By Derrick Norman Lehmer

Meant to offer, As easily As attainable, The necessities of artificial Projective Geometry - Chapters: One-To-One Correspondence - kin among primary varieties In One-To-One Correspondence With one another - blend of 2 Projectively comparable primary types - Point-Rows Of the second one Order - Pencils Of Rays Of the second one Order - Poles And Polars - Metrical houses Of The Conic Sections - Involution - Metrical homes Of Involutions - at the background of man-made Projective Geometry - Index

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**Extra resources for An Elementary Course In Synthetic Projective Geometry **

**Example text**

6. A line is drawn cutting the sides of a triangle ABC in the points A', B', C' the point A' lying on the side BC, etc. The harmonic conjugate of A' with respect to B and C is then constructed and called A". Similarly, B" and C" are constructed. [28] 30 An Elementary Course in Synthetic Projective Geometry Show that A"B"C" lie on a straight line. Find other sets of three points on a line in the figure. Find also sets of three lines through a point. [29] CHAPTER III - COMBINATION OF TWO PROJECTIVELY RELATED FUNDAMENTAL FORMS 47.

16 [45] 52 An Elementary Course in Synthetic Projective Geometry FIG. 17 For let the vertices be A, B, C, and D, and call the vertex A the point 1, 6; B, the point 2; C, the point 3, 4; and D, the point 5 (Fig. 16).

66. Lines joining four points of the locus to a fifth. Suppose that the points S, S', B, C, and D are fixed, and that four points, A, A1, A2, and A3, are taken on the locus at the intersection with it of any four harmonic rays through B. , on the fixed ray SD. , on the fixed line DS'. These last four harmonic points give four harmonic rays CA, CA1, CA2, CA3. Therefore the four points A which project to B in four harmonic rays also project to C in four harmonic rays. But C may be any point on the locus, and so we have the very important theorem, Four points which are on the locus, and which project to a fifth point of the locus in four harmonic rays, project to any point of the locus in four harmonic rays.