Analytical geometry of three dimensions, Mccrea

PREFACE

THIs book is based upon a short oourse of lectures to first­year Honours students who have just completed a oourseon Algebra approximating to that oovered by Dr Aitken'sDeterminants and Mah'ice8 in these Texts. and who will havelater in their ourrioulum a course of modern projectivegeometry. While the original lecture notes· have beendrastically revised so that the book may. one hopes, meetthe needs also of students whose oourses are differentlyarranged, it j, still designed primarily for students atabout the same stage as those to whom the lectureswere addressed.

This explanation, 88 well 88 the smallness of the book,will acoount for various omissions. For instanoe, homo­graphio oorrespondence is not introduoed. largely on theground that it plays its fundamental part in non-metrioalgeometry whioh the student will normally encounter at

. a later stage. On the other hand, it is hoped that thetopios included will be found to be treated with a reasonablestandard of rigour. In partioular, oare has been taken toframe the theory so that it does striotly apply to realspace. This explains the avoidanoe of oertain familiarshort-outs, which actually depend on jumping difficultiesabout reality oonditions.

The book purports to be a "University Text.u Thispresumably means that it will normally be used in con­junction with lectures or other personal instruction. It

v

CONTENTSOBAPTBB

PBElrACE •UGH

V

I. CoORDINATE SYSTEM: DIRECTIONS.

II. PLANES AND LINES

m. SPHERE

•

1

14

32

IV. HOMOGENEOUS CoORDINATES - POINTS AT

!Nll'INITY • 41

V. GENERAL EQUATION OF THE SEOOND DEGREE. 04

VI. QUADRIO IN CARTESIAN COORDINATES; STAN-

DARD FORMS 89

VII. 1N'l'ERSECTION OF QUADRICS: SYSTEMS OF

QUADRIOS. 125

NOTE ON ABSTRACT GEOMETRY •

SUBJEar INDEX •

vii

139

143