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Analytical geometry of three dimensions, Mccrea
 

Analytical geometry of three dimensions, Mccrea

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    Analytical geometry of three dimensions, Mccrea Analytical geometry of three dimensions, Mccrea Document Transcript

    • PREFACE THIs book is based upon a short oourse of lectures to first- year Honours students who have just completed a oourse on Algebra approximating to that oovered by Dr Aitkens Determinants and Mahice8 in these Texts. and who will have later in their ourrioulum a course of modern projective geometry. While the original lecture notes· have been drastically revised so that the book may. one hopes, meet the needs also of students whose oourses are differently arranged, it j, still designed primarily for students at about the same stage as those to whom the lectures were addressed. This explanation, 88 well 88 the smallness of the book, will acoount for various omissions. For instanoe, homo- graphio oorrespondence is not introduoed. largely on the ground that it plays its fundamental part in non-metrioal geometry whioh the student will normally encounter at. a later stage. On the other hand, it is hoped that the topios included will be found to be treated with a reasonable standard of rigour. In partioular, oare has been taken to frame the theory so that it does striotly apply to real space. This explains the avoidanoe of oertain familiar short-outs, which actually depend on jumping difficulties about reality oonditions. The book purports to be a "University Text. u This presumably means that it will normally be used in con- junction with lectures or other personal instruction. It v
    • CONTENTSOBAPTBB UGH PBElrACE • V I. CoORDINATE SYSTEM: DIRECTIONS. 1 II. PLANES AND LINES • 14m. SPHERE 32 IV. HOMOGENEOUS CoORDINATES - POINTS AT !NllINITY • 41 V. GENERAL EQUATION OF THE SEOOND DEGREE. 04 VI. QUADRIO IN CARTESIAN COORDINATES; STAN- DARD FORMS 89VII. 1NlERSECTION OF QUADRICS: SYSTEMS OF QUADRIOS. 125 NOTE ON ABSTRACT GEOMETRY • 139 SUBJEar INDEX • 143 vii