An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina vi
... shew their admir- able simplicity and naturalness to induce the reader to attack the Lectures and the Elements ; where he will find , in profusion , stores of valuable results , and of elegant yet powerful analytical investiga- tions ...
... shew their admir- able simplicity and naturalness to induce the reader to attack the Lectures and the Elements ; where he will find , in profusion , stores of valuable results , and of elegant yet powerful analytical investiga- tions ...
Pagina 23
... Shew that the mean point may also be found by bisecting the line joining the middle points of a pair of opposite sides . 3. Verify that the property of the coefficients of three vectors whose extremities are in a line ( § 30 ) is not ...
... Shew that the mean point may also be found by bisecting the line joining the middle points of a pair of opposite sides . 3. Verify that the property of the coefficients of three vectors whose extremities are in a line ( § 30 ) is not ...
Pagina 24
... Shew that where p = x3a + y3ß + 23y , x + y + 2 = 0 , x + y + z = represents a cone of the third order , and that its section by the plane pa + q B + ry P = is a cubic curve , of which the lines p + q + r p = pa + qB , & c . p + q are ...
... Shew that where p = x3a + y3ß + 23y , x + y + 2 = 0 , x + y + z = represents a cone of the third order , and that its section by the plane pa + q B + ry P = is a cubic curve , of which the lines p + q + r p = pa + qB , & c . p + q are ...
Pagina 30
... shew that MN = AB , and join NL . Then LN- MN . LM = p.qr. p.qr = pq.r = all that is requisite is to prove that LN , and KG , described as above , are equal arcs of the same great circle , since , by the figure , they are evidently ...
... shew that MN = AB , and join NL . Then LN- MN . LM = p.qr. p.qr = pq.r = all that is requisite is to prove that LN , and KG , described as above , are equal arcs of the same great circle , since , by the figure , they are evidently ...
Pagina 32
... shew . B A For if the planes of two quaternions , q and r , intersect in the line 04 , we may take any vector OA in that line , and at once find two others , OB and OC , such that And 0 and OB = qOA , OC = r OA . ( q + r ) OA = OB + OC ...
... shew . B A For if the planes of two quaternions , q and r , intersect in the line 04 , we may take any vector OA in that line , and at once find two others , OB and OC , such that And 0 and OB = qOA , OC = r OA . ( q + r ) OA = OB + OC ...
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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