An Elementary Treatise On Quaternions
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Eliminating the first power of r, we evidently must obtain a result such as (|O-e)He^ + r-'' = 0, where (by what precedes) e is the vector of the centre, and e the radius, of a fixed sphere (p - if + e^ = 0, which is cut at right angles by all the varying spheres. By effect- ing the elimination exactly we easily find e and e in terms of given quantities.
247. If two vectors divide one another into parts a and — ea, p and -p, respectively, the lines joining the free ends meet in (1 + e) p - lea....
CT= .
1 — e We may write this as e,p = CT + aj, ■f 1 + e 2ea " e, = , a = : 1-e' ^ 1-, 247-] THE SPHERE AND CYCLIC CONE. 187 For another such pair of vectors, passing through the same point, we have, say, /^or = ^ + /3,.
Thus the plane quadrilateral, whose diagonals are made up respectively of the complete a and ^ vectors, will be projected (by lines from the point ■bt) as a square on the plane of p, a; provided Tp=TS.(^ + aJ(tT + ^J=0 (2).
What to read after An Elementary Treatise On Quaternions?
You can find similar books in the "Read Also" column, or choose other free books by Peter Guthrie Tait to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Eliminating the first power of r, we evidently must obtain a result such as (|O-e)He^ + r-'' = 0, where (by what precedes) e is the vector of the centre, and e the radius, of a fixed sphere (p - if + e^ = 0, which is cut at right angles by all the varying spheres. By effect- ing the elimination exactly we easily find e and e in terms of given quantities.
247. If two vectors divide one another into parts a and — ea, p and -p, respectively, the lines joining the free ends meet in (1 + e) p - lea....
CT= .
1 — e We may write this as e,p = CT + aj, ■f 1 + e 2ea " e, = , a = : 1-e' ^ 1-, 247-] THE SPHERE AND CYCLIC CONE. 187 For another such pair of vectors, passing through the same point, we have, say, /^or = ^ + /3,.
Thus the plane quadrilateral, whose diagonals are made up respectively of the complete a and ^ vectors, will be projected (by lines from the point ■bt) as a square on the plane of p, a; provided Tp=T
What to read after An Elementary Treatise On Quaternions?
You can find similar books in the "Read Also" column, or choose other free books by Peter Guthrie Tait to read onlineMoreLess
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