Maths Analytical Geometry  National Department of Basic ...
Analytical geometry of three dimensions, Mccrea

Upload
changarrodegorditasyquesadillas 
Category
Education

view
352 
download
2
description
Transcript of 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 nonmetrioalgeometry 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 familiarshortouts, 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