An Elementary Treatise on Quaternions |
From inside the book
Results 1-5 of 56
Page xviii
... Another transformation is φρ = = aaVap + bBSBp . §§ 167-169 . Other properties of p . Proof that Sp ( p + g ) 1p = 0 ... SECOND ORDER . EXAMPLES TO CHAPTER VIII . 120-132 132-134 · 135-151 • 151-154 CHAPTER IX . - GEOMETRY OF CURVES AND ...
... Another transformation is φρ = = aaVap + bBSBp . §§ 167-169 . Other properties of p . Proof that Sp ( p + g ) 1p = 0 ... SECOND ORDER . EXAMPLES TO CHAPTER VIII . 120-132 132-134 · 135-151 • 151-154 CHAPTER IX . - GEOMETRY OF CURVES AND ...
Page 17
... second order , of which a , ß , y are the directions of conjugate diameters . If a , b , c be all positive , the surface is an ellipsoid . 32. ] In Example ( ƒ ) above we performed an operation equi- valent to the differentiation of a ...
... second order , of which a , ß , y are the directions of conjugate diameters . If a , b , c be all positive , the surface is an ellipsoid . 32. ] In Example ( ƒ ) above we performed an operation equi- valent to the differentiation of a ...
Page 26
... another , in general depends upon four distinct numbers , whence the name ... order , being per- fectly independent of each other . Thus it appears that a ... second operation in § 47 , is called the VERSOR , and is denoted by the ...
... another , in general depends upon four distinct numbers , whence the name ... order , being per- fectly independent of each other . Thus it appears that a ... second operation in § 47 , is called the VERSOR , and is denoted by the ...
Page 42
... order of the factors , else he is certain to make mistakes . This ( 80 ) resolves itself into the four equations 0 ... second , and then multiply the product by the first ; next , multiply the second factor by the first and employ the ...
... order of the factors , else he is certain to make mistakes . This ( 80 ) resolves itself into the four equations 0 ... second , and then multiply the product by the first ; next , multiply the second factor by the first and employ the ...
Page 43
... second application of the process . In words , we have the theorem — the scalar of the product of any number of given quaternions depends only upon the cyclical order in which they are arranged . 89. ] An important case is that of three ...
... second application of the process . In words , we have the theorem — the scalar of the product of any number of given quaternions depends only upon the cyclical order in which they are arranged . 89. ] An important case is that of three ...
Other editions - View all
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