Conceived dynamically, as projective geometry requires, Point and Plane represent a pair of opposites, the Point standing for utmost contraction, the Plane for utmost expansion.
As referred to in Chapter I, it was Rudolf Steiner who first pointed to the significance in this respect of the branch of modern mathematics known as Projective Geometry.
Projective geometry is able to state that a point moving along this line in one direction will eventually return from the other.
To Mr Whitehead I owe, also, the inestimable assistance of constant criticism and suggestion throughout the course of construction, especially as regards the philosophical importance of projective Geometry.
And which are nearly equivalent to the three axioms of projective Geometry 52 50.
Projective Geometry: primarily Euclidean, but differing from I.
A second important advance followed the recognition that conics could be regarded as projections of a circle, a conception which led at the hands of Desargues and Pascal to modern projective geometry and perspective.
A final word is necessary in order to explain a phrase which is in constant use in the study of projective geometry.
This correspondence is of such fundamental importance in the study of projective geometry that a special name is given to it.
In projective geometry, however, the circle, which is not a figure that remains unaltered by projection, and is essentially a metrical notion, ought not to be used to build up the purely projective part of the theory.
And this is true even of such apparently essentially intuitional fields as projective geometry, where entities can be substituted for directional lines and the axioms be turned into relational postulates governing their configurations.
It is astonishing that this subject [projective geometry] should be so generally ignored, for mathematics offers nothing more attractive.
There exist a small number of very simple fundamental relations which contain the scheme, according to which the remaining mass of theorems [in projective geometry] permit of orderly and easy development.
The above list will hopefully provide you with a few useful examples demonstrating the appropriate usage of "projective geometry" in a variety of sentences. We hope that you will now be able to make sentences using this group of words.
