ...
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Veelvoorkomende woorden en zinsdelen
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
Populaire passages
Pagina 138 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Pagina 11 - The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. Let the -l. bisectors EE' and DD