A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry
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In our eReader you can find the full English version of the book. Read A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry
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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..
What to read after A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Scott Robert Forsyth to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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..
What to read after A Treatise On the Theory of Determinants And Their Applications in Analysis And Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Scott Robert Forsyth to read onlineMoreLess
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