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In the case of the plane being at infinity, it would be a journey along a radius of the infinitely large sphere from its centre to a point at its circumference. In projective geometry the operation is of a different character.
Lazare is a charmingly graceful, though not great, structure, mainly of the style "ogivale premier," its early Lombard work of the nave and west front being of the foundation of Robert I., Duke of Burgundy. This vast western portal is encased in a great projective porch, a feature indigenous apparently to Burgundy, and commonly referred to as the "Burgundian narthex."
Projective geometry is able to state that a point moving along this line in one direction will eventually return from the other. We observe this point moving along a, as a result of the rotation of b, until, when both lines are parallel, it reaches infinity. As a result of the continued rotation of b, however, P does not remain in infinity, but returns along a from the other side.
Again they came more than a hundred strong, with heads held back, and arms at fullest tension to give their spears the greatest projective force, when, just as they came within spear shot, for we knew the exact distance now, we gave them another volley, striking the sand up just before their feet; again they halted, consulting one another by looks and signs, when the discharge of Gibson's gun, with two long-distance cartridges, decided them, and they ran back, but only to come again.
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 such, they form a polarity of the first order. Both together constitute Space. Which sort of space this is, depends on the relationship in which they are envisaged.
During the days since his return from Paris the faculty of projective imagination, which had endowed his childhood with a second world, and peopled it with the incidents and creatures of his books, had grown to an abnormal strength.
We ought rather to ask: 'How does Anthroposophy help us to read more clearly this or that otherwise enigmatical chapter of the script of existence? 3 See Space and the Light of Creation, by G. Adams, where this 'weaving' is shown with the help of projective geometry. 4 Translation by J. Darrell.
Our other and much more convenient, if less powerful, projective weapon has also its own disadvantage. It can be used only at short distances; and at these it is apt to burn and tear a skin so soft and delicate as that of the thernee. Moreover, it so terrifies the caldecta as to render it unmanageable; and we are compelled to dismount before using it, as you may presently see.
To travel from the point to the infinitely distant plane in the sense of projective geometry, therefore, means that we have first to identify ourselves with the point and 'become' the plane by a process of uniform expansion in all directions.
That projective impulse is seen in the male nature everywhere; the constant urge toward expression, to all boasting and display. This spirit, like all things masculine, is perfectly right and admirable in its place. It is the duty of the male, as a male, to vary; bursting forth in a thousand changing modifications the female, selecting, may so incorporate beneficial changes in the race.
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