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**Sample text**

Of planes is intersected by a straight line which does not lie in a plane with its axis, in a range of points ; and every range of points is projected from an axis which does not lie in a plane with it, by a sheaf of planes. to characterize the From these relations of points, range sheaf of planes as primitive first grade. forms is certainly permissible sheaf of rays, and the of the same, namely, of the For, from what has been of points contains just as many it the said, it is clear that a range points as a sheaf contains rays or planes.

To find the point of intersection of a straight line and a plane not incident with it. Through a straight line and a point not incident with it to pass a plane. Through three Through two the common point of three planes. To find the common point of To points to pass a plane. incident straight find two incident straight a plane. lines to pass 27 lines. 39. For the sake of practice, I shall cite a few double theorems which are in frequent use. yourselves, from the I strongly urge one half of each of deduce to you for these, the other reciprocal half.

But even so we shall very soon reach new theorems which offset each other in just the same way as do those already denoted as reciprocals. 56. We If, in have just now found that hvo complete quadrangles which are correlated to each other, Jive pairs of homologous sides intersect in points of a straight line u which passes through none of the eight vertices, then the sixth pair also intersect in a point of this straight line. This theorem holds true for the case in which the quadrangles same plane, as well as when they lie in different planes.