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1
Geometry of Four Dimensions
0, 1, of the two right-hand sides are irrelevant for the moment; the right- hand
sides, here and later, remain unevaluated until the formation of the equations of
all the normal homaloids.) We denote this normal homaloid byNt. There is a
normal ...
2
The Collected Mathematical Papers of James Joeseph Sylvester
and lying in the tangent homaloid thereto, 1.2 n right lines may be drawn
coinciding throughout with the n-theme. Thus one right line can be drawn at each
point of a line of the first order lying on the line ; two right lines at each point of a
surface ...
3
Philosophy of Science: The Historical Background
Now whenever the value of this measure of curvature in any space is everywhere
zero, that space everywhere conforms to the axioms of Euclid; and it may be
called a flat (homaloid) space in contradistinction to other spaces, analytically ...
4
Geometry of Four Dimensions
We denote this normal homaloid There is a normal homaloid, with three-fold
normality and of (n-3) dimensions : it is orthogonal to the contact homaloid T3
which has three-fold contact and is of three dimensions. It is the amplitude
common to ...
Andrew Russell Forsyth, 1930
This Euclidean space is a tridimensional homaloid, and so, in distinction from it,
spaces with positive or negative curvature are called non-Euclidean. Through all
the centuries up to the present Euclid's space contained at least the thought- ...
6
The Quarterly Journal of Pure and Applied Mathematics ...
10. In the case of an ellipsoid, if the plane of relation be a tangent plane, the
centre of forces is at three-fifths of the distance along the diameter through the
point of contact. In space of four dimensions let a homaloid three-dimensional
solid be ...
James Joseph Sylvester, James Whitbread Lee Glaisher, 1879
7
The Quarterly Journal of Pure and Applied Mathematics
10. In the case of an ellipsoid, if the plane of relation be a tangent plane, the
centre of forces is at three-fifths of the distance along the diameter through the
point of contact. In space of four dimensions let a homaloid three-dimensional
solid be ...
8
Geometry of Four Dimensions
... half-plane (of a plano-trihedral angle); — a trois dimensions, dihedral angle; -
— a quatre dimensions, hyperplane angle; Jouffret, 62-63. First, vertex-edge,
Schoute, II, 4. Flat noun and adjective), linear, homaloid (or omaloid), eben, flach.
9
The World of Mathematics
may be as completely and consistently worked out for such spaces as ordinary
geometry can for our actually existing homaloid space. If the measure of
curvature is positive we have spherical space, in which straightest lines return
upon ...
10
Revisiting the Foundations of Relativistic Physics: ...
Now any continuum of four dimensions, having a quadratic line-element,
however complex, is expressible as a hypersurface in this homaloid [flat]
continuum of five dimensions. If these considerations are correct, the Einstein
generalization, ...
John J. Stachel, Jürgen Renn, Abhay Ashtekar, 2003
