A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry
The book A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry was written by author Scott Robert Forsyth Here you can read free online of A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry a good or bad book?
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34—37.] APPLICATIONS TO GEOMETBT. 211 For two systems of five spheres we should get = 576 iv,r, + ...+ V5) «ft + . • • + v^Ps), tn- •«.a. 1 t.- ■• 1 1 . .. 1 using the notation of Art. 31. If t^ is the angle at which the plane of similitude of the first four spheres of the first system cuts each of these spheres, and (r^t^ the angle at which it cuts the fifth sphere, and similarly for the second system, we can reduce this to the form cos (p,T,)N tn- •«.. 1 ts.- ■%.> 1 1 . . 1 576v,r^v:p,(l- cos...i. COST. Hence the determinant vanishes if one of the systems of five spheres has a common plane of similitude. For two sets of four spheres, after some reduction we can prove that in- K.> 1 ^41 • • • *«' 1 1 ... 1 = 288..' (1--^^), \ cos t COS T/ where ^ is the angle between the planes of similitude of the two systems, and t, t the angles at which they cut their sets of spheres. 37. By compounding the arrays whose i'" rows are and - 2^„ - 2v„ - 2^„ 2p„ |/ + 7,/ + ?f - p^ 1, we get the homogeneous relation between the sets of tangents common to two sets of seven spheres in- i..
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