Projective Geometry - Volume I

Projective Geometry - Volume I
Pages:352 | DJVU | 4 MB

Geometry, which had been for centuries the most perfect example of a deductive science, during the creative period of the nineteenth century outgrew its old logical forms. The most recent period has however brought a clearer understanding of the logical foundations of mathematics and thus has made it possible for the exposition of geometry to resume the purely deductive form. But the treatment in the books which have hitherto appeared makes the work of lay ing the foundations seem so formidable as either to require for itself a separate treatise, or to be passed over without attention to more than the outlines. This is partly due to the fact that in giving the complete foundation for ordinary real or complex geometry, it is necessary to make a study of linear order and continuity, a study which is not only extremely delicate, but whose methods are those of the theory of functions of a real variable rather than of elemen tary geometry. The present work, which is to consist of two volumes and is in tended to be available as a text in courses offered in American uni versities to upper-class and graduate students, seeks to avoid this difficulty by deferring the study of order and continuity to the sec ond volume.

 

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