By Derrick Norman Lehmer

Meant to offer, As easily As attainable, The necessities of artificial Projective Geometry - Chapters: One-To-One Correspondence - family members among primary varieties In One-To-One Correspondence With one another - blend of 2 Projectively similar basic varieties - 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 houses Of Involutions - at the heritage of artificial Projective Geometry - Index

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

**Example text**

We may also give an illustration of a case where two superposed projective point-rows have no self-corresponding points at all. Thus we may take two lines revolving about a fixed point S and always making the same angle a with each other (Fig. 10). They will cut out on any line u in the plane two point-rows which are easily seen to be projective. For, given any four rays SP which are harmonic, the four corresponding rays SP' must also be harmonic, since they make the same angles with each other.

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. Superposed fundamental forms. Self-corresponding elements. We have seen (§ 37) that two projective point-rows may be superposed upon the same straight line. This happens, for example, when two pencils which are projective to each other are cut across by a straight line.

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. Superposed fundamental forms. Self-corresponding elements. We have seen (§ 37) that two projective point-rows may be superposed upon the same straight line. This happens, for example, when two pencils which are projective to each other are cut across by a straight line.