A Paper On the Foundations of Projective Geometry Read Before the Aristotelian
A Paper On the Foundations of Projective Geometry Read Before the Aristotelian
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' 25. If in a complete group we collate the rays of a pencil of {U^)s by means of the units in each in the section, we shall PROJECTIVE GEOMETRY. 41 collate each ray twice over, with each of the two antipodal units. To evade this difficulty we must collate together the half-rays as divided by the origin of the pencil, collating together the units in the origin, and two other units in each half-ray. This would require the arbitrary selection of two units in each half-ray, besides the origin ; bu...t by the method I am about to describe it is sufficient to chose two units in the whole ray, one in each half of it, to collate a single ray, and only two more, besides the origin, in one other ray of a pencil of the first order, to collate the whole of the rays of the pencil ; and, generally, 2« units besides the origin, to collate a pencil of the order (w — 2).
I shall call this process of collation of half-rays in a pencil reversion ; and in reference to the process I shall speak of the origin as the 'pivot of reversion, and the section of the pencil as the equator of the reversion.
What to read after A Paper On the Foundations of Projective Geometry Read Before the Aristotelian?
You can find similar books in the "Read Also" column, or choose other free books by Edward T Edward Travers Dixon to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
' 25. If in a complete group we collate the rays of a pencil of {U^)s by means of the units in each in the section, we shall PROJECTIVE GEOMETRY. 41 collate each ray twice over, with each of the two antipodal units. To evade this difficulty we must collate together the half-rays as divided by the origin of the pencil, collating together the units in the origin, and two other units in each half-ray. This would require the arbitrary selection of two units in each half-ray, besides the origin ; bu...t by the method I am about to describe it is sufficient to chose two units in the whole ray, one in each half of it, to collate a single ray, and only two more, besides the origin, in one other ray of a pencil of the first order, to collate the whole of the rays of the pencil ; and, generally, 2« units besides the origin, to collate a pencil of the order (w — 2).
I shall call this process of collation of half-rays in a pencil reversion ; and in reference to the process I shall speak of the origin as the 'pivot of reversion, and the section of the pencil as the equator of the reversion.
What to read after A Paper On the Foundations of Projective Geometry Read Before the Aristotelian?
You can find similar books in the "Read Also" column, or choose other free books by Edward T Edward Travers Dixon to read onlineMoreLess
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