Analytical Geometry of Three Dimensi

7/28/2019 Analytical Geometry of Three Dimensi

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PREFACETHIs 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 andMah'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 includedwill 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

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CONTENTSOBAPTBB

PBElrACE UGH

V

I. CoORDINATE SYSTEM: DIRECTIONS.II. PLANES AND LINESm. SPHERE

1

1432

IV. HOMOGENEOUS CoORDINATES - POINTS AT!Nll'INITY 41

V. GENERAL EQUATION OF THE SEOOND DEGREE. 04VI. QUADRIO IN CARTESIAN COORDINATES; STAN-

DARD FORMS 89VII. 1N'l'ERSECTION OF QUADRICS: SYSTEMS OF

QUADRIOS. 125NOTE ON ABSTRACT GEOMETRY SUBJEar INDEX

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Analytical Geometry of Three Dimensi