Principles of Geometry Volume 1 - Hardcover

Baker, Henry Frederick; Baker, H F (Henry Frederick)

Hardcover

ISBN 10: 141816464X ISBN 13: 9781418164645

Publisher: University of Michigan Library, 1922

Synopsis

The present volume is devoted to the indispensable logical preliminaries. It assumes only those relations of position, for points, lines and planes, which, furnished with a pencil, a ruler, some rods and some string, a student may learn by drawing diagrams and making models. It seeks to set these relations in an ordered framework of deduction, gradually rendered comprehensive and precise enough to include all the subsequent theory; to this end it puts aside, at first, most of those intricate details which make up the burden of what is generally called elementary geometry. That such a plan can be carried through, thanks to the work of many generations of thinkers, is well enough known; and experience has shewn that many students, especially of the class who look forward to becoming Engineers or Physicists, to whom the geometry of the ill 11 usual textbooks is tiresome, find such a course stnnulatmg and easy, when the matter is properly presented to them. The mathematician who has followed such a course will find that he has no cause to think he has learnt the wrong things. The preliminary theorems in this method of approaching the subject are indeed of Greek origin; only, these are here made to lead to general principles, giving a command of detail unknown to the Greeks. Subsequent volumes will deal, on the basis of the results obtained in this volume, with conies (and circles), with quadric surfaces and cubic cui ves in space, and with cubic surfaces and certain quartic surfaces. These volumes are ready to print; it is hoped that they may appear in no long time. Speaking in more detail of the present volume, it rejects the consideration of distance, and of congruence, as fundamental ideas; these are, in effect, replaced by a theory of related ranges; the geometry usually described with the help of the notion of distance appears later, in a more general, but
(Typographical errors above are due to OCR software and don't occur in the book.)

Edition details

• Publisher: University of Michigan Library
• Publication date: 1922
• ISBN 10: 141816464X
• ISBN 13: 9781418164645
• Binding: Hardcover
• Language: English
• Number of pages: 200