Introduction to Quaternions: With Numerous Examples |
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Page 9
... prove that AC is equal and parallel to BD . Let vector AB be represented by a , then ( Art . 1 ) vector CD is also repre- c sented by a . D B If now vector CA be represented by ß , vector DB by y , we shall have ( Art . 5 ) vector CB CA ...
... prove that AC is equal and parallel to BD . Let vector AB be represented by a , then ( Art . 1 ) vector CD is also repre- c sented by a . D B If now vector CA be represented by ß , vector DB by y , we shall have ( Art . 5 ) vector CB CA ...
Page 18
... triangle ABD triangle AEF . We shall presently exemplify a very elegant method due to Sir W. Hamilton of proving three points to be in the same straight line . 8. It is often convenient to take a vector of 18 [ CHAP . II . QUATERNIONS .
... triangle ABD triangle AEF . We shall presently exemplify a very elegant method due to Sir W. Hamilton of proving three points to be in the same straight line . 8. It is often convenient to take a vector of 18 [ CHAP . II . QUATERNIONS .
Page 22
... proved generally ( Art . 11 ) . 13. Conversely , if a , ß , y are coinitial coplanar vectors , and if both aa + bB + cy = 0 and a + b + c = 0 , then do a , ß , y terminate in a straight line . For ay + by + cy = 0 ; therefore by ...
... proved generally ( Art . 11 ) . 13. Conversely , if a , ß , y are coinitial coplanar vectors , and if both aa + bB + cy = 0 and a + b + c = 0 , then do a , ß , y terminate in a straight line . For ay + by + cy = 0 ; therefore by ...
Page 30
... prove that BD , BC , BE form an harmonical progression . 12 . The diagonals of a parallelepiped bisect one another . 13. The mean point of a tetrahedron is the mean point of the tetrahedron formed by joining the mean points of the ...
... prove that BD , BC , BE form an harmonical progression . 12 . The diagonals of a parallelepiped bisect one another . 13. The mean point of a tetrahedron is the mean point of the tetrahedron formed by joining the mean points of the ...
Page 31
... prove that AC , DE being joined will trisect each other . 17. ABCD is a parallelogram ; PQ any line parallel to CD ; PD , QC meet in S , PA , QB in R ; prove that AD is parallel to RS . CHAPTER III . VECTOR MULTIPLICATION AND DIVISION ...
... prove that AC , DE being joined will trisect each other . 17. ABCD is a parallelogram ; PQ any line parallel to CD ; PD , QC meet in S , PA , QB in R ; prove that AD is parallel to RS . CHAPTER III . VECTOR MULTIPLICATION AND DIVISION ...
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Common terms and phrases
ALGEBRA ARITHMETIC Assistant Master aßy axis BEGINNERS bisects Cambridge centre chord circle Clifton College cone CONIC SECTIONS conjugate diameters constant drawn Edited ELEMENTARY TREATISE ellipse ellipsoid ENGLISH equal EXAMPLES FASNACHT Fcap find the locus G. E. FASNACHT GEOMETRY given lines given point gives GRAMMAR GREEK Hence hyperbola Illustrated intersection Introduction and Notes ISAAC TODHUNTER J. P. MAHAFFY LATIN Lecturer LL.D M.A. Cr m₁ MACMILLAN'S Mathematics middle points Owens College p₁ parabola parallelepiped parallelogram PRIMER Prof Professor quaternion revised right angles rotation Sapa Saß scalar School shews squares strain tangent plane tetrahedron Translated triangle Trinity College unit vectors Vaß vector parallel vector perpendicular Vẞy whence yẞ αβγ φρ
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