cover image: The Analytical Geometry of Hyper-Spaces

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The Analytical Geometry of Hyper-Spaces

1922

Since the expression (1) involves only the functions of angles between the four lines determining the planes it is independent of the orientation of the system of axes and depends only on the initial lines. [...] The two planes are called isoeline*.* 3. If two half-lines in the plane a make equal angles with another plane then the half-line bisecting the angle between them and the half-line bisecting the angle between their projections upon 13 will lie in one of the common perpendicular planes of a and #3 and the angle between them is equal to the equal angles between the two planes. [...] 4. The generalised form of the above theorem is the following :- If A and p. be taken one in each plane dividing the angles between the "minima/ lines" in the same ratio then the plane of (A p) is perpendicular to both a and /3 and the angle between A and p is equal to the isoclinal angle. [...] the planes a and 13 are isoclines." 7. If (I in) and (p q) are the " minimal lines " of two planes a and /3 and if two half-lines A and p. be taken one in each of the planes dividing the angles between the lines in the same ratio the plane of (A pt) is equally inclined to a and ft. [...] The constants in transformatioU may be shown to be proportional to the direction-coAines of the (r-2)-way space if we extend the notion of direction-cosines of a.k-way space and define them to be the cosine-products" of the angles befween the k-way space and the axial k-way spaces.
technology medicine science
Pages
121
Published in
India
SARF Document ID
sarf.144499
Segment Pages Author Actions
Preface
i-vi Surendramohan Ganguli view
Chapter I——Isocline Planes
1-19 Surendramohan Ganguli view
Chapter II—-Motion in Hyper-Space
20-60 Surendramohan Ganguli view
Chapter III—. Complexes in n-Dimensions
61-82 Surendramohan Ganguli view
Chapter IV. Hyper-Surfaces
83-105 Surendramohan Ganguli view
Chapter V. Parametric Representation
106-115 Surendramohan Ganguli view

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